Mr Gogia invested an amount of ₹13,900 divided into two different schemes A and B at the simple interest rate of 14%p.a. and 11%p.a., respectively. If the total amount of simple interest earned in 2 years is ₹3,508, what was the amount invested in scheme B?
- A₹7,200
- B₹6,500
- C₹6,400
- D₹7,500
Solution & Step-by-step Explanation
Let the amount invested in scheme B be ₹y.
Then, the amount invested in scheme A is ₹(13900−y).
The total interest earned in 2 years is ₹3,508, so the interest earned in 1 year is:
Interest in 1 year=
2
3508
=₹1754
The interest equation for 1 year is:
14% of (13900−y)+11% of y=1754
100
14
(13900−y)+
100
11
y=1754
14×13900−14y+11y=175400
194600−3y=175400
3y=194600−175400
3y=19200
y=
3
19200
=6400
Thus, the amount invested in scheme B was ₹6,400.
Then, the amount invested in scheme A is ₹(13900−y).
The total interest earned in 2 years is ₹3,508, so the interest earned in 1 year is:
Interest in 1 year=
2
3508
=₹1754
The interest equation for 1 year is:
14% of (13900−y)+11% of y=1754
100
14
(13900−y)+
100
11
y=1754
14×13900−14y+11y=175400
194600−3y=175400
3y=194600−175400
3y=19200
y=
3
19200
=6400
Thus, the amount invested in scheme B was ₹6,400.