Mr. Thomas invested an amount of Rs. 13,900 divided in 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 be Rs. 3508, what was the amount invested in Scheme B?
Question
Mr. Thomas invested an amount of Rs. 13,900 divided in 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 be Rs. 3508, what was the amount invested in Scheme B?
Solution
Let's denote the amount invested in Scheme A as 'a' and the amount invested in Scheme B as 'b'.
Given that the total amount invested is Rs. 13,900, we can write this as:
a + b = 13,900 ---- (equation 1)
We also know that the total interest earned from both schemes after 2 years is Rs. 3508.
The interest from Scheme A (at 14% per annum) would be (14/100)a2 and the interest from Scheme B (at 11% per annum) would be (11/100)b2.
So, we can write this as:
(14/100)a2 + (11/100)b2 = 3508 ---- (equation 2)
We can simplify equation 2 to:
0.28a + 0.22b = 3508 ---- (equation 3)
Now we have a system of two equations, and we can solve them to find the values of 'a' and 'b'.
Let's multiply equation 1 by 0.22:
0.22a + 0.22b = 3068 ---- (equation 4)
Now, subtract equation 4 from equation 3:
0.06a = 440
Solving for 'a' gives:
a = 440 / 0.06 = 7333.33
Substitute a = 7333.33 in equation 1:
7333.33 + b = 13900
Solving for 'b' gives:
b = 13900 - 7333.33 = 6566.67
So, Mr. Thomas invested approximately Rs. 6567 in Scheme B.
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