Question Bank  100 Arithmetic Questions From Previous CAT Papers (Solved)

Let say it takes t seconds to strike once.
At 4 o'clock the pendulum should strike 4 times and it will take 3t seconds (Considering first strike happened at zero'th second)
3t = 7
t = 7/3
Similarly at 11 o'clock pendulum should strike 11 times and it will take 10t seconds (first strike happens at zero'th second and t is the time elapsed between each consecutive strike)
10 x 7/3 = 23.33 seconds

Q71. (CAT 1994)
A man buys spirit at Rs. 60 per litre, adds water to it and then sells it at Rs. 75 per litre. What is the ratio of spirit to water if his profit in the deal is 37.5%?
(a) 9 : 1
(b) 10 : 1
(c) 11 : 1
(d) None of these

I L spirit cost 60 Rs
If he adds x L of water to it then the total quantity is (1 + x) L
At the rate of 75, this should yield 75 (1 + x) which is 37.5% higher than the cost price, 60 = 82.5
x = 82.5/75 = 0.1
So required ratio is 10 : 1

Q72. (CAT 1994)
A and B walk from X to Y, a distance of 27 km at 5 kmph and 7 kmph respectively. B reaches Y and immediately turns back meeting A at Z. What is the distance from X to Z?
(a) 25 km
(b) 22.5 km
(c) 24 km
(d) 20 km

X  < d >  Z  < 27  d >  Y
here time taken is same.
d/5 = (27 + 27  d)/7
d/5 = (54  d)/7
7d = 270  5d
12d = 270
d = 270/12 = 22.5 km.

Q73. (CAT 1994)
There is a leak in the bottom of the tank. This leak can empty a full tank in 8 hours. When the tank is full, a tap is opened into the tank which admits 6 litres per hour and the tank is now emptied in 12 hours. What is the capacity of the tank?
(a) 28.8 litres
(b) 36 litres
(c) 144 litres
(d) Cannot be determined

To empty a full tank  8 hours
Time took for emptying the tank in the given question  12 hours
Tap was open for 12 hours adding an extra 12 x 6 = 72 L of water into the tank.
Hence the extra 4 hours was required to empty this 72 L of water.
In 8 hours it can empty 72 x 2 = 144 L of water which is the capacity of the tank.

Q74. (CAT 1994)
A dealer offers a cash discount of 20% and still makes a profit of 20%, when he further allows 16 articles to a dozen to a particularly sticky bargainer. How much percent above the cost price were his wares listed?
(a) 100%
(b) 80%
(c) 75%
(d) 66 2/3%

say CP = 100
For 12 articles, CP = 12 x 100 = 1200
After 20% discount, SP = 1200  240 = 960
SP of 16 articles = 960
SP of 1 article = 60
20% profit means Actual CP = 60/1.2 = 50
Assumed CP = 100, Actual CP = 50
So it was listed 100% above the actual cost price

Q75. (CAT 1994)
The winning relay team in a high school sports competition clocked 48 minutes for a distance of 13.2 km. Its runners A, B, C and D maintained speeds of 15 kmph, 16 kmph, 17 kmph, and 18 kmph respectively. What is the ratio of the time taken by B to than taken by D?
(a) 5 : 16
(b) 5 : 17
(c) 9 : 8
(d) 8 : 9

All runners covered the same distance.
Time taken is inversely proportional to speed
For B and D, ratio of time taken is 1/16 : 1/18 = 18 : 16 = 9 : 8

Q76. (CAT 1993)
The rate of increase of the price of sugar is observed to be two percent more than the inflation rate expressed in percentage. The price of sugar, on January 1, 1994, is Rs. 20 per kg. The inflation rate for the years 1994 and 1995 are expected to be 8% each. The expected price of sugar on January 1, 1996 would be
(a) 23.60
(b) 24.00
(c) 24.20
(d) 24.60

Price of sugar on January 1, 1996 = 20 [ 1 + 10/100]^2 = 20 x 1.21 = 24.20 Rs

Q77. (CAT 1993)
Q started to move from point B towards point A exactly an hour after P started from A in the opposite direction. Q’s speed was twice that of P. When P had covered onesixth of the distance between the points A and B, Q had also covered the same distance. The point where P and Q would meet is
(a) Closer to A
(b) Exactly between A and B
(c) Closer to B
(d) P and Q will not meet at all

Let the total distance be d.
After each covering 1/6 of the total distance, P and Q has a distance of (d  d/6  d/6) = 2d/3 between them.
Q moves at 2S and P moves at S.
distance covered by Q will be double that by P once they meet
So Q travels 4d/9 and P travels 2d/9
Meeting point will be closer to A

Q78. (CAT 1993)
In the above question, how many hours would P take to reach B?
(a) 2
(b) 5
(c) 6
(d) 12

Time for covering 1/6th of total distance,
For P = (d/6) / S
For Q = [ (d/6) / (2S)] + 1
d/6S  d/12S = 1
d = 12S
So for P will take 12S/S = 12 hours to cover the whole distance.

Q79. (CAT 1993)
ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.Then D is
a) 3 km east and 1 km north of A
b) 3 km east and √3 km north of A
c) √3 km east and 1 km south of A
d) √3 km west and 3 km north of ATotal distance walked by the person is
a) 3 km
b) 4 km
c) 2√3 km
d) 6 km

Part 1 :
From the figure, D is 3 km east and √3 km north of A
Note  DBG forms a right triangle with hypotenuse, DB = 2 and BG = 1. Apply Pythagoras, DG = √3Part 2 :
From the figure, person travels 2 + 2 + 2 = 6 km

Q80. (CAT 1993)
A group of workers was put on a job. From the second day onwards, one worker was withdrawn each day., The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in twothirds the time. How many workers were there in the group?
(a) 2
(b) 3
(c) 5
(d) 11