The simple interest on a certain sum for 10 years at 9.5% p.a. is ₹ 2,832 less…
2023
The simple interest on a certain sum for 10 years at 9.5% p.a. is ₹ 2,832 less than the amount of the same sum for 3½ years at 7% p.a., simple interest. The sum (in ₹) is:
- A.
9200
- B.
9500
- C.
9600
- D.
9800
Attempted by 19 students.
Show answer & explanation
Correct answer: C
Let the principal be P.
Simple interest for 10 years at 9.5% = P × 9.5% × 10 = 0.95P.
Simple interest for 3½ years at 7% = P × 7% × 3.5 = 0.245P, so the amount for 3½ years = P + 0.245P = 1.245P.
Given that the 10-year simple interest is ₹2,832 less than that amount, set up the equation: 0.95P = 1.245P − 2832.
Rearrange: 1.245P − 0.95P = 2832 ⇒ 0.295P = 2832 ⇒ P = 2832 ÷ 0.295 = 9600.
Therefore the sum is ₹9600.