GATE Questions and Answers with Explanation

Q:

Rs. 69 were divided among 115 family members so that each lady gets 50 paise less than each gentleman, and each gentleman received twice the paise as each lady received. Find the number of gentlemen in the family?

A) 23	B) 92
C) 48	D) 52

Answer & Explanation Answer: A) 23

Explanation:

Total number of female members = 115

Let the number of males = x

Number of females = y

=> x + y = 115 ......(1)

According to the given data,

x + y(0.50) = 69 ......(2)

From (1) & (2), we get

0.5y = 46

=> y = 46 x 2 = 92

=> x = 115 - 92 = 23

Hence, required number of gentlemen in the family = x = 23.

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8 9171

Q:

Two boys are playing on a ground. Both the boys are less than 10 years old. Age of the younger boy is equal to the cube root of the product of the age of the two boys. If we place the digit representing the age of the younger boy to the left of the digit representing the age of the elder boy, we get the age of the father of the younger boy. Similarly, we place the digit representing the age of the elder boy to the left of the digit representing the age of the younger boy and divide the figure by 2, we get the age of the mother of the younger boy. The mother of the younger boy is younger than his father by 3 years. Then, what are the ages of elder and younger boys ?

A) E = 15 & Y = 3	B) E = 14 & Y = 12
C) E = 40 & Y = 22	D) E = 4 & Y = 2

Answer & Explanation Answer: D) E = 4 & Y = 2

Explanation:

Let the the age of the elder boy = E

Let the the age of the younger boy = Y

Given that Y = cube root of EY

=> $Y^{3}$ = EY => E = $Y^{2}$ .....(1)
By the condition of number replacement the age of the father is YE

The Mother's age = EY/2

But she is 3 years less than father => EY/2 + 3 = YE
2YE = EY + 6 ......(2)

Then now from the given options we can identify which satisfies the all the conditions.

Here Y =2 and E = 4 satisfies all the conditions.

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8 9170

Q:

Which one of the following is an element?

A) Topaz	B) Rruby
C) Diamond	D) Sapphire

Answer & Explanation Answer: C) Diamond

Explanation:

Here in the given options, Diamond is an element as it is the allotrope of the carbon atom.

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14 9165

Q:

Sripad has scored average of 65 marks in three objects. In no subjects has he secured less than 58 marks. He has secured more marks in Maths than other two subjects. What could be his maximum score in Maths ?

A) 79	B) 77
C) 76	D) 73

Answer & Explanation Answer: A) 79

Explanation:

Assuming Sripad has scored the least marks in subject other than science,
Then the marks he could secure in other two are 58 each.
Since the average mark of all the 3 subject is 65.
i.e (58+58+x)/3 = 65
116 + x = 195
x = 79 marks.

Therefore, the maximum marks he can score in maths is 79.

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5 9164

Q:

A tin a mixture of two liquids A and B in the proportion 4 : 1. If 45 litres of the mixture is replaced by 45 litres of liquid B, then the ratio of the two liquids becomes 2 : 5. How much of the liquid B was there in the tin? What quantity does the tin hold?

A) 58 l	B) 65 l
C) 50 l	D) 62 l

Answer & Explanation Answer: C) 50 l

Explanation:

Let the tin contain 5x litres of liquids

$\frac{(5 x - 45) x \frac{4}{5}}{(5 x - 45) x \frac{1}{5} + 45} = \frac{2}{5}$

=> 5(4x - 36) = 2(x + 36)

=> 20x - 180 = 2x + 72

=> x = 14 litres

Hence, the initial quantity of mixture = 70l

Quantity of liquid B

= $(70 - 45) x \frac{1}{5} + 45$

= 50 litres.

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Filed Under: Alligation or Mixture
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29 9163

Q:

A laborer is engaged for 30 days on the condition that he receives Rs.25 for each day he works and is fined Rs.7.50 for each day is absent. He gets Rs.425 in all. For how many days was he absent ?

A) 10 days	B) 14 days
C) 11 days	D) 9 days

Answer & Explanation Answer: A) 10 days

Explanation:

For 30 days he receives

30 x 25 = 750

Actually he gets 425

Therefore, Fine is 750 - 425 = 325

=> No of days absent = 325/(25+7.50)= 10

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5 9148

Q:

Alloy of copper and zinc is called

A) Bronze	B) Gold
C) Silver	D) Brass

Answer & Explanation Answer: D) Brass

Explanation:

alloy_of_copper_and_zinc_is_called1556100441.jpg image

Alloy of copper and zinc is called as Brass.

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3 9144

Q:

If 25% of three-seventh of 26% of a number is 145.5, what is the number?

A) 4987	B) 5784
C) 5223	D) 4741

Answer & Explanation Answer: C) 5223

Explanation:

Given,

25% of three-seventh of 26% of a number is 145.5

Let the required number be 'N'

i.e, $\frac{25}{100} x \frac{3}{7} x (\frac{26}{100} x N) = 145.5$

N = $\frac{145.5 x 7 x 10000}{75 x 26}$

=> N = 5223.07

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