GATE Questions and Answers with Explanation

Q:

There are two numbers such that the sum of twice the first number and thrice the second number is 100 and sum of thrice the first number and twice the second number is 120. Which is the larger number ?

A) 32	B) 24
C) 26	D) 38

Answer & Explanation Answer: A) 32

Explanation:

Let the first number be K and second number be L
Then, 2K + 3L = 100.....(1)
3K + 2L = 120.......(2)
solving (1)&(2), we get
K = 32 and L = 12

Hence the largest number is 32.

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Filed Under: Numbers
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Q:

Ashwin fires two bullets from the same place at an interval of 15 minutes but Rahul sitting in a bus approaching the place hears the second sound 14 minutes 30 seconds after the first. If sound travels at the speed of 330 meter per second, what is the approximate speed of bus?

A) 330/29 m/s	B) 330 x 30 m/s
C) 330/14 m/s	D) 330/900 m/s

Answer & Explanation Answer: A) 330/29 m/s

Explanation:

Second gun shot take 30 sec to reach rahul imples distance between two.

given speed of sound = 330 m/s

Now, distance = 330 m/s x 30 sec

Hence, speed of the bus = d/t = 330x30/(14x60 + 30) = 330/29 m/s.

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Filed Under: Time and Distance
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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 12645

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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Q:

16 men and 12 women can complete a work in 20 days. 18 women can complete the same work in 40 days. In how many days will 12 men 27 women complete the same work?

A) 16 days	B) 18 days
C) 19 days	D) 21 days

Answer & Explanation Answer: A) 16 days

Explanation:

(16M + 12W) x 20 = 18W x 40

=> 2M = 3W

Then,
Convert all men into women

12M + 27W = 27 + 12 x 3/2W = 45W

Let number of days required be 'D'

=> 18 x 40 = 45 x D

=> D = 16 days.

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Filed Under: Time and Work
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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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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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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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