Common Admission Test (CAT) Questions and Answers with Explanation

Q:

Rahul went to purchase a Nokia mobile handset, the shopkeeper told him to pay 20% tax if he asked the bill. Rahul manages to get the discount of 5% on the actual saleprice of the mobile and he paid the shopkeeper Rs. 3325 without tax. Besides he manages to avoid to pay 20% tax on the already discounted price, what is the amount of discount that he has gotten?

A) 750	B) 375
C) 875	D) 525

Answer & Explanation Answer: C) 875

Explanation:

CP = 100, SP (with tax) =120

New SP = 100 - 5 = 95

Effective discount = 120 - 95 = 25

So, at SP of 95 ----> discount = 25

and at SP of 3325 -----> discount = $\frac{25}{95} \times 3325 = 875$

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Q:

Due to reduction of 25% in price of oranges a customer can purchase 4 oranges more for Rs. 16. what is original price of an orange?

A) Rs 1	B) Rs 1.33
C) Rs 1.5	D) Rs 1.6

Answer & Explanation Answer: B) Rs 1.33

Explanation:

Recall it is based on inverse proportion or product constancy concept.

Reducion in price increase in amount

25% 1/4 1/3 33.33% = 4 oranges

It means original number of oranges = 4 x 3 = 12

original price of oranges = 16/12 = Rs. 1.33

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Q:

A trader sold an article at a loss of 5% but when he increased the selling price by Rs.65 he gained 3.33% on the cost price. If he sells the same article at Rs. 936, what is the profit percentage?

A) 15%	B) 16.66%
C) 20%	D) data insufficient

Answer & Explanation Answer: C) 20%

Explanation:

103.33 CP- 0.95 CP = 65

CP = Rs. 780

profit (%) = (936 - 780)/780 x 100 = 20%

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Q:

ITC sells one product at a profit of 20% another at a loss of 20% at the same selling price. What is the loss incurred by ITC?

A) 1%	B) 2%
C) 4%	D) 0%

Answer & Explanation Answer: C) 4%

Explanation:

loss % = ${(\frac{c o m m o n g a i n o r l o s s}{10})}^{2}$ %

= (20/10)x(20/10)% = 4%

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Q:

A person sold two cows each for Rs.9900. If he gained 10% on one and lost 20% on the other, then which of the following is true?

A) He Gained Rs. 200	B) He lost Rs. 200
C) He neither gained nor lost	D) None of the above

Answer & Explanation Answer: D) None of the above

Explanation:

The CP of profitable cow = 9900/1.1 = 9000

and profit = Rs. 900

The CP of loss yielding cow = 9900/0.8 = 12375

and loss = Rs. 2475

so, the net loss = 2475 - 900 = 1575

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Q:

The ratio of cost price and marked price of an article is 2:3 and ratio of percentage profit and percentage discount is 3:2 . what is the discount percentage?

A) 16.66%	B) 20%
C) 25%	D) 33.33%

Answer & Explanation Answer: A) 16.66%

Explanation:

CP : MP = 2x : 3x

=> Profit = x

( %) profit : (%) discount = 3:2

Let CP = 2000, SP = 300

But $\frac{3 x}{100} \times 200 + \frac{2 x}{100} \times 300 = 100$

=> x = 8.33%

Discount 2x = 16.66%

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Q:

A milkman purchases the milk at Rs. x per litre and sells it at Rs. 2x per litre still he mixes 2 litres water with every 6 litres of pure milk. What is the profit percentage?

A) 116%	B) 166.66%
C) 60%	D) 100%

Answer & Explanation Answer: B) 166.66%

Explanation:

Let the cost price of 1-liter pure milk be Re.1, then

$\{\begin{cases} 6 l i t e r s (m i l k) \to C . P = R s . 6 \\ 2 l i t e r s (w a t e r) \to C . P = R s . 0 \end{cases} \to C P = R s . 6 o n l y$

8 litre mixture =>

SP => 8 x 2 = Rs. 16

Profit % = $\frac{16 - 6}{6} x 100 = \frac{1000}{6} = 166.66 %$

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Q:

A Shepherd had n goats in the year 2000. In 2001 the no.of goats increased by 40% . In 2002 the no. of goats declined to 70%. In 2003 the no. of goats grew by 30%. In 2004, he sold 10% goats, then he had only 34,398 goats. The percentage increase of the no.of goats in this duration was:

A) 14.66%	B) 16.66%
C) 20%	D) 33.33%

Answer & Explanation Answer: A) 14.66%

Explanation:

There is no need to use the no of goats i.e (34,398). let initially thete be 1000 goats then

1000 -----> 1400 -----> 980 -----> 1274 ----->1146.6

Thus the % increase = (1146.6-1000)/100 x 100= 14.66%

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