Question

A sum was put at simple interest at a certain rate for 4 years. Had it been put at 2% higher rate, it would have fetched Rs 56 more. Find the sum.
Rs 680
Rs 700
Rs 720
None of these

Answer 1

Hint: In this question it is given that a sum was put at simple interest at a certain rate for 4 years. Had it been put at $2\%$ higher rate, it would have fetched Rs 56 more. We have to find the sum. So to find the solution we need to know the expression of simple interest(S.I),
$$\text{S.I} =\dfrac{p\times r\times t}{100}$$.......(1)
Where, p = initial principal amount
r = annual interest rate
t = time (in years)
So by using the above formula we will find the two different values of simple interests for the given data, and since their difference is 56 so by that information we will get our required solution.

Complete step-by-step solution:
Let us consider the initial principal amount (sum) is Rs $x$.
Here it is given that a sum is put at simple interest for 4 years, therefore we can say that the value of t is 4, i.e, t = 4.
Let us also consider the annual interest rate is r %.
Therefore by the formula (1) we can say that,
$$\text{S.I} =\dfrac{x\times r\times 4}{100}$$
  $$\text{S.I} =\dfrac{x\times r}{25}$$
  $$\text{S.I} =\dfrac{xr}{25}$$...........(2)
Now if we increase the rate by 2 % then,
$R = r \% + \text{increase}$
    = $r \% + 2 \% $
    =$ (r + 2) \% $
Therefore the new simple interest (when we put the same amount of money for 4 years)
$$\text{S.I}_{1} =\dfrac{x\times R\times 4}{100}$$
  $$=\dfrac{x\times \left( r+2\right) \times 4}{100}$$
  $$=\dfrac{x\times \left( r+2\right) }{25}$$
  $$=\dfrac{xr+2x}{25}$$
  $$=\dfrac{xr}{25} +\dfrac{2x}{25}$$.........(3)
Now it is given that the new S.I is 56 more that the previous one,
Therefore we can write the difference between them is 56,
i.e,$$\text{S.I}_{1} -\text{S.I} =56$$
$$\Rightarrow \left( \dfrac{xr}{25} +\dfrac{2x}{25} \right) -\dfrac{xr}{25} =56$$ [from equation (2) and (3)]
$$\Rightarrow \dfrac{xr}{25} +\dfrac{2x}{25} -\dfrac{xr}{25} =56$$
$$\Rightarrow \dfrac{2x}{25} =56$$
$$\Rightarrow 2x=56\times 25$$
$$\Rightarrow 2x=1400$$
$$\Rightarrow x=\dfrac{1400}{2}$$
$$\Rightarrow x=700$$
Therefore the sum(principle amount) is Rs 700.
Hence the correct option is option B.

Note: Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.