Question

The simple interest on a certain sum for 8 months at 4% simple interest is Rs.129 less than the simple interest on the same sum for 15 months at 5% per annum. Then the sum is
A. Rs.3,400
B. Rs.3,500
C. Rs.3,600
D. Rs.3,700

Answer 1

Hint: Let the sum be x. Change given months into years by dividing it with 12. Find the simple interest on x for 8 months at 4% interest, say a and the simple interest on the same x for 15 months at 5% interest, say b. a is Rs. 129 less than b. Find simple interest using the below formula.
Formula used:
Simple interest can be calculated by $ \dfrac{{PTR}}{{100}} $ , where P is the principal sum, T is the time period and R is the rate of interest.

Complete step-by-step answer:
Let the given sum be x.
12 months is equal to 1 year then 8 months is equal to $ \dfrac{8}{{12}} = \dfrac{2}{3} $ years and 15 months is equal to $ \dfrac{{15}}{{12}} = 1.25 $ years.
Simple interest on the sum x for 8 months (0.75 years) at 4% interest is a.
 $ a = \dfrac{{PTR}}{{100}} = \dfrac{{x \times \left( {\dfrac{2}{3}} \right) \times 4}}{{100}} = \dfrac{{2x}}{{75}} $
 Simple interest on the sum x for 15 months (1.25 years) at 5% interest is b.
 $ b = \dfrac{{PTR}}{{100}} = \dfrac{{x \times \left( {1.25} \right) \times 5}}{{100}} = \dfrac{{6.25x}}{{100}} $
It is also given a is Rs. 129 less than b.
This gives $ a = b - 129 $
On substituting the values of a and b in the above equation, we get
 $ \Rightarrow \dfrac{{2x}}{{75}} = \dfrac{{6.25x}}{{100}} - 129 $
Putting the terms containing ‘x’ one side, we get
 $ \Rightarrow \dfrac{{6.25x}}{{100}} - \dfrac{{2x}}{{75}} = 129 $
On taking LCM in LHS and multiplying, we get
 $ \Rightarrow \dfrac{{18.75x - 8x}}{{300}} = 129 $ (LCM of 100 and 75 is 300)
 $ \Rightarrow 10.75x = 129 \times 300 = 38700 $
 $ \therefore x = \dfrac{{38700}}{{10.75}} = Rs.3600 $
Therefore, the sum is $ Rs.3,600 $ .
So, the correct answer is “Option C”.

Note: The interest can be either simple or compound. In simple interest, the interest amount does not change till the end of the return period whereas in compound interest, the interest amount constantly changes as the interest is imposed on the principal amount plus the previous accumulated interest combined. Compound interest is much greater than Simple interest.