BIBM Combined Bank Recruitment Math Suggestion- Most Important 150 Type.
Last All Combined Bank exam is taken by BIBM. The Panacea for all to make the best outcome IN BIBM exams, every one should focus on Math.
Here I am sharing 150+ BIBM's most Favourite Math Type .
1. A Seller sells an articles at a profit of 20%. If he had bought it at 20% less and sold it for Tk. 5 less, he would have gained 25%. Find the cost price of the article?
2. A water tank has two taps (Tap-1 and tap-2). Tap-1 can fill
a tank in 8 hours and Tap-2 can empty the tank in 16 hours. How long will they
to fill the tank if both taps are opened simultaneously but tap-2 is closed
after 8 hours?
3.
Malek spends
75% of his income. His income is increased by 20% and he increases his
expenditure by 10% Calculate the percentage of his increased amount of savings?
4.
10% fruit of
a seller was damaged during transportation, another 15% was rotten.At what
profit in percentage should he sell rest fruit so that he can make an overall
profit of 20%?
5. The length of a rectangle is 7 more than its width. If the
perimeter of the rectangle is the same as the perimeter of a square of side
8.5, what is the length of a diagonal of the rectangle?
6. In a school. there are equal number of bovs and girls. Amons
the students. 1/8 of the girls and 5/6th of the boys are residing in the
hostel. What percent of the students consists of boys who do not reside in the
hostel among all students?
7.
Taxi fare is
described by the following relationship:
Total taxi Fare = Fired Charge: Tk. A up to 2 km + Tk. B per
km run exceeding 2 km + Tk. 60 for per hours waiting.
A person paid Tk. 432 for running 52 km and 2 hours of
waiting charge. The same person paid Tk. 732 for running 102 km and 2 hours of
waiting charge. Find the value of A and B.
8.
In
a stream running at 2 kmph, a motor boat goes 10 km upstream and back again to
the starting point in 55 minutes. Find the speed of the motorboat in still
water.
9.
In
a shop, the cost of 4 shirts, 4 pairs of trousers and 2 hats is Tk. 560. The
cost of 9 shirts, 9 pairs of trousers and 6 hats is Tk. 1290. What is the total
cost of 1 shirt, 1 pair of trousers and 1 hat?
10. A team of 2 men
and 5 women completed 1/4 of a job in 3 days. After that another man joined
them and they all complete the next 1/4 of the job in 2days.How many men can
complete the whole job in 4 days?
11. If 12 candies are
sold for Tk. 10 then there is a loss of x%.
If 12 candies are sold for Tk. 12 then there is a profit of %. What is the value
of x?
12. A merchant
purchased a jacket for Tk. 60 and then determined a selling price that equaled
the purchase price of the jacket plus a markup that was 25 percent of the
selling price. During a sale, the merchant discounted the selling price by 20
percent and sold the jacket. What was the merchant's gross profit on this sale?
13. A sum of money is to be distributed equally among a
group of children. If there were 25 children less than each would get Tk. 1.50
more, and if there 50 children more, each would get TK. 1.50 less. Find the
number of children and the amount of money distributed.
14. A, B and C can do a piece of work in 16, 32 and 48 days
respectively. They started working together but C left after working 4 days and
B left 2 days before the completion of work. How many days it took to complete
the work?
15. Mr. Karim borrowed
Tk. 500 at 5% simple interest per year. After some time, he borrowed Tk. 400 at
3% simple inferest per year for the second time. Six months after the second
time borrowing, he repaid both borrowed money along with interest and the amount
repaid was Tk. 994.50. How many years after the first time borrowing Mr. Karim
repaid the borrowed money?
16. A boat can take 8 hours to go 32 km against the current
and take 4 hours for same distance with the current, what is the speed of the
boat and current?
17. Daily earnings of two persons are in
the ratio 4:5 and their daily expenses are in the ratio 7:9. If each saves Tk.
50 per day, their daily incomes in Tk. are?
18. Robi drove 100
miles to visit a friend. If he had driven 8 miles per hour faster than he did,
he would have arrived in 5/6 of the time, he actually took. How many minutes
did the trip take?
