A sum of ₹ 8000 on simple interest becomes ₹ 9600 in 5 years at a certain rate…
2025
A sum of ₹ 8000 on simple interest becomes ₹ 9600 in 5 years at a certain rate of interest. If the rate of interest becomes double of itself, then the same sum in 6 years will become:-
- A.
₹ 11640
- B.
₹ 12680
- C.
₹ 11840
- D.
₹ 14240
Attempted by 3 students.
Show answer & explanation
Correct answer: C
Simple interest is calculated as SI = (P × R × T) / 100, and the amount is Amount = P + SI. When only the amount after a certain time is given, the unknown rate R can first be found from the known data, and then re-applied for the new conditions asked in the question.
The original data gives SI = ₹9600 − ₹8000 = ₹1600 on a principal of ₹8000 over 5 years. Using SI = (P × R × T)/100: R = (1600 × 100) / (8000 × 5) = 4% per annum.
The question states that the rate becomes double of itself, so the new rate is R' = 2 × 4% = 8% per annum.
The new interest is worked out on the same ₹8000 principal for the new 6-year period: SI' = (8000 × 8 × 6) / 100 = ₹3840.
The new amount is Principal + New interest = ₹8000 + ₹3840 = ₹11840.
As a check, the original rate of 4% gives an annual interest of ₹320, so ₹320 × 5 = ₹1600, which correctly reproduces the given amount of ₹9600 after 5 years — confirming R = 4% is right before it is doubled and reapplied.