GATE Questions and Answers with Explanation

Q:

The present average age of a family of five members is 26 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest)

A) 19 years	B) 16 years
C) 18 years	D) 20 years

Answer & Explanation Answer: D) 20 years

Explanation:

Present total age of the members = 26(5) = 130 years.

Present age of the youngest member = 10 years

Present total age of the remaining four members = 130 -10 = 120 years

Their average age at the time of the birth of the youngest member = $\frac{[120 - (4 \times 10)]}{4}$ = 30 - 10 = 20 years.

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Filed Under: Problems on Ages
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19 18934

Q:

Three friends, P, Q and R started a partnership business investing money in the ratio of 5 : 4 : 2 respectively for a period of 3 years. What is the amount received by P as his share in the total profit ?

a. Total amount invested in the business in Rs. 22,000.

b. Profit earned at the end of 3 years is 3/8 of the total investment.

c. The average amount of profit earned per year is Rs. 2750.

A) Only c is sufficient	B) Both a & b are sufficient
C) Both A & B gives result	D) None

Answer & Explanation Answer: C) Both A & B gives result

Explanation:

a and b give, profit after 3 years = Rs.(3/8 x 22000) = Rs.8250.

From c also, profit after 3 years = Rs. (2750 x 3) = Rs. 8250.

∴ P's share = Rs.(8250 x 5/11) = Rs. 3750.

Thus, (either C is redundant) or (a and b are redundant).

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Filed Under: Partnership
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5 18871

Q:

If 2 men and 3 women can do a piece of work in 8 days and 3 men and 2 women in 7 days. In how many days can the work be done by 5 men and 4 women working together?

A) 3 days	B) 6 days
C) 4 days	D) 2 days

Answer & Explanation Answer: C) 4 days

Explanation:

From the given data,

=> (2 M + 3W) 8 = (3M + 2W)7

=> 16M + 24W = 21M + 14 W

=> 10W = 5M

=> 2W = M

=> 14W × ? = 7W × 8

? = 4 days

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Filed Under: Time and Work
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30 18845

Q:

Find the appropriate relation for quantity 1 and quantity 2 in the following question:

An artificial kund is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the kund at the same time during which the kund is filled by the third pipe alone. The second pipe fills the kund 5 hours faster than the first pipe and 4 hours slower than the third pipe.

Quantity 1: The time required by the first pipe?

Quantity 2: Time taken by all three pipes to fill the Kund simultaneously

A) Quantity 1 > Quantity 2	B) Quantity 1 ≥ Quantity 2
C) Quantity 1 < Quantity 2	D) Quantity 1 ≤ Quantity 2

Answer & Explanation Answer: A) Quantity 1 > Quantity 2

Explanation:

Quantity 1:
Let the first pipe alone takes x hours to fill the
tank.
⇒The second and third pipes will take (x-5) and
(x-9) hours respectively.
According to the given information:
∴ $\frac{1}{x - 9}$

⇒ (x-9)(2x-5) = x2 – 5x
⇒ 2x2 – 5x – 18x + 45 = x2 – 5x
⇒ x
2 -18x + 45 = 0
⇒ (x-15) (x-3) = 0
⇒ x = 15, 3

The first pipe can take 15 hours to fill the kund.
∵ 3 hours doesn’t satisfy the statement.
Quantity 2:
∴ Time taken by second pipe = x-5
⇒ Time taken by second pipe = 15-5 = 10hours
∴ Time taken by third pipe = x -9
⇒ Time taken by third pipe = 15- 9 = 6 hours
Now,

Net part filled in 1 hour = $\frac{1}{15} + \frac{1}{10} + \frac{1}{6}$
⇒ Net part filled in 1 hour = $\frac{4 + 6 + 10}{60}$
⇒Net part filled in 1 hour = $\frac{20}{60} = \frac{1}{3}$
∴The Kund will be full in 3/1 hours if all the pipes are opened simultaneously
Now, comparing
15 > 3
Thus, Quantity 1 > quantity 2

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Filed Under: Quantitative Aptitude - Arithmetic Ability
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2 18762

Q:

Amar can do a piece of work in 10 days. He works at it for 4 days and then Arun finishes it in 9 days. In how many days can Amar and Arun together finish the work ?

A) 4 days	B) 8 days
C) 3 days	D) 6 days

Answer & Explanation Answer: D) 6 days

Explanation:

4/10 + 9/x = 1 => x = 15

Then both can do in

1/10 + 1/15 = 1/6 => 6 days

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19 18740

Q:

The number of ways in which 8 distinct toys can be distributed among 5 children?

A) 5P8	B) 5^8
C) 8P5	D) 8^5

Answer & Explanation Answer: B) 5^8

Explanation:

As the toys are distinct and not identical,

For each of the 8 toys, we have three choices as to which child will receive the toy. Therefore, there are $5^{8}$ ways to distribute the toys.

Hence, it is $5^{8}$ and not $8^{5}$ .

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Filed Under: Permutations and Combinations
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16 18691

Q:

How many different words can be made using the letters of the word ' HALLUCINATION ' if all constants are together?

A) 129780	B) 1587600
C) 35600	D) None of these

Answer & Explanation Answer: B) 1587600

Explanation:

H L C N T A U I O

L N A I

There are total 131 letters out of which 7 are consonants and 6 are vowels. Also ther are 2L's , 2N's, 2A's and 2I's.

If all the consonants are together then the numberof arrangements = $\frac{7!}{2!}$ x 1/2! .

But the 7 consonants can be arranged themselves in $\frac{7!}{2!}$ x 1/2! ways.

Hence the required number of ways = ${(\frac{7!}{2! 2!})}^{2}$ = 1587600

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Filed Under: Permutations and Combinations
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8 18659

Q:

Book is to chapter as organization is to

Answer

A book is consists of various chapters, so as the Organization consists of various departments. Therefore if Book is to chapter so organization is to department.

Hence, Book : Chapter :: Organisation : Department.

Workspace

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Subject: Analogy Exam Prep: AIEEE , Bank Exams , CAT , GATE , GRE
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