19. A person sold two
articles. Each for the same price of Tk. 1040. He incurs 20% loss on the first
and 10% loss on the second. Find his overall percentage of loss.
20. The annual incomes
and expenditures of a man and his wife are in the ratios 5:3 and 3:1,
respectively. If they decide to save equally and find a balance of Tk. 4000 at
the end of the year, what was their income?
21. In the figure
below, ABC is a right angle and AB = BD = AD = 20 feet. Find out the length
of BC.
22. Mr. X sold two
properties PI and P2 for Tk. 100,000 each. He sold property PI for 20%
loss than what he paid for it. What is the percentage of profit of property P2
so that he is not in gain or loss on the sale of the two properties?
23. A number consists
of two digits. The sum of the digits is 15. If 27 is subtracted from the
number, its digits are interchanged. Find the number.
24. In the
accompanying diagram ABCD is a rectangle. The area of isosceles right triangle
ABE = 7, and EC = 2BE. What would be the area of ABCD?
25. Arif and Mukul
start running at the same time and from the same point around a circle of 216
meters circumference. If Arif can complete one round in 40 seconds and Mukul in
50 seconds, how many seconds will it be before they both reach the starting
point simultaneously and how many rounds they will complete by this time?
26. On a certain X-Y
committee, 2/3th of the members are men, and 3/8th of the men from country Y. If
3/5th of the committee members are from country X, what fraction of the members
are women from country Y?
27. A person earns
yearly interest of Tk. 920 by investing Tk. X at 4% and Ik. Y at 5%
simple interest rate. If he had invested Tk. X at 5% and Tk. Y at 4% simple
interest rate, then his yearly interest earning would have been reduced by Tk.
40. Find out the amount of X and Y.
28. An article is sold
for Tk. 190, hence gaining a certain amount. Had thee
article been sold for Tk. 175, he would have suffered loss equal to
50% of the gain in the first case. Find cost price of the article
29. A trader bought
some mangoes for Tk. 150 per dozen and equal number of apples for Tk. 100 per
dozen. If he sells all the fruits Tk. 140 per dozen, what will be his
profit/loss in percentage?
30. Two partners A and
B have 70% and 30% shares respectively in a business. After sometimes, a third
partner C joined by investing Tk. 10 lakh and thus having 20% share in the
business. What is the percentage of share of A's now in the business?
31. A boy covers a
distance of 6 km partly by walking and partly by cycling. If he cycles at 18 km
per hour and walks at 6 kan per hour and takes 35 minutes in all, find the
distance he covers by walking.
32. A square office,
1000 feet by 1000 feet, is to be partitioned into two offices by a single
interior wall. The difference between the perimeters of the resulting two
officers be 400 feet. What are their dimensions?
33. A manufacturer of
bores wants to make a profit of r taka. When he sells 5,000 bores it costs Tk.
5 a bor to make the first 1000 boxes and then it costs Tk. y a bor to make the
remaining 4,000 boxes. What price in taka should he charge for the 5000 boxes?
34. In an increasing
sequence of 10 consecutive integers, the sum of the first 5 integers is 560.
What is the sum of the last 5 integers in the sequence?
35. In a survey, 60%
of those surveyed owned a car and 80% of those surveyed owned a TV. If 55%
owned both a car and a TV, what percent of those surveyed owned a car or a TV
or both?
36. The cost price of
two watches taken together is Tk. 840. If by selling one at a profit of 16% and
the other at a loss of 12%, there is no loss or gain in the whole transaction,
find the cost price of the two watches.
37. Tk. 1500 is
invested at a rate of 10% simple interest and interest is added to the
principal after every 5 years .in how many years will it amount to Tk. 2500?
38. A basketball team
has won 15 games and lost 9. If these games represent 16.67% of the games to
the played, then how many more games must the team win to average 75% for the
season?
39. According to a car
dealer's sale report, 1/3 of the cars sold during a certain period were Sedans
and 1/5 of the other cars sold were station wagons. If N station wagons were
sold during that period, how many Sedans, in terms of N, were sold?
40. If 
years ago Samad was 12, and 
years from now he will be 2x years old,
how will he be 3r years from now?
