Discussion of Question with ID = 084 under Simple-Interest

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Question

A certain amount is split into two parts. The first part is invested at 8% p.a. and the second at 4% p.a. What is the total amount if the total simple interest at the end of 3 years is Rs. 312, and if the amount invested at 8% is Rs. 1800?

A

Rs. 800.

B

Rs. 900.

C

Rs. 700.

D

Rs. 1000.

Soln.
Ans: a

Let the amount x be invested at r1% and remaining (P - x) at r2%, and let the sum of interests be I. Then, I = ${x × r_1 × 3}/100$ + ${(P - x) × r_2 × 3}/100$, which simplifies to 100I = 3 × ($x × (r_1 - r_2) + P × r_2$). Putting r1 = 8, r2 = 4, x = 1800, I = 312, we get P = Rs. 800.

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