Common Admission Test (CAT) Questions and Answers with Explanation

Q:

Water flows into a tank which is 200 m long and 150 m wide, through a pipe of cross-section (0.3m x 0.2m) at 20 km/h. In what time will the water level be 12m ?

A) 200 hrs	B) 240 hrs
C) 300 hrs	D) 270 hrs

Answer & Explanation Answer: C) 300 hrs

Explanation:

Volume of water collected in the tank in 1 hour

⇒ (0.3 × 0.2 × 20km × 1000mts) = 1200 m cubic

If after t hours, the water is at height of 12m,

1200t=200×150×12

⇒ t = 300 Hours.

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Filed Under: Pipes and Cistern
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25 12654

Q:

At an examination in which maximum marks are 500. P got 10% less than Q, Q got 25% more than R and R got 20% less than S. If P got 360 marks what percentage of marks was obtained by S ?

A) 77	B) 74
C) 80	D) 83

Answer & Explanation Answer: C) 80

Explanation:

Let marks obtained by S = M

R's marks = 0.80M

Q's marks = 1.25 (0.80M)

P's marks = (0.90) (1.25) (0.80M)

= 0.9M

But 0.9M = 360

M = ?

M = 400

Hence % of marks obtained by S

= 400/500 x 100 = 80%.

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Filed Under: Percentage
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Q:

Errata : Books :: flaws :?

A) Speech	B) Manuscripts
C) Charter	D) Metals

Answer & Explanation Answer: D) Metals

Explanation:

Errata comprises from the books. Similarly, Flaws are the defects in the metals.

Hence, Errata : Books :: flaws : Metals.

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Filed Under: Analogy
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6 12640

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 12638

Q:

If $a^{2} + b^{2} = c^{2}$ , then $\frac{1}{l o g_{c + a} (b)} + \frac{1}{l o g_{c - a} (b)} = ?$

A) 1	B) 2
C) 4	D) 8

Answer & Explanation Answer: B) 2

Explanation:

Given $a^{2} + b^{2} = c^{2}$

Now $\frac{1}{\log_{c + a} (b)} + \frac{1}{\log_{c - a} (b)}$

= $\log_{b} (c + a) + \log_{b} (c - a)$

= $\log_{b} (c^{2} - a^{2})$

= $2 \log_{b} (b) = 2$

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Filed Under: Logarithms
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32 12637

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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Filed Under: Profit and Loss
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19 12634

Q:

A trader marked the price of the T.V. 30% above the cost price of the T.V. and gave the purchaser 10% discount on the marked price, thereby gaining Rs.340. Find the cost price of the T.V ?

A) Rs. 2000	B) Rs. 1600
C) Rs. 2200	D) Rs. 2100

Answer & Explanation Answer: A) Rs. 2000

Explanation:

Let 'x' be the cost price.
Now Marked price = x + 30x/100 = 13x/10
10% discount = 10/100 x 13x/10 = 13x/100
Selling price = 13x/10 - 13x/100 = 117x/100
Given gain = 340
Here gain = 117x/100 - x = 17x/100 = 340 => x = Rs. 2000.

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Filed Under: Profit and Loss
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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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