Question

If the sum of Rs. 80 amounts to Rs.140 in a time period of 4 years, what will Rs. 96 amount to in a time period of 10 years at the same rate of interest per annum?
(a) Rs. 276
(b) Rs. 306
(c) Rs. 386
(d) Rs. 300

Answer 1

Hint: We start solving the problem by recalling the concepts of interest and principal amounts. We assume the rate of interest per annum as x% and start finding the value of interest that is to be added every year. We add this interest to Rs. 80 and solve for the value of x by using the final amount. Now, we use this rate of interest and find the interest amount every year and add them later to get the required value.

Complete step by step answer:
According to the problem, we have given that the sum of Rs. 80 amounts to Rs. 140 in a time period of 4 years. We need to find the value that Rs. 96 amounts to in a time period of 10 years with the same rate of interest per annum.
Let us assume the interest is simple. We know that every year, Interest amount is added to the actual principal amount. Let us assume the rate of interest per annum be x% and the interest amount per year be I.
We have principal amount Rs. 80 and interest amount I is added to Rs. 80 each year for four years to get the total amount to Rs. 140.
So, we have $Rs.140=Rs.80+4I$ ---(1).
We know that the interest amount is calculated by taking % to the principal amount.
So, Interest $I=x\%\text{ of Rs}\text{.80}$.
$\Rightarrow I=\dfrac{x}{100}\times \text{80}$.
$\Rightarrow I=x\times \text{0}\text{.8}$.
$\Rightarrow I=0.8x$ ---(2).
Let us substitute equation (2) in equation (1).
$\Rightarrow Rs.140=Rs.80+4\left( 0.8x \right)$.
$\Rightarrow Rs.140=Rs.80+3.2x$.
$\Rightarrow 3.2x=140-80$.
$\Rightarrow 3.2x=60$.
$\Rightarrow x=\dfrac{60}{3.2}$.
$\Rightarrow x=\dfrac{75}{4}$.
We have got the rate of interest per annum as $\dfrac{75}{4}%$. We use this interest to find the amount that Rs. 96 increases to in a period of 10 years. Let us assume the new interest amount that is added to the principal amount every year will be ${{I}_{1}}$.
So, we have ${{I}_{1}}=\dfrac{75}{4}\%\text{ of Rs}.96$.
$\Rightarrow {{I}_{1}}=\dfrac{\dfrac{75}{4}}{100}\times 96$.
$\Rightarrow {{I}_{1}}=\dfrac{75}{400}\times 96$.
$\Rightarrow {{I}_{1}}=\dfrac{7200}{400}$.
$\Rightarrow {{I}_{1}}=Rs.18$.
These interests ${{I}_{1}}$ will be added to principal amount Rs. 96 every year for 10 years.
So, we have a new amount(N) = $96+10\left( 18 \right)$.
$\Rightarrow N=96+180$.
$\Rightarrow N=Rs.276$.
We have found that the principal amount Rs. 96 amounts to Rs. 276 in a time period of 10 years.

So, the correct answer is “Option A”.

Note: We should not multiply the percentage directly to any number as we know that percentage is defined as the parts per 100. In this problem, we have assumed the rate of interest is simple. Whenever we find a problem without mentioning what type is the rate of interest, we take it as simple unless it is mentioned. In compound interest, we take interest for the total amount we get after one year.