Question

Rs.\(177\frac{7}{9}\) amounts to Rs. 400 in 2 years at compound interest. If the same amount on the same rate at simple interest for 3 years, then find the simple interest.(correct to one decimal place)
1. Rs. 386.6
2. Rs. 250.4
3. Rs. 266.6
4. Rs. 280.7

Answer 1

Correct Answer - Option 3 : Rs. 266.6

Given:
Principal (P) = Rs. (177 + 7/9) = 1600/9
Amount (A) = Rs. 400
Time (T) = 2 years

Concept used:
Amount = P(1 + R/100)T
S.I. = (P × R × T)/100

Calculation:
Let the rate of interest per annum be R.
400 = 1600/9(1 + R/100)²
⇒ 400/(1600/9) = (1 + R/100)²
⇒ √(400 × 9/1600) = 1 + R/100
⇒ √3600/1600 = 1 + R/100
⇒ 6/4 = 1 + R/100
⇒ 3/2 – 1 = R/100
⇒ 1/2 = R/100
S.I. = 1600/9 × 1/2 × 3
⇒ 4800/18
⇒ 266.6
∴ The simple interest is Rs. 266.6.