Mathematics & Aptitude Test
Exam date: 20.05.2016
36. A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of the total time; to cover the remaining distance in the remaining time, his speed (in km/hr) must be.
(a) 15 (b) 6 (c) 8 (d) 12
Ans. (d) 12
Solution: One half of the distance of 6 km in 3 km. He has to cover remaining 3 km in one-third of time 45 minutes which is or 15 minutes or hours.
His speed in km/hr =
37. Which decimal of an hour is a second?
(a) 0.000126 (b) 0.0025 (c) 0.0256 (d) 0.00027
Ans. (d) 0.00027
Solution: 1 hour=3600 seconds
1 second = hours = 0.00027
38. One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
(a) 192 min (b) 81 min (c) 108 min (d) 144 min
Ans. (d) 144 min
Solution: Lets assume, slower pipe fills in 3t mins and faster in t mins together in one minutes they fill = portion
total time taken,
t = 48 min
slower one takes = 3t =
39. Anik, Kamal and Jamal invested Tk. 8000, Tk. 4000 and Tk. 8000 respectively in a business. Anik left after six months. If after eight months, there was a gain of Tk. 4005, then what will be the share of Kamal?
(a) Tk.1780 (b) Tk.890 (c) Tk.1335 (d) Tk.1602
Ans. (b) Tk.890
Solution: Anik invested=8000×6=48000 portion
Kamal invested=4000×8=32000 portion
Jamal invested=8000×8=64000 portion
Total = 48000+32000+64000=144000 portion
40. The ratio of two numbers is 3:4 and their H.C.F is 4. Their L.C.M is:
(a) 48 (b) 12 (c) 16 (d) 24
Ans. (a) 48
Solution: Given, two number’s ratio is 3:4;
Let the numbers be 3x and 4x. Now thier HCF (the common number) is x.
1st number×2nd number=their HCF×their LCM
or, 3x×4x=x × LCM
41. If selling price of an article is of its cost price, the profit in the transaction is:
(a) % (b) % (c) % (d) %
Ans. (a) %
Solution: Let, the cost price be x
selling price is of x =
42. Tk. 800 becomes Tk. 956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4%, what amount will Tk. 800 become in 3 years?
(a) Tk. 1052 (b) Tk. 1020.80 (c) Tk. 1025 (d) None of these
Ans. (a) Tk. 1052
Solution: For Simple interest, A=Principal+interest
When the interest rate (r) is increased by 4%,
it becomes =6.5+4=10.5
new i = Pnr=
So total amount A=P+i=800+252=1052
43. The smallest 6 digit number exactly divisible by 111 is:
(a) 11111 (b) 110011 (c) 110101 (d) 100011
Ans. (d) 100011
Solution: They asked for the smallest number, so we will start from the smallest number given in the answer options and check if it is divisible by 111.
The smallest is here 100011.
100011 ÷ 111=901
So, 100011 is divisible by 111 and the this number is smallest. That is the correct option.
44. If m and n are whole numbers such that , then the value of is :
(a) 1000 (b) 1 (c) 10 (d) 121
Ans. (a) 1000
45. The ages of A and B are in the ratio 3:1. Fifteen years hence, the ratio will be 2:1. Their present ages are:
(a) 21 years, 7 years (b) 30 years, 10 years
(c) 45 years, 15 years (d) 60 years, 20 years
Ans. (c) 45 years, 15 years
Solution: Given that, their present age ratio is 3:1;
so assume their present age is 3x and x respectively
After 15 years ratio will be 3x+15: x+15
In 15 years the ratio becomes 2:1
3x=3×15=45 and x=15
Their present ages are 45 and 15 years respectively.
46. is equal to:
(a) (b) (c) (d)
47. 15 men take 21 days of 8 hours each to do a pice of work. How many days of 6 hours each would 21 women take; if 3 women do as much work as 2 men?
(a) 30 (b) 18 (c) 20 (d) 25
Ans. (a) 30
3 women’s work is equivalent to 2 men’s work
1 women’s work is equivalent to men’s work
21 women’s work is equivalent to men’s work
15 men working 8 hr takes 21 days
1 men working 1 hr takes 15×8×21 days
14 men working 6 hr takes days=30 days.
48. If 25% of a number is subtracted from a second number, the second number reduces to its five-sixth. What is the ratio of the first number to the second number?
