Question

Mr. Thomas invested an amount of Rs. 13,900 divided into two different schemes A and B at the simple interest rate of 14 % p.a. and 11 % respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?
(a). Rs. 6400
(b). Rs. 6500
(c). Rs. 7200
(d). Rs. 7500

Answer 1

Hint: Recall the formula for the simple interest which is \[SI = \dfrac{{PNR}}{{100}}\]. Determine the amount invested in scheme A and subtract it from the total amount to get the amount invested in scheme B.

Complete step-by-step answer:
Mr. Thomas invested an amount of Rs. 13,900 into two schemes A and B.
Let the amount invested into scheme A be x.
Then the amount invested in scheme B is 13,900 – x.
We know the formula for the simple interest for a principal amount P invested for N years at the rate of R % p.a. is given as follows:
\[SI = \dfrac{{PNR}}{{100}}\]
It is given that the total amount of simple interest earned at a rate of 14 % p.a. is Rs. 3508. Then, we have:
\[3508 = \dfrac{{x \times 2 \times 14}}{{100}} + \dfrac{{(13,900 - x) \times 2 \times 11}}{{100}}\]
\[350800 = 28x + 22(13,900 - x)\]
Simplifying, we have:
\[350800 = 28x + 305800 - 22x\]
\[6x = 350800 - 305800\]
\[6x = 45000\]
Solving for x, we have:
\[x = \dfrac{{45000}}{6}\]
\[x = 7500\]
Hence, the amount invested in scheme A is Rs. 7500.
The amount invested in scheme B is given by:
\[13900 - x = 13900 - 7500\]
\[13900 - x = 6400\]
Hence, the amount invested in scheme B is Rs. 6400.

Note: The total interest amount is Rs. 3508 and it is not just the interest amount gained in scheme A. Hence, you must use the simple interest formula for both scheme A and scheme B and add them to get Rs. 3508.