GATE Questions and Answers with Explanation

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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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 12680

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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11 12678

Q:

Rajeev start a business with Rs. 10000, Deepu joins him after 2 month with 20% more investment than Rajeev, after 2 month Shakti joins him with 40% less than Deepu. If the profit earned by them at the end of the year is equal to the twice of the difference between investment of Rajeev and ten times the investment of Shakti. Find the profit of Rajeev ?

A) 50000	B) 48000
C) 38000	D) 40000

Answer & Explanation Answer: C) 38000

Explanation:

Here from the given information,

The ratio of investments of Rajeev, Deepu & Shakti is

R : D : S = (10000 × 12) : (12000 × 10) : (7200 × 8)

= 25 : 25 : 12

Now the Profit = 2 × (72000-10000) = 124000

Share of Rajeev = 124000 x 25/62 = 48000

Profit of Rajeev = 48000 - 10000 = 38000

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Filed Under: Partnership
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21 12670

Q:

Chief component of first generation computer was

A) Vacuum tubes	B) integrated circuits
C) transisters	D) None of the above

Answer & Explanation Answer: A) Vacuum tubes

Explanation:

chief_component_of_first_generation_computer_was1538216221.jpg image

The chief component in the first generation computers are Vacuum tubes.

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Q:

Karthik read $\frac{6}{13}$ th of a book in 1st week and $\frac{5}{9}$ th of the remaining book in 2nd week. If there were 100 pages unread after 2nd week, how many pages were there in the book ?

A) 404	B) 415
C) 418	D) 420

Answer & Explanation Answer: C) 418

Explanation:

Let the total book be 1

Then, in the 1st week $\frac{6}{13}$ th of book is read

i.e remaining pages = $1 - \frac{6}{13} = \frac{7}{13}$

in 2nd week he read $\frac{5}{9}$ th of it

i.e $\frac{5}{9} \times \frac{7}{13} = \frac{35}{117}$
Remaining pages after 2nd week = $\frac{7}{13} - \frac{35}{117} = \frac{28}{117}$

But given remaining pages after 2nd week = 100

$\frac{28 x}{117} = 100$

--> x = 418

The total pages in the book are 418

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Filed Under: Decimal Fractions
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Q:

How many meaningful English words can be formed with the letters LGEU using each letter only once in each word ?

A) Zero	B) One
C) Two	D) Four

Answer & Explanation Answer: B) One

Explanation:

'GLUE' is the only meaningful word that can be formed using the letters given.

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Q:

If the given two numbers are respectively 7% and 28% of a third number, then what percentage is the first of the second ?

A) 24%	B) 29%
C) 34%	D) 25%

Answer & Explanation Answer: D) 25%

Explanation:

Here, k = 7 and l = 28
Therefore, first number = $\frac{k}{l}$ x100 % of second number = 7/28 x 100% of second number = 25% of second number.

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Filed Under: Percentage
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