(a) 3:2 (b) 1:3 (c) 2:3 (d) None of these
Ans. (c) 2:3
Solution: Assume that, the first number be x and the second number be y
49. A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?
(a) 21 days (b) 11 days (c) 13 days (d) None of these
Ans. (c) 13 days
Solution: Here, 30% more =
Since A is 30% more efficient than B, B would take 30% more time that is, 23×1.30 days =29.9 30 days to finish the work.
or, portion of work is done by both A and B in 1 day
So portion is done by both in 1 day
Total work is done by both is days
50. What mathematical operation should come at the place of ‘?’ in the equation: 2 ? 6-12÷4+2=11
(a) ÷ (b) + (c) – (d) ×
Ans. (d) ×
L.H.S= 2 ? 6-12÷4+2
= 2 ? 6-3+2
so we see that only multiplication can place of ‘?’ for come 11
2 × 6-3+2 =11
51. Two numbers are such that the ratio between them is 4:7. If each is increased by 4, the ratio becomes 3: 5. The larger number is:
(a) 64 (b) 36 (c) 48 (d) 56
Ans. (d) 56
Solution: Let the number be 4x and 7x
If increased 4 then ratio will be 4x+4:7x+4
larger number = 7×8=56
52. The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is :
(a) 46% (b) 40% (c) 42% (d) 44%
Ans. (d) 44%
Solution: Shortcut system:
53. How many seconds will a 500 meter 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 ?
(a) 45 (b) 25 (c) 30 (d) 40
Ans. (c) 30
Solution: As the direction of train and man is same,
the relative velocity of the train would be =(63-3)=60 km/hr. =
time need to pass
54. A person’s present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?
(a) 48 years (b) 32 years (c) 36 years (d) 40 years
Ans. (d) 40 years
Solution: Lets the mother’s present age be x years
then the person’s present age is years
After 8 years mother’s age will be (x+8)
and person’s age will be
the mother’s present age is 40 years
55. The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers?
(a) 8 (b) 2 (c) 5 (d) None of these
Ans. (a) 8
Solution: For average of consecutive number, the average value is always the middle number. So, the consecutive odd numbers are 57,59,61,63,65
And the difference between highest and lowest number = (65-57)=8
56. If A + B = 2C and C + D =2A, then
(a) A + C = 2B (b) A + C = B + D (c) A + C = 2D (d )A + D = B + C
Ans. (b) A + C = B + D
A + B = 2C
C + D = 2A
A + B + C + D = 2C + 2A (adding)
B + D = 2C + 2A – A – C
B + D = C + A
A + C = B + D
57. A, B and C are sisters. D is the brother of E and E is the daughter of B. How is A related to D ?
(a) Aunt (b) Sister (c) Cousin (d) Niece
Ans. (a) Aunt.
58. In a class of 60, where girls are twice that of boys, Kamal ranked seventeenth from the top. If there 9 girls ahead of Kamal, how many boys are after him in rank?
(a) 23 (b) 3 (c) 7 (d) 12
Ans. (d) 12
Solution: Let, number of girls be and boys
boys 20 and girls 40
Now, Kamal is 17th, Ahead of him are 16 people. Among them, 9 are girls. So no. of boys ahead = (16-9)=7 boys including him, 8 boys upto his position. So no. of boys after him is (20-8)=12 boys.
59. Choose the number pair/group which is different from others.
(a) 63-77 (b) 50-66 (c) 32-48 (d) 64-80
Ans. (a) 63-77
Solution: Here only option A is odd number pair and the other options has even number pair.
60. If A =26, SUN = 27, then CAT = ?
(a) 58 (b) 24 (c) 27 (d) 57
Ans. (d) 57
Solution: Here, Reverse number assigned to letters.
A = 26, B=25, C=24 , …………..
61. Choose out the odd one.
(a) WHO (b) IMF (c) SAARC (d) UNICEF
Ans. (c) SAARC
Solution: All other’s are Global. SAARC is not .
62. Arrange the following in a logical order:
1.Euphoria, 2. Happiness,3.Ambivalence, 4.Ecstasy, 5.Pleasure
(a) 4,1,3,2,5 (b) 1,4,2,5,3 (c) 2,1,3,4,5 (d) 3,2,5,1,4
Ans. (d) 3,2,5,1,4
Solution: All the given words stand for joy, but these increase in the order Ambivalence, happiness, pleasure, Euphoria, Ecstasy
63. Cyclone is related to Anticyclone in the same way as Flood is related to…………..?
(a) Drought (b) Devastation (c) Havoc (d) River
Ans. (a) Drought
Solution: Flood and Drought is opposite of each other, exact like Cyclone and Anticyclone.
64. How many sons does X have?
I. Q and U are brother of T. II. R is sister of P and U.
III. R and T are daughters of X
(a) All I, II and III (b) Only I and II
(c) Only II and III (d) I,II and III together are not sufficient
Ans. (d) I,II and III together are not sufficient
Solution: Here, Q,U are sons, T, R are daughters. But we can not determine P’s gender. So not sufficient information.
65. Root: Stem: Branch: ?
(a) Fertiliser (b) Wood (c) Leaf (d) Tree
Ans. (c) Leaf
Solution: As root caries stem of a tree, branch caries the leaf of a tree.