41. A father has
divided his property between his two sons A and B. A invests the amount at a
compound profit of 8%. B invests the amount of 10% simple profit. At the end of
2 years, the profit received by B is Tk. 1336 more than A. Find the amount of
both. Total amount of his father is Tk. 25000.
42. Two equal glasses are respectively 
and 
full of milk. They are then filled up with water
and the contents mixed in a tumbler. What is the ratio of milk and water in the
tumbler?
43. One day, Mr. Wahid
started 30 minutes late from home and reached his office 50 minutes late, while
driving 25% slower than his usual speed. How much time in minutes does Mr.
Wahid usually take to reach her office from home?
44. A, B and C enter
into a partnership in the ratio 
.Affer 4 months, A increases his
share by 50%. If the total profit at the end of one year is Tk. 21,600, then
what is B's share in the profit?
45. In a certain
Accounting class, the ratio of the number of Accounting majors to the under of
students who are not Accounting major is 2 to 5. If 2 more Accounting majors
were to enter the class, the ratio would be 1 to 2. How many students are in
the class?
46. What is perimeter
of △ABC show in the
figure?
47. An old man
distributed all the gold coins he had to his two sons into two different
numbers such that the difference between the squares of the two numbers is 36
times the difference between the two numbers. How many coins did the old man
have?
48. In the following
diagram, if BC = CD = BD = 1 and angle ADC is a right angle,
what
is the perimeter of triangle ABD?
49. A series has 3
numbers a, ar, ar2 In the series,
the first term is twice of the second term. What is the ratio of the sum of the
first 2 terms to the sum of the last 2 terms?
50. A man travels from
A to B at a speed r km/hr. He then rests at B for x hours.
He then travels from B to C at a speed 2x
km/hr and rests for 2x hours. He moves further to D at a speed twice as that
between B and C. He thus reaches D in 16 hr. If distance A-B, B-C and C-D are
all equal to 12 km, then find the time for which he rested at B.
51. A sum of Tk. 1260
is borrowed from a money lender at 10% p.a. compounded annually. If the amount
is to be paid in two equal annual installments, find the annual installments.
52. The speed of a
railway engine is 42 Km per hour when no compartment is attached, and the
reduction in speed is directly proportional to the square root of the number of
compartinents attached. If the speed of the train carried by this engine is 24
Km per hour when 9 compartments are attached, the maximum number of
compartments that can be carried by the engine?
53. At The percentage profit earned by selling an article for
Tk. 1920 is equal to the percentage loss incurred by selling the same article
for Tk 1280. At what price should the article be sold to make 25% profit?
54. If the sum of five
consecutive integers is S, what is the largest of those integers in terms of S?
55. The perimeter of a
square field is equal to the perimeter of a rectangle field. The length
of the rectangle is thrice the width of it and the area is 768 square meters. How
many square sized tiles of 80 centimeters will be required to cover the square
filed?
56. A trader, while
selling an item, was asking for such a price that would enable him to offer a
20% discounts and still make a profit of 30% on cost. If the cost of the item
was Tk. 50 what was his asking price?
57. The simple interest rate of a bank was reduced to 5% from 7%. As a consequences Mr. B's income was reduced by Tk. 2100 in 5 years. How much is Mr. B's initial deposit in the bank?
59. When the price of
an article is reduced by 15%, the sales increases by 35%. The percentage change
in the total amount of receipts is-
60. If A’s income is
25% less than that of B, then how much percent is B’s Income more than A.
61. If simmple
interest on a certain amount of money is TK. 256 and the rate of ineterest per
annum is equals the number of years, then the rate of interest is.-
62. If Salina’s salary
is 25% more than that of Sauna’s salary, then what percent is Sauna’s salary
less than that of Salina.
63. Four students aged
11, 9, 7, and 4 share a sum of money in the ratio of there ages. If the
youngest student receives TK. 1200, what is the sum of money?
64. A watch is correct
at noon, after which it started to lose 17 minutes per hour, and stopped
completely at 2.52 pm. What time is it now?
65. A man has 53 socks
in his drawer; 21 identical blue, 15 identical black and 17 identical red. The
lights are fused and it is completely in the dark. How many socks must he take
out to take 100% percent certain he has a pair of black socks?
