Question

Prakash lent altogether Rs. 6000 to Anima and Elina for 2 years. Anima agrees to pay simple interest at 10% per annum and Elina agrees to pay compound interest at the rate of 8% p.a. If Elina paid Rs. 50 more than Anima as the interest, find how much did he lend to each.

a) Prakash lent Rs. 2000 to Anima and Rs. 4000 to Elina
b) Prakash lent Rs. 2500 to Anima and Rs. 3500 to Elina
c) Prakash lent Rs. 3000 to Anima and Rs. 3000 to Elina
d) Prakash lent Rs. 3500 to Anima and Rs. 2500 to Elina

Answer 1

Prakash lent Rs. 3000 to both Anima and Elina.

Step-by-step explanation:

To solve this problem, we can set up two equations. Let's represent the amount lent to Anima as 'x' and the amount lent to Elina as 'y'.

According to the given information:

For Anima: Simple Interest = Principal (x) × Rate (10%) × Time (2) = 0.1x × 2 = 0.2x

For Elina: Compound Interest = Principal (y) × (1 + Rate (8%))^Time (2) - Principal (y) = y × (1.08^2) - y = 1.1664y - y = 0.1664y

We are also given that the compound interest paid by Elina is Rs. 50 more than the simple interest paid by Anima:

0.1664y = 0.2x + 50

Now, we can set up a system of equations:

0.1664y = 0.2x + 50

x + y = 6000

Solving these equations, we find that x = 3000 and y = 3000.

Therefore, Prakash lent Rs. 3000 to both Anima and Elina.