GATE Questions and Answers with Explanation

Q:

On her deathbed, a grand mother called upon his three grand sons and told them to distribute all her assets worth Rs. 52,500 in the ratio of 1/35 : 1/21 : 1/15 amongst themselves. Find the smallest share amongst the three portions ?

A) Rs. 5422	B) Rs. 10,500
C) Rs. 12,800	D) Rs. 15,000

Answer & Explanation Answer: B) Rs. 10,500

Explanation:

The ratio of distribution should be:
21 x 15 : 15 x 35 : 35 x 21
= 315 : 525 : 735
= 3 : 5 : 7
The smallest share will be of worth:
3/15 x 52,500 = Rs. 10,500

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Filed Under: Ratios and Proportions
Exam Prep: AIEEE , Bank Exams , CAT , GATE , GRE
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6 5123

Q:

The ratio of efficiencies of two filling pipes is 4 : 5. There is a third emptying pipe which efficiency is two third of the average efficiency of first two filling pipes can empty a filled tank in 36 minutes. In how much time both the filling pipes can fill the tank when it is empty?

A) 16 min	B) 12 min
C) 14 min	D) 20 min

Answer & Explanation Answer: B) 12 min

Explanation:

Let the efficiencies of filling pipes is 4p and 5p respectively.

Efficiency of pipe which empty the tank = 2/3 x 9p/2 = 3p

Total work = 3p x 36 = 108p

Time to fill the tank by both the pipes = 108p/9p = 12 min.

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Filed Under: Pipes and Cistern
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17 5118

Q:

How many rectangles can be drawn with 36 cm as the perimeter, given that the sides are positive integers in cm?

A) 8	B) 9
C) 10	D) 11

Answer & Explanation Answer: B) 9

Explanation:

Perimeter = 36

⇒ 2 ( l + w ) = 36

⇒ l + w = 18

Since length and width are positive integers in centimeters.

Therefore, possible dimensions are :

( 1, 17 )cm , ( 2, 16 ) cm , ( 3, 15 ) cm, (4 , 14) cm, ( 5,13) cm, ( 6, 12) cm , ( 7, 11) cm, ( 8, 10 ) cm, ( 9, 9) cm.

Hence, there are 9 rectangles.

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Filed Under: Arithmetical Reasoning
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10 5115

Q:

Nine different letters of alphabet are given, words with 5 letters are formed from these given letters. Then, how many such words can be formed which have at least one letter repeated ?

A) 43929	B) 59049
C) 15120	D) 0

Answer & Explanation Answer: A) 43929

Explanation:

Number of words with 5 letters from given 9 alphabets formed = $9^{5}$

Number of words with 5 letters from given 9 alphabets formed such that no letter is repeated is = $9 P_{5}$

Number of words can be formed which have at least one letter repeated = $9^{5} - 9 P_{5}$

= 59049 - 15120

= 43929

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Filed Under: Permutations and Combinations
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11 5109

Q:

A person lends Rs. 300 to A at 4% and Rs.540 to B at 6% for the same time. if the total amount that he gets at the end is Rs. 1032. What is the time?

Answer

Money lent to A+B = (300 + 540) = Rs. 840

Amount received = Rs. 1032

Interest received = Rs. 1032 - Rs.840 = Rs. 192

Interest on Rs. 300 lent to A for 1 year = $\frac{300 \times 1 \times 4}{100}$ = Rs. 12

Interest on Rs.540 lent to B for 1 year = $\frac{540 \times 6 \times 1}{100}$ = Rs. 36

Total yearly interest = Rs.(12+36) = Rs.48

If interest is Rs. 48, time = 1 year

If interest is Rs. 192, time = 192/48 = 4 years

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Subject: Simple Interest Exam Prep: GATE , CAT , Bank Exams , AIEEE
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12 5106

Q:

A shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes?

A) 2%	B) 4%
C) 3%	D) 2.5%

Answer & Explanation Answer: B) 4%

Explanation:

SP of first article = 1000

Profit = 20%

CP = $\frac{100}{100 + P} \times S P$ = 5000/6 = 2500/3

SP of second article = 1000

Loss = 20%

CP = $\frac{100}{100 - L} \times S P$ = 5000/4 = 1250

Total SP = 2000

Total CP = $\frac{2500}{3}$ + 1250 = 6250/3

CP is more than SP, he makes a loss.

Loss = CP-SP = (6250/3)- 2000 = 250/3

Loss Percent = $\frac{\frac{250}{3}}{\frac{6250}{3}} \times 100$ = 4%

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Filed Under: Profit and Loss
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5 5101

Q:

A began a business with Rs. 85000. He was joined afterwards by B with Rs. 42,500. For how much perod does B join, if the profits at the end of the year are divided in the ratio of 3:1 ?

A) 8 months	B) 6 months
C) 7 months	D) 9 months

Answer & Explanation Answer: A) 8 months

Explanation:

Suppose B joined for x months.

Given profit is divided in the ratio 3:1. Then,

$\frac{85000 \times 12}{42500 \times x} = \frac{3}{1}$

--> x = 8 months.

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Filed Under: Partnership
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6 5097

Q:

Direction: What should come in the place of question mark (?) in the following number series?

2, 3, 6, 15, 45, ?

A) 90	B) 135
C) 157.5	D) 200

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