Common Admission Test (CAT) Questions and Answers with Explanation

Q:

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is ?

A) 1 : 2	B) 3 : 1
C) 4 : 7	D) 3 : 2

Answer & Explanation Answer: D) 3 : 2

Explanation:

Let the speeds of the two trains be x m/sec and y m/sec respectively.

Then, length of the first train = 27 x meters, and

length of the second train = 17 y meters.

(27 x + 17 y) / (x + y) = 23

=> 27 x + 17 y = 23 x + 23 y

=> 4 x = 6 y

=> x/y = 3/2.

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11 12137

Q:

Detect an error part labelled (1), (2), (3) & (4) in the following question.

$\frac{w h o l e n o r t h e r n s t a t e s i n}{(1)} / \frac{i n d i a a r e r e e l i n g u n d e r t h e}{(2)} / \frac{d e v a s t a t i n g}{(3)} / \frac{o f t h e d r o u g h t}{(4)}$

A) 1	B) 2
C) 3	D) 4

Answer & Explanation Answer: A) 1

Explanation:

Error is in the first part of the sentence. 'Whole' is used with singular nouns.
The correct sentence is - 'All Northern states in India are reeling under the devastating of the drought.

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19 12124

Q:

After working for 8 days, Arun finds that only $\frac{1}{3}$ rd of the work has been done. He employs Akhil who is 60% as efficient as Arun. How many days more would Akhil take to complete the work?

A) 24.5 days	B) 26.6 days
C) 25 days	D) 20 days

Answer & Explanation Answer: B) 26.6 days

Explanation:

Arun has completed $\frac{1}{3}$ rd of the work in 8 days

Then he can complete the total work in

$\frac{1}{3}$ ---- 8

1 ---- ?

= 24 days

But given Akhil is only 60% as efficient as Arun

Akhil = $\frac{1}{24} \times \frac{60}{100} = \frac{1}{40}$

Akhil can complete the total work in 40 days

Now, remaining 2/3rd of work can be completed in

1 ------ 40

$\frac{2}{3}$ ------ ?

= 26.66 days.

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Filed Under: Time and Work
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18 12114

Q:

How many days in 4 years?

A) 1460	B) 1461
C) 1462	D) 1459

Answer & Explanation Answer: A) 1460

Explanation:

Days in 4 years =>

Let the first year is Normal year i.e, its not Leap year. A Leap Years occurs once for every 4 years.

4 years => 365 + 365 + 365 + 366(Leap year)

4 years => 730 + 731 = 1461

Therefore, Number of Days in 4 Years = 1461 Days.

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Filed Under: Calendar
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23 12094

Q:

Two boys and a girl can do a work in 5 days, while a boy and 2 girls can do it in 6 days. If the boy is paid at the rate of 28$ a week, what should be the wages of the girl a week ?

A) 24 $	B) 22 $
C) 16 $	D) 14 $

Answer & Explanation Answer: C) 16 $

Explanation:

Let the 1 day work of a boy=b and a girl=g, then
2b + g = 1/5 ---(i) and
b + 2g = 1/6 ---(ii)
On solving (i) & (ii), b=7/90, g=2/45
As payment of work will be in proportion to capacity of work and a boy is paid $ 28/week,
so a girl will be paid $28 \times \frac{\frac{2}{45}}{\frac{7}{90}}$ = 16 $.

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5 12087

Q:

Two solutions have milk & water in the ratio 7:5 and 6:11. Find the proportion in which these two solutions should Be mixed so that the resulting solution has 1 part milk and 2 parts water ?

A) 7 : 12	B) 8 : 13
C) 9 : 4	D) 2 : 5

Answer & Explanation Answer: B) 8 : 13

Explanation:

To get the solution that contains 1 part of milk and two parts of water,
they must be mixed in the ratio as
7x+6x/5y+11y = 1/2
26x = 16y
x/y = 16/26
x/y = 8/13

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Filed Under: Ratios and Proportions
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19 12073

Q:

Arjun and Bhishma are running on a circular track of length 600m. Speed of Arjun is 30 m/s and that of Bhishma is 20 m/s .They start fro the same point at the same time in the same direction. When will they meet again for the first time?

Answer

Sol : $Time = \frac{Circumference}{Relative Speed} = \frac{600}{10} = 60 \sec .$

Actually Arjun has to make a lead of 600 m, because when Arjun will be 600m ahead of Bhishma, they will be together again as a person when completes the total length it starts retracing he same path and thus Arjun and Bhishma can be together again.

Since , they make a difference of 10 m in 1 second. so, he will create 600m difference in 60 second.

Workspace

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Subject: Time and Distance Exam Prep: AIEEE , Bank Exams , CAT
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14 12073

Q:

A driver of auto rickshaw makes a profit of 20% on every trip when he carries 3 passengers and the price of petrol is Rs. 30 a litre. Find the % profit for the same journey if he goes for 4 passengers per trip and the price of petrol reduces to Rs. 24 litres ?

A) 68%	B) 80%
C) 75%	D) 100%

Answer & Explanation Answer: D) 100%

Explanation:

When 3 passengers income was 3x
expense= Rs.30
profit =20% of 30 = Rs.6
That means his earning is Rs.36. so that per passenger fare must be Rs.12.

When 4 passengers
earning = 12x4=Rs.48.
expense =Rs.24.
profit = Rs.24 = 100%

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