# Discussion of Question with ID = 024 under Simple-Interest

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### Question

A certain amount is split into two parts. The first part is invested at 10% p.a. and the second at 5% p.a. What is the total amount if the total simple interest at the end of 2 years is Rs. 240, and if the amount invested at 10% is Rs. 1400?

A

Rs. 1000.

B

Rs. 1100.

C

Rs. 900.

D

Rs. 1200.

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 × 2}/100\$ + \${(P - x) × r_2 × 2}/100\$, which simplifies to 100I = 2 × (\$x × (r_1 - r_2) + P × r_2\$). Putting r1 = 10, r2 = 5, x = 1400, I = 240, we get P = Rs. 1000.