Question

A sum of money at simple interest amounts to Rs.815 in 3 years and to Rs.854 in 4 years. The sum is
A. Rs.650
B. Rs.698
C. Rs.690
D. Rs.700

Answer 1

Hint: Given that, a sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. Therefore, simple interest in one year is the difference between the given amounts. So simple interest for three years will be thrice the interest in one year. Now, amount = principal + interest. So initial sum = amount after 3 years – interest for 3 years.

Formula used: Amount = principle + simple interest

Complete step-by-step solution:
Given that a sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years.
So, amount after 4 years = amount after 3 years + simple interest in one year
Therefore, simple interest in one year $ = 854 - 815 = {\text{Rs}}{\text{. }}39$
So simple interest for 3 years will be $ = 39 \times 3 = 117$ Rs.
The initial sum of money amounts to be Rs. 815 in three years with simple interest. Therefore the principle is = amount - interest$ = 815 - 117 = 698$ Rs.
Therefore, the sum is $Rs. 698$

Hence, the correct answer is option (B).

Note: Note the few important formulae of simple and compound interest.
Amount = principle + simple interest
${\text{simple interest = }}\dfrac{{P \times r \times t}}{{100}}$ , where principal=P , rate of simple interest= r% per annum, time = t years
If principal=P , rate of compound interest=R% per annum, time =n years, then
Amount= $P{\left( {1 + \dfrac{R}{{100}}} \right)^n}$, when interest is compounded annually
Amount= $P{\left( {1 + \dfrac{{\dfrac{R}{2}}}{{100}}} \right)^{2n}}$, when interest is compounded half-yearly
Amount= $P{\left( {1 + \dfrac{{\dfrac{R}{4}}}{{100}}} \right)^{4n}}$, when interest is compounded quarterly