66. In the figure, DE
is paralle to BC. If thearea of atriangle ADE is half the area of that
trapezoid DECB. What is the ratio of AE to AC.
67. Mamun bought 50
shares at Tk. 60, and 2 months later he purchased 25 shares at Tk. 56, at what
price should he purchase 25 additional shares in order to have an average price
of Tk. 58 per share?
68. Pooja is twice as
efficient as Aarti and takes 90 days less than Arti to complete the job. Find
the time in which they can finish the job together.
69. In a club, 60%
members are male and 70% members are graduates. Also 505 of the garduate
members are male. What percentage of the club members are female and
non-graduate?
70. A shopper spends
Tk. 1,000 to purchase CDs at Tk. 20 each The next day, the disks go on sale for
Tk. 16 each and the shopper spends Tk. 2,400 to purchase more CDs. What was the
average price per disk purchased?
71. Rina and Shila entered
into a partnership with their capitals in the ratio 5:6. At the end of 8
months, Rina withdraws her capital. If
they receive the profit in the ratio of 5:9, find how long Shila’s capital was
used?
72. Anita had to do a
multiplcation. Instead of taking 35 as one of the multipliers, she took 53. As
a result, the product went up by 540. What is the new product?
73. Bilkis invests Tk.
2,400 in a bank at 5% interest rate. How much additional money must she invest
at 8% so that the total annual income will be equal to 6% of her entire
inevstment?
74. A popular website
requires users to create a password consisting of digits only. If no digit may
be repeated and each password must be at least 9 digits long, how many
passwords are possible?
75. Rahim wants to cut
a rectangular board into identical square pieces. If the Board is 18 inches by
30 inches, what is the least number of square pieces he can cut without wasting
any of the board?
76. In a certain game,
a large bag is filled with blue, green, purple and red chips worth 1, 5, x and
11 points each, respectively. The purple chips are worth more than the green
chips, but less than the red chips. A certain number of chips are then selected
from the bag. If the product of the point values of the selected chips is
88,000, how many purple chips were selected?
77. In how many
different ways can 3 identical green shirts and 3 identical red shirts be
distributed among 6 children such that each child receives a shirt?
78. If x is the
average (arithmetic mean) of m and 9,y is the average of 2m and 15 and z is the
average of 3m and 18, what is the average of x,y and z in terms of m ?
79. For every novel in
the school library there are 2 science books; for each science book there are 7
economics books. Express the ratio of economics books to science books to
novels in the school library as a triple ratio.
80. If Arif is making
a profit of 25% of his selling price, what is his actual profit percentage?
81. A train 100m Long
passes a bridge at the rate of 72Km/hr in 25 seconds. What is the length of the
bridge?
82. A can do a piece
of work in 10 days, B can do the same in 30 days and c in 60 day . If A is
assisted on alternate days by B and C, in how many days would the work get
completed?
83. A train running at
36 kmph passes another train completely in 12 sec, which is half of its length,
running in the opposite direction at 54 kmph. If it also passes a railway
platform in 1.5 minutes, what is the length of the platform (in meters)?
84. A florist has 200
roses and 180 jasmines with him. He was asked to make garlands of flowers with
only roses or only jasmines each containing the same number of flowers. What
will be the largest number of flowers, he can join together without leaving a
single flower?
85. The distance
between two stations, Dhaka and Chittagong is 450 km. A train starts at 5 p.m
from Dhaka and moves towards Chittagong at an average speed of 60 km. Another
train starts from Chittagong at 4.20 pm. and moves towards Dhaka at an average
speed of 80 km. How far from Dhaka will the two trains meet? and find out the
time they will meet?
86. Together, Andrea
and Brian weigh P pounds; Brian weighs 10 pounds more than Andrea. Brian and
Andrea's dog, Cubby, weighs P/4 pounds more than Andrea. In terms of P, what is
Cubby's weight in pounds?
87. Set X contains 10
consecutive integers. If the sum of the 5 smallest members of Set X is 265,
then what is the sum of the 5 largest members of Set X?
