A person invested a certain amount in two different schemes A and B at the rate of interest 10% and 15% respectively. If the amount invested in scheme B was two-third of the amount invested in scheme A and the total interest in one year was Rs.2400, what was the amount invested in scheme B?
Question
A person invested a certain amount in two different schemes A and B at the rate of interest 10% and 15% respectively. If the amount invested in scheme B was two-third of the amount invested in scheme A and the total interest in one year was Rs.2400, what was the amount invested in scheme B?
Solution
Let's denote the amount invested in scheme A as x.
According to the problem, the amount invested in scheme B is two-thirds of the amount invested in scheme A. So, the amount invested in scheme B is 2x/3.
The interest for scheme A for one year is 10% of x, which is 0.10x.
The interest for scheme B for one year is 15% of 2x/3, which is 0.15 * 2x/3 = 0.10x.
The total interest from both schemes for one year is Rs.2400. So, we can set up the following equation:
0.10x (from scheme A) + 0.10x (from scheme B) = 2400
Combining like terms gives:
0.20x = 2400
Solving for x gives:
x = 2400 / 0.20 = Rs.12000
So, the amount invested in scheme A is Rs.12000.
The amount invested in scheme B is two-thirds of this, which is 2/3 * 12000 = Rs.8000.
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