A certain sum of money amounts to ₹1,860 in 2 years and to ₹2,130 in 3
2
1
years at simple interest. Find the sum and the rate of interest, respectively.
- A₹1,500,12%
- B₹1,200,10%
- C₹1,500,15%
- D₹1,200,12%
Solution & Step-by-step Explanation
Let the principal (sum) be P and the rate of interest be R%.
Amount in 2 years=P+SI for 2 years=₹1,860
Amount in 3.5 years=P+SI for 3.5 years=₹2,130
Subtracting the first equation from the second equation:
SI for (3.5−2) years=2,130−1,860
SI for 1.5 years=₹270
SI for 1 year=
1.5
270
=₹180
Now, calculate the SI for 2 years:
SI for 2 years=180×2=₹360
Find the principal (P):
P=Amount in 2 years−SI for 2 years
P=1,860−360=₹1,500
Now, find the rate of interest (R):
SI=
100
P×R×T
180=
100
1,500×R×1
180=15×R
R=
15
180
=12%
Hence, the sum is ₹1,500 and the rate of interest is 12%.
Amount in 2 years=P+SI for 2 years=₹1,860
Amount in 3.5 years=P+SI for 3.5 years=₹2,130
Subtracting the first equation from the second equation:
SI for (3.5−2) years=2,130−1,860
SI for 1.5 years=₹270
SI for 1 year=
1.5
270
=₹180
Now, calculate the SI for 2 years:
SI for 2 years=180×2=₹360
Find the principal (P):
P=Amount in 2 years−SI for 2 years
P=1,860−360=₹1,500
Now, find the rate of interest (R):
SI=
100
P×R×T
180=
100
1,500×R×1
180=15×R
R=
15
180
=12%
Hence, the sum is ₹1,500 and the rate of interest is 12%.