GATE Questions and Answers with Explanation

Q:

A person lends Rs. 300 to A at 4% and Rs.540 to B at 6% for the same time. if the total amount that he gets at the end is Rs. 1032. What is the time?

Answer

Money lent to A+B = (300 + 540) = Rs. 840

Amount received = Rs. 1032

Interest received = Rs. 1032 - Rs.840 = Rs. 192

Interest on Rs. 300 lent to A for 1 year = $\frac{300 \times 1 \times 4}{100}$ = Rs. 12

Interest on Rs.540 lent to B for 1 year = $\frac{540 \times 6 \times 1}{100}$ = Rs. 36

Total yearly interest = Rs.(12+36) = Rs.48

If interest is Rs. 48, time = 1 year

If interest is Rs. 192, time = 192/48 = 4 years

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Subject: Simple Interest Exam Prep: GATE , CAT , Bank Exams , AIEEE
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12 5151

Q:

$\frac{23 x 12 + 49 x 15}{31^{2} + 50} = ?$

A) 0.5	B) 1
C) 2	D) 3

Answer & Explanation Answer: B) 1

Explanation:

$\frac{276 + 35}{961 + 50} = \frac{1011}{1011} = 1$

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Filed Under: Simplification
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1 5317

Q:

In how many ways can 100 soldiers be divided into 4 squads of 10, 20, 30, 40 respectively?

A) 1700	B) 18!
C) 190	D) None of these

Answer & Explanation Answer: D) None of these

Explanation:

$100 C_{10} + 90 C_{20} + 70 C_{30} + 40 C_{40} = \frac{100!}{10! x 20! x 30! x 40!}$

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Filed Under: Permutations and Combinations
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3 9040

Q:

What is the total no of ways of selecting atleast one item from each of the two sets containing 6 different items each?

A) 2856	B) 3969
C) 480	D) None of these

Answer & Explanation Answer: B) 3969

Explanation:

We can select atleast one item from 6 different items = $2^{6} - 1$

Similarly we can select atleast one item from other set of 6 different items in $2^{6} - 1$ ways.

Required number of ways = $(2^{6} - 1) (2^{6} - 1) = {(2^{6} - 1)}^{2}$ = 3969

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Filed Under: Permutations and Combinations
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1 6567

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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7 15428

Q:

If $A = \frac{l o g_{3} (2187)}{5}$ and $B = l o g_{243} (2187)$ , then which one of the following is correct?

A) A	B) A=B
C) A>B	D) can't be determined

Answer & Explanation Answer: B) A=B

Explanation:

Given $A = \frac{\log_{3} (2187)}{5} a n d B = \log_{243} (2187)$

$B = \log_{3^{5}} (2187) = \frac{\log_{3} (2187)}{5}$

=> A

Therefore, A = B

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Filed Under: Logarithms
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7 4836

Q:

A milkman purchases the milk at Rs. x per litre and sells it at Rs. 2x per litre still he mixes 2 litres water with every 6 litres of pure milk. What is the profit percentage?

A) 116%	B) 166.66%
C) 60%	D) 100%

Answer & Explanation Answer: B) 166.66%

Explanation:

Let the cost price of 1-liter pure milk be Re.1, then

$\{\begin{cases} 6 l i t e r s (m i l k) \to C . P = R s . 6 \\ 2 l i t e r s (w a t e r) \to C . P = R s . 0 \end{cases} \to C P = R s . 6 o n l y$

8 litre mixture =>

SP => 8 x 2 = Rs. 16

Profit % = $\frac{16 - 6}{6} x 100 = \frac{1000}{6} = 166.66 %$

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Filed Under: Profit and Loss
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384 56638

Q:

A Shepherd had n goats in the year 2000. In 2001 the no.of goats increased by 40% . In 2002 the no. of goats declined to 70%. In 2003 the no. of goats grew by 30%. In 2004, he sold 10% goats, then he had only 34,398 goats. The percentage increase of the no.of goats in this duration was:

A) 14.66%	B) 16.66%
C) 20%	D) 33.33%

Answer & Explanation Answer: A) 14.66%

Explanation:

There is no need to use the no of goats i.e (34,398). let initially thete be 1000 goats then

1000 -----> 1400 -----> 980 -----> 1274 ----->1146.6

Thus the % increase = (1146.6-1000)/100 x 100= 14.66%

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Filed Under: Percentage
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7 8552

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