Question : Dalajit lent Rs. 10800 to Jaabir for 3 years and Rs. 7500 to Kabir for 2 years on simple interest at the same rate of interest and received Rs.1422 in all from both of them as interest. The rate of interest per year is:
Option 1: 3.5 percent
Option 2: 4 percent
Option 3: 3 percent
Option 4: 4.5 percent
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Correct Answer: 3 percent
Solution :
Let's assume the rate of interest per annum as $r$.
Calculating Interest for Jaabir:
The principal amount lent to Jaabir = Rs. 10,800
Time period = 3 years
Rate of interest per annum = $r$
Using the formula for simple interest,
Simple interest = $\frac{\text{Principal×Rate×Time}}{100}$
The interest received from Jaabir can be calculated as interest from Jaabir = $\frac{(10800 ×3 × r)} {100}$
Calculating Interest for Kabir:
The principal amount lent to Kabir = Rs. 7,500
Time period = 2 years
Rate of interest per annum = $r$
The interest received from Kabir can be calculated as interest from Kabir = $\frac{(7500 ×2 × r)} {100}$
Total Interest Received:
The total