GRE Questions and Answers with Explanation

Q:

A father left a will of Rs.35 lakhs between his two daughters aged 8.5 and 16 such that they may get equal amounts when each of them reach the age of 21 years. The original amount of Rs.35 lakhs has been instructed to be invested at 10% p.a. simple interest. How much did the elder daughter get at the time of the will?

A) 17.5 lakhs	B) 21 lakhs
C) 15 lakhs	D) 20 lakhs

Answer & Explanation Answer: B) 21 lakhs

Explanation:

Let Rs.x be the amount that the elder daughter got at the time of the will. Therefore, the younger daughter got (3,500,000 - x).

The elder daughter’s money earns interest for (21 - 16) = 5 years @ 10% p.a simple interest.

The younger daughter’s money earns interest for (21 - 8.5) = 12.5 years @ 10% p.a simple interest.

As the sum of money that each of the daughters get when they are 21 is the same,

$x + \frac{5 * 10 * x}{100} = (3, 500, 000 - x) + \frac{12.5 * 10 * (3, 500, 000 - x)}{100}$

$x + \frac{50}{x} = 3, 500, 000 - x + \frac{125}{100} * 3, 500, 000 - \frac{125 x}{100}$

$2 x + \frac{50 x}{100} + \frac{125 x}{100} = 3, 500, 000 * (1 + \frac{5}{4})$

$\frac{200 x + 50 x + 125 x}{100} = \frac{9}{4} * (3, 500, 000)$

=> $x = 2, 100, 000 = 21 l a k h s$

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Q:

A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?

A) Rs.35	B) Rs.245
C) Rs.350	D) cannot be determined

Answer & Explanation Answer: D) cannot be determined

Explanation:

We need to know the S.I, principal and time to find the rate. Since the principal is not given, so data is inadequate.

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Q:

What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?

A) 1:3	B) 1:4
C) 2:3	D) data is inadequate

Answer & Explanation Answer: C) 2:3

Explanation:

Let the principal be P and rate of interest be R%.

Required ratio = $[(\frac{\frac{P * R * 6}{100}}{\frac{P * R * 9}{100}})] = \frac{6 P R}{9 P R} = \frac{6}{9} = \frac{2}{3}$

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Q:

A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?

A) 3.46%	B) 4.5%
C) 5%	D) 6%

Answer & Explanation Answer: A) 3.46%

Explanation:

Let the original rate be R%. Then, new rate = (2R)%.

Note: Here, original rate is for 1 year(s); the new rate is for only 4 months i.e.1/3 year(s).

$(\frac{725 * R * 1}{100}) + (\frac{362.50 * 2 R * 1}{100 * 3}) = 33.50$

=> (2175 + 725) R = 33.50 x 100 x 3

=> (2175 + 725) R = 10050

=> (2900)R = 10050

=> $R = \frac{10050}{2900} = 3.46$

Original rate = 3.46%

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Q:

A Rent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:

A) 5%	B) 7%
C) 7.5%	D) 10%

Answer & Explanation Answer: D) 10%

Explanation:

Let the rate be R% p.a.

Then, $\frac{5000 \times r \times 2}{100} + \frac{3000 \times r \times 4}{100} = 2200$

Rate = 10%

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Q:

An automobile financier claims to be lending money at simple interest, but he includesthe interest every six months for calculating the principal. If he is charging an interest of10%, the effective rate of interest becomes:

A) 10%	B) 10.25%
C) 10.5%	D) none of these

Answer & Explanation Answer: B) 10.25%

Explanation:

Let the sum be Rs. 100. Then,

S.I. for first 6 months = Rs.[ (100 x 10 x 1)/(100 x 2) ]= Rs.5

S.I. for last 6 months =Rs.[(102 x 10 x 1)/(100 x 2) ] = Rs.5.25

So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25

Effective rate = (110.25 - 100) = 10.25%

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Q:

A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest

A) 3%	B) 4%
C) 5%	D) 6%

Answer & Explanation Answer: D) 6%

Explanation:

S.I. = Rs. (15500 - 12500) = Rs. 3000.

Rate = $(\frac{100 * 3000}{12500 * 4})$ % = 6%

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Q:

Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of Interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?

A) 3.6	B) 6
C) 18	D) cannot be determined

Answer & Explanation Answer: B) 6

Explanation:

Let rate = R% and time = R years.

Then, $(\frac{1200 \times R \times R}{100}) = 432$

$12 R^{2} = 432$

=> R = 6.

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