The difference between the simple interest on a sum of money for 3
2
1
years at the rate of 12% per annum and simple interest on the same sum of money for 4
2
1
years at 10% per annum is ₹360. Find the sum (in ₹).
- A12,000
- B14,000
- C10,000
- D16,000
Solution & Step-by-step Explanation
Let the principal sum of money be P.
Case 1:
Time T
1
=3
2
1
=
2
7
years
Rate R
1
=12%
Effective interest rate =
2
7
×12%=42%
Case 2:
Time T
2
=4
2
1
=
2
9
years
Rate R
2
=10%
Effective interest rate =
2
9
×10%=45%
The difference between the simple interests is given as ₹360:
Difference in effective percentage=45%−42%=3%
3% of P=360
100
3
×P=360
P=
3
360×100
=12000
Thus, the sum is ₹12,000.
Case 1:
Time T
1
=3
2
1
=
2
7
years
Rate R
1
=12%
Effective interest rate =
2
7
×12%=42%
Case 2:
Time T
2
=4
2
1
=
2
9
years
Rate R
2
=10%
Effective interest rate =
2
9
×10%=45%
The difference between the simple interests is given as ₹360:
Difference in effective percentage=45%−42%=3%
3% of P=360
100
3
×P=360
P=
3
360×100
=12000
Thus, the sum is ₹12,000.