A certain sum amounts to ₹15,179 in 8
2
1
years at 9% p.a. simple interest. What will be the simple interest (in ₹) on the same sum in 5
2
1
years at the same rate of interest?
- A4,158
- B4,257
- C4,356
- D4,455
Solution & Step-by-step Explanation
Let the Principal sum be P.
For the first case:
Time (T
1
) = 8
2
1
years=
2
17
years
Rate (R) = 9% p.a.
Total simple interest percentage for T
1
years:
SI
1
%=R×T
1
=9×
2
17
=
2
153
%=76.5%
The total amount becomes:
Amount=P+SI
1
=P×(100%+76.5%)=P×176.5%
Given that Amount = ₹15,179:
1.765×P=15179
P=
1.765
15179
=8600
For the second case:
Time (T
2
) = 5
2
1
years=
2
11
years
Rate (R) = 9% p.a.
The required Simple Interest (SI
2
) is:
SI
2
=
100
P×R×T
2
SI
2
=
100
8600×9×
2
11
SI
2
=43×9×11=387×11=4257
For the first case:
Time (T
1
) = 8
2
1
years=
2
17
years
Rate (R) = 9% p.a.
Total simple interest percentage for T
1
years:
SI
1
%=R×T
1
=9×
2
17
=
2
153
%=76.5%
The total amount becomes:
Amount=P+SI
1
=P×(100%+76.5%)=P×176.5%
Given that Amount = ₹15,179:
1.765×P=15179
P=
1.765
15179
=8600
For the second case:
Time (T
2
) = 5
2
1
years=
2
11
years
Rate (R) = 9% p.a.
The required Simple Interest (SI
2
) is:
SI
2
=
100
P×R×T
2
SI
2
=
100
8600×9×
2
11
SI
2
=43×9×11=387×11=4257