GATE Questions and Answers with Explanation

Q:

If 5 men and 2 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time ?

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

Answer & Explanation Answer: D) 2:1

Explanation:

5M + 2B = 4(1M + 1B)

5M + 2B = 4M + 4B

1M = 2B

The required ratio of work done by a man and a boy = 2:1

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Filed Under: Time and Work
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8 14313

Q:

A shopkeeper sold a mobile phone for Rs. 12000. Had he offered discount of 10% on the selling price, there would be a loss of 4%. What is the cost price of that Mobile phone?

A) Rs. 12,500	B) Rs. 11,250
C) Rs. 12,750	D) Rs. 11,680

Answer & Explanation Answer: B) Rs. 11,250

Explanation:

Given that SP = Rs. 12000 - 10% = Rs. 10,800

Loss% = 4

We know that, C.P = 100/(100 - Loss%) x 100

=> 100/100-4 x 10800

=> 1080000/96

C.P = Rs. 11,250

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Filed Under: Profit and Loss
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14 14312

Q:

In a 40 litre mixture of alcohol & water, the ratio of alcohol and water is 5 : 3. If 20% of this mixture is taken out and the same amount of water is added then what will be the ratio of alcohol and water in final mixture?

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

Answer & Explanation Answer: A) 1:1

Explanation:

Quantity of alohol in the mixture = 40 x 5/8 = 25 lit

Quantity of water = 40 - 25 = 15 lit

According to question,

Required ratio = $\frac{20 - (40 x \frac{20}{100} x \frac{5}{8})}{15 - (40 x \frac{20}{100} x \frac{3}{8}) + 40 x \frac{20}{100}} = \frac{20}{15 - 3 + 8} = 1 : 1$

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Filed Under: Alligation or Mixture
Exam Prep: AIEEE , Bank Exams , CAT , GATE
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27 14309

Q:

Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is ?

A) 16/19	B) 1
C) 3/2	D) 17/20

Answer & Explanation Answer: D) 17/20

Explanation:

n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(E U P) = 10/20 + 8/20 - 1/20 = 17/20

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Filed Under: Probability
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15 14299

Q:

The cost of 7 tables and 12 chairs is Rs 48,250. What is the cost of 21 tables and 36 chairs ?

A) Rs. 1,44,750	B) Rs. 2,35,745
C) Rs. 89,489	D) Rs.74,256

Answer & Explanation Answer: A) Rs. 1,44,750

Explanation:

3T+12C = 48,250----(1)

21T+36C = ?

multiply eq (1) with 3
i.e,, 3(7T+12C) = 48,250*3
21T+36C = 1,44,750/-

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Filed Under: Arithmetical Reasoning
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25 14256

Q:

The ratio of investments of two partners A and B is 7:5 and the ratio of their profits is 7:10. If A invested the money for 5 months, find for how much time did B invest the money ?

A) 11 months	B) 9 months
C) 7 months	D) 10 months

Answer & Explanation Answer: D) 10 months

Explanation:

7x5: 5xk = 7:10
k = 10 months

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Filed Under: Partnership
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7 14214

Q:

Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction ?

A) 2 9/7 km	B) 3 7/5 km
C) 1 3/4 km	D) 4 3/8 km

Answer & Explanation Answer: D) 4 3/8 km

Explanation:

Relative Speed = 5 ¾ - 4 ½ = 1 ¼

Time = 3 ½ h.

Distance = 5/4 x 7/2 = 35/8 = 4 3/8 km.

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Filed Under: Time and Distance
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9 14212

Q:

If $\log_{7} (2)$ = m, then $\log_{49} (28)$ is equal to ?

A) 1/(1+2m)	B) (1+2m)/2
C) 2m/(2m+1)	D) (2m+1)/2m

Answer & Explanation Answer: B) (1+2m)/2

Explanation:

$\log_{49} (28) = \frac{1}{2 \log_{7} (7 \times 4)}$

= $\frac{1}{2} + \frac{1}{2} (2 \log_{7} (2))$
= $\frac{1}{2} + \log_{7} (2)$
= $\frac{1}{2} + m$
= $\frac{1 + 2 m}{2}$ .

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Filed Under: Logarithms
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63 14191

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