A certain sum amounts to ₹ 756 in 2 years and to ₹ 873 is \(3\frac{1}{2}\) years at a certain rate of simple interest. The rate of interest per annum is:
1. 11%
2. 13%
3. 10%
4. 12%
A certain sum amounts to ₹ 756 in 2 years and to ₹ 873 is \(3\frac{1}{2}\) years at a certain rate of simple interest. The rate of interest per annum is:
1. 11%
2. 13%
3. 10%
4. 12%
1. 11%
2. 13%
3. 10%
4. 12%
Correct Answer – Option 2 : 13%
Given:
First Amount = Rs. 756
Time = 2 years
Second Amount = Rs. 873
Time = \(3\frac{1}{2}\) years = 7/2 years
Formula Used:
Simple Interest = Amount – Principal
Simple Interest = (Principal × Rate × time)/100
Calculation:
Let the principal be ‘x’.
Simple Interest = Amount – Principal
⇒ 756 – x
Simple Interest = (Principal × Rate × time)/100
Rate = (S.I × 100)/ P × t
⇒ Rate = ((756 – x) × 100)/ (x × 2)
Simple Interest = Amount – Principal
⇒ 873 – x
Rate = ((873 – x) × 100)/ (x × 7/2)
According to the Question,
((756 – x) × 100)/ (x × 2) = ((873 – x) × 100)/ (x × 7/2)
⇒ ((756 – x) × 100)/2 = 2((873 –- x) × 100)/ 7
⇒ 7((756 – x) × 100)= 4((873 – x) × 100)
⇒ 529200 – 700x = 349200 – 400x
⇒ 300x = 180000
⇒ x = 600
Rate = ((756 – x) × 100)/ (x × 2)
⇒ ((756 – 600) × 100)/(600 × 2)
⇒ (156 × 100)/ 1200
⇒ 13%
∴ The rate of interest per annum is 13%.