88. At a college
football game, 4/5 of the seats in the lower deck of the stadium were sold. If
one-fourth(1/4) of all the seating in the stadium is located in the lower deck,
and if 2/3 of all the seats in the stadium were sold, what fraction of the
unsold seats in the stadium were in the lower deck?
# [ Method: One of the
ways of finding the units digit of a power is by finding the remainder when
that number is divided by 10.
Another general and one of the easier ways to find the units digit of a number
in the form xy , is done with the help of the following
steps:
a. Identify
the units digit in the base ‘x’ and call it say ‘p’. {For example, If x = 24,
then the units digit in 24 is 4. Hence p = 4.}
b. Divide
the exponent ‘y’ by 4.
·
If the exponent y is exactly divisible by 4. i.e, y
leaves a remainder 0 when divided by 4. Then,
·
the units digit of xy is 6, if p
= 2, 4, 6, 8(even)
·
the units digit of xy is 1,
if p = 3, 7, 9(odd)
·
If y leaves a non-zero remainder r, when divided by 4
(i.e y = 4k + r). Then,
·
the units digit of xy = the
units digit of pr
Example
1: What is the units digit of 2014 to the power of 2012?
Here,
we have to find the units digit of 20142012
1. The
base is 2014 and hence its units digit is 4. Therefore, p = 4.
2. The
exponent is 2012, which is divisible by 4.
·
Since p is even and the exponent is divisible by 4, we
have the units digit of 2014 to the power of 2012 is 6.
Example
2: What is the units digit of 334?
Here,
1. The
base is a single digit 3. Therefore, p = 3.
2. The
exponent 34, when divided by 4 leaves reminder 2.
·
Now the units digit of 334 is
given by the units digit of 32 = 9
Example 3: what is the
units digit in the expansion 1453 raised to 71?
Here, we have to
find the units digit of 145371
1. The
base is 1453 and hence its units digit is 3. Therefore, p = 3.
2. The
exponent is 71, which when divided by 4 gives a remainder 3.
·
Since p is 3 and the exponent leaves a remainder 3
when divided by 4, we have the units digit of 145371 = the units digit of 33 =
the units digit of 27 = 7
]
89. The Average of 5
consecutive integers, in increasing order of size, is 9. What is the average of
the last three integers?
90. A man can row
4km/h in still water and he finds that it takes him thrice as long to row upstream
as to row downstream the river. Find the rate of stream?
91. In a class of 60 students, the number of boys
and girls participating in the annual sports is in the ratio
3
: 2 respectively. The number of girls not participating in the sports is 5 more
than the number of boys not participating in the sports. If the number of boys
participating in the sports is 15, then how many girls are there in the class?
92. If a man travels p
hours at an average rate of q miles per hour and then r hours at an average
rate of s miles per hour, what is his overall average rate of speed?
93. All the page
numbers from book are added, beginning at page 1. However one page number was
added twice by mistake. The sum obtained was 1000. Which page number was added
twice?
94. A red light
flashes 3 times per minute and a green light flashes 5 times in two minutes at
regular intervals. If both lights start flashing at the same time, how many
times do they flash together in each hour?
95. If 2/3 of the
number of women attending a certain dance is equal to 1/2 of the number of men
attending, what fraction of those attending are women?
96. The larger of two
numbers exceeds twice the smaller number by 9. The sum of twice the larger and
5 times the smaller number is 74. If a is the smaller number, which eqution
below determines the correct value of a ?
97. The present ratio
of students to teachers at a certain school is 30 to 1. If the student
enrollment were to increase by 50 students and the number of teachers were to
increase by 5, the ratio of students to teachers would then be 25 to 1. What is
the present number of teachers?
98. Leona bought a
1-year, TK. 10,000 certificate of deposit that paid interest at an annual rate
of 8 percent compounded semiannually. What was the total amount of interest
paid on this certificate at maturity?
99. A culprit was
spotted by a policeman from a distance of 250 meter. When the policeman started
running towards the culprit at a speed of 10 km/h, the culprit also fled. If
his speed was 8 km/h, find how far the culprit had run before he was
overpowered.
100.
Of the total amount that Jill spent on a
shopping trip, excluding taxes, she spent 50 percent on clothing, 20 percent on
food, and 30 percent on other items. If Jill paid a 4 percent tax on the
clothing, no tax on the food, and an 8 percent tax on all other items, then the
total tax that she paid was what percent of the total amount that she spent,
excluding taxes?
101.
A
corporation that had $115.19 billion in profits for the year paid out $230.10
million in employee benefits. Approximately what percent of the profits were
the employee benefits?
102.
The
average age of a group of 10 students was 15. The average age increased by 1
years when 5 new students joined the group. What is the average age of newly
joined students?
103.
If
d = 2.0453 and d* is the decimal obtained by rounding d to the nearest
hundredth, what is the value of d* - d ?
|
Rounding rules Rounding is
simplifying a number to a certain place value. To round the decimal drop the
extra decimal places, and if the first dropped digit is 5 or greater, round
up the last digit that you keep. If the first dropped digit is 4 or smaller,
round down (keep the same) the last digit that you keep. Example: 5.3485 rounded
to the nearest tenth = 5.3, since the dropped 4 is less than 5. 5.3485 rounded
to the nearest hundredth = 5.35, since the dropped 8 is greater than 5. 5.3485 rounded
to the nearest thousandth = 5.349, since the dropped 5 is equal to 5. |
104.
A
ferry can travel twice as fast when empty as when it is full. It travels 20
miles with full load, spends 1 hour for unloading and returns to its original
port empty. It took 11 hours to complete the journey. What is the speed when
the ferry was empty?
105.
The
persons, X & Y, are standing 50 yards apart on a North-South axis. X walks
65 yards to west and Y walks 55 yards to the East and both stop. Find the
straight line distance in yeards between these two positions?
106.
If
a, b and c are constants, a>b>c, and x3 -x=(x-a)(x-b)(x-c) for
all numbers x, what is the value of b?
107.
The
arithmetic mean of the list of numbers 3, k, 2, 8, m, 3 is 4. If k and m
are integers and k ≠ m, what is the median of the list?
108.
A
certain population of bacteria doubles every 10 minutes. If the number of
bacteria in the population initially was 104 , what was the number
in the population 1 hour later?
109.
In
the correctly worked addition problem shown, where the sum of the two-digit
positive integers AB and BA is the three-digit integer AAC, and A, B, and C are
different digits, what is the units digit of the integer AAC?
110.
AB
+ CD = AAA, where AB and CD are two-digit numbers and AAA is a three digit
number; A, B, C, and D are distinct positive integers. In the addition problem
above, what is the value of C?
|
Soln:
Since AB and CD
are two-digit integers, their sum can give us only one three digit integer of
a kind of AAA: 111 So, A=1 and we
have 1B+CD=111 Now, C can not
be less than 9, because no two-digit integer with first digit 1 (1B<20)
can be added to two-digit integer less than 90, so that to have the sum 111
(if CD<90, so if C<9, CD+1B<111). Hence C=9. |
111.
How
many randomly assembled people are needed to have a better than 50% probability
that at least 1 of them was born in a leap year?
|
Soln:
Probability of a
person to be born in a leap year = 1/4 , <1/2 Probability of
atleast one person out of two to be born in a leap year = 1/4+1/4=1/2, not
>1/2 Probability of
atleast one person out of 3 to be born in a leap year = 1/4+1/4+1/4=3/4, >1/2 Hence minimum 3
people are required. |
112.
If
Himel saved more than TK. 10 by purchasing a sweater at a 15 percent discount,
what is the smallest amount the original price of the sweater could be, to the
nearest taka?
113.
The
maximum recommended pulse rate R, when exercising, for a person who is x years of
age is given by the equation R= 176- 0.8x. What is the age, in years, of a
person whose maximum recommended pulse rate when exercising is 140?
114.
There
are 10 books on a shelf, of which 4 are paperbacks and 6 are hardbacks. How
many possible selections of 5 books from the shelf contain at least one
paperback and at least one hardback?
115.
A
dishonest trader mixes 2 kg of vegetable ghee costing Tk 45 a kg with 3 kg of
standard ghee costing Tk. 70 per kg. He sells the mixed ghee at Tk. 65 per kg.
116.
The
price of a certain stock increased by 0.25 of 1 percent on a certain day. By
what fraction did the price of the stock increase that day?
117.
If
the range of the six numbers 4, 3, 14, 7, 10 and x is 12, what is the
difference between the greatest possible value of x and least possible value of
x?
118.
If
(1050 – 74) is written as an integer in base 10 notation, what is
the sum of the digits in that integer?
119.
If
10 ships require 10 tanks of oil in 10 days. How long is 1 tank of oil enough
for a ship?
120.
A
father's age was 5 times his son's age 5 years ago and will be 3 times son's
age after 2 years. The ratio of their present ages is-
121.
The
scale of a local map is 1cm to 5km. An area is represented on the map by a
rectangle of dimensions 5cm x 9cm. The actual area in km is-
122.
A
cricketer has a certain average for 9 innings. In the 10th innings he scores
100 runs, thus increasing his average by 8 runs. His new average is –
123.
In a survey, 30% of the people surveyed owned
a personal computer and 75% owned a cellular telephone. If 25% owned both a
cellular telephone and a personal computer, then the percentage of the people
who does not have either of the instrument?
124.
How
many seconds will a 500 metre long train take to cross a man walking with a
speed of 3 km/hr in the direction of the moving train if the speed of the train
is 63 km/hr?
125.
How
many 3-digit numbers can be formed from the digits 1,2,3,4 and 5 assuming that.
i) Repetition of the digits is
allowed? ii) Repetition of the
digits is not allowed?
|
Soln: i) There are 5 ways to fill ones place. Since,
repetition is allowed , so tens place can also be filled by 5 ways. Similarly,hundreds
place can also be filled by 5 ways. So, number of
ways in which three digit numbers can be formed from the given digits is
5×5×5=125 ii) There are 5
ways to fill ones place. Since,
repetition is not allowed , so tens place can be filled by remaining 4
digits. So, tens place
can be filled in 4 ways. Similarly, to
fill hundreds place, we have 3 digits remaining. So,hundreds can
be filled by 3 ways. So, required
number of ways in which three digit numbers can be formed from the given
digits is 5×4×3=60 |
126.
How
many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which
are divisible by 5 and none of the digits is repeated?
|
Soln: Since each
desired number is divisible by 5, so we must have 5 at the unit place. So,
there is 1 way of doing it. The tens place
can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there
are 5 ways of filling the tens place. The hundreds
place can now be filled by any of the remaining 4 digits. So, there are 4
ways of filling it. ∴
Required number of numbers = (1 x 5 x 4) = 20. |
127.
How
many numbers between 30000 and 40000 can be formed with the digits 2,3,5,6,9 if
each digits can be repeated any numbers of times?
|
Soln: We cannot put
any digit other than 3 on the ten thousandth place because they will either
lie lower to 30000 or greater than 40000. So now the digit
on the ten thousandth place is fixed. So we will arrange or manage the
remaining 4 numbers on their places to form a five digit number. So the
possible number will be 54. |
128.
The
average age of husband, wife and their child 3 years ago was 27 years and that
of wife and the child 5 years ago was 20 years. The present age of the husband
is-
|
Soln: Sum of the
present ages of husband, wife and child =(27+3)×3 years = 90 years. Sum of the
present ages of wife and child =(20×+5)×2 years = 50 years. ∴
Husband's present age =(90−50) years =40 years. |
129.
Father
is aged three times more than his son Ronit. After 8 years, he would be two and
a half times of Ronit's age. After further 8 years, how many times would he be
of Ronit's age?
130.
At
a party, everyone shook hands with everybody else. There were 253 handshakes.
How many people were at the party?
|
Well, let’s try
posing a hypothetical scenario to understand the situation, If there were 4
people, how many handshakes would there be? P, Q, R, and S:
each letter denotes a unique person Person P could shake
hands with Q, R and S. Person Q could shake
hands with R, and S. Do note that,
since we have already kept track of P shaking hands with Q, let’s not recount
it here. Person R could shake hands with only S. In total, there
are 3+2+1 = 6 unique handshakes. If you look
closely, the number of handshakes is equal to the sum of natural numbers up
to n-1, where n is the total number of people. Huh, that’s interesting… Now, the
handshake problem can simply be solved. The sum of natural numbers up to n is
given by Sum=n(n+1)/2 For sum upto
n-1, the above equation will reduce to, S=(n-1)(n-1+1)/2 S=n(n-1)/2 Where, S represents the
total number of unique handshakes. |
131.
The
average of the two-digit numbers, which remain the same when the digits
interchange their positions is-
132.
Lubana
has purchased a square sheet of plywood of 289 square feet area. To cover a
wall she must cut of two feet from side what is the area,in square feet of the
wall?
133.
A
store sells an item for tk.1.50 each,or 3 item amounted to tk. 3.50. if 202
items were sold and revenue amounted to tk.279.00, how many of these items were
sold one at a time?
134.
A
father told his son, “I was as old as you are at present at the time of your
birth”. If the father’s age is 42 years now, the son’s age 4 years back was-
135.
To
avoid paying a toll on a direct road, I go west 10 miles, south 5 miles, west
30 miles and north 35 miles. What is the length of the toll road and the
alternative path?
136.
How
many times does 8 occur in the number from 1 to 100 ?
|
Soln: {From 1-100 the
we see the digits 2,3,4,5,6,7,8,9 for 20 times. And We will see
1 for 21 times}. The digit 8
occurs in the ones place ten times from the number 1 to the number 100. Also,
the digit 8 occurs 10 times from the number 80 to the number 89 in the tens
place. Hence, the total
number of times the number 8 occurs from 1 to 100 can be calculated as shown
below. 10+10=20 Therefore, 8
occur 20 times in the number from 1 to 100. For digit 1 we
will see it for extra 1 time at 100. |
137.
What
is 10% of Y/3, 2Y/3 is 10% of 400?
138.
P
is now 8 years older than Q. 17 years ago P was twice as old as Q. How old will
Q be in 10 years ?
139.
A
man sells 2 commodities for Tk. 4000 each, neither losing nor gaining in the
deal. If he sold one commodity at a gain 25% then what is the cost price of
another commodity?
|
Soln: Total S.P. = Tk.
8000 and Total C.P. = Tk.
8000 S.P. of 1st
commodity = Tk. 4000 Gain on it = 25% ∴
C.P. of 1st commodity = Tk. {(100/125)×4000}
= Tk. 3200 C.P. of 2nd
commodity = Tk. (8000−3200) = Tk. 4800 Ans |
140.
A
worker is hired for 7 days. Each day, he is paid 10 Tk. more than what he is
paid for the preceding day one work. The total amount he was paid in the first
4 days of work equaled the total amount he was paid in the last 3 days. What
was his starting pay?
|
Soln: Let Salary
for the 1st day is x. Sum of the
salary of the 1st 4 days = Sum of the salary of the last 3 days or, x+(x + 10)+(
x + 20)+( x + 30) = (x + 40)+(x + 50) +(x + 60) or, 4x + 60 = 3x
+ 150 ∴
x = 90. (Ans) |
141.
The
average daily wage of 10 workers is Tk. 400. If the lowest wage is Tk. 300 what
is the possible maximum wage in Tk?
|
Soln: Average Daily wage= 400 Totat Wage for
!0 workes= 10×400=4000 Again, Minimum Wage for 9 Workers= 9×300=2700 ∴Maximum wage for 1 worker= 4000-2700= 1300. (Ans) |
142.
In a class, 120 students are male and 100
students are female. 25% of the male students and 20% of the female students
are engineering students. 20% of the male engineering students and 25% of the female
engineering students passed the final exam. What percentage of engineering
students passed the exam?
|
Soln: Eng. male = 120×.25 = 30 Eng.female = 100×.20 = 20 Total eng. student = 30 + 20 = 50 Eng.male passed = 30×.20 = 6 Eng female passed = 20×.25 = 5 So, percentage passed = (6 + 5)/50×100% = 22% |
143.
A monkey climbs a 12-meters-high slippery
pillar. In his first minute, he climbs 2 meters, and in the next minute, he
slips one meter down. In this way, how much time will he take to reach the top
of the pillar?