Question 7 Single Cholce An amount of INR 1200 is obtained by lending INR X at 10% simple interest for 2 years. And an amount of INR 2400 is obtained by lending an amount Y at 12% simple interest for 5 years. What is the interest accrued if (X+Y) is lent at a rate of 8% interest for 1 year? Options 550 O 290 O 200 320
Answers
Given: An amount of INR 1200 is obtained by lending INR X at 10% simple interest for 2 years.
An amount of INR 2400 is obtained by lending an amount Y at 12% simple interest for 5 years.
To find: The interest accrued if (X+Y) is lent at a rate of 8% interest for 1 year
Solution: For the first case,
Amount = INR 1200, P = INR X, r = 10%, T = 2 years
Accordingly, Amount = P(1 + rT/100)
⇒ 1200 = X(1 + (10 × 2)/100)
⇒ 1200 = X(1 + 1/5)
⇒ 1200 = X × 6/5
⇒ X = 1200 × 5/6
⇒ X = INR 1000
For the second case,
Amount = INR 2400, P = INR Y, r = 12%, T = 5 years
Accordingly,
2400 = Y(1 + (12 × 5)/100)
⇒ 2400 = Y(1 + 3/5)
⇒ 2400 = Y × 8/5
⇒ Y = 2400 × 5/8
⇒ Y = INR 1500
Now, P = (X + Y) = INR (1000 + 1500) = INR 2500, r = 8%, T = 1 year
Hence, the interest accrued = (P × r × T)/100
= (2500 × 8 × 1)/100
= 25 × 8
= INR 200
Answer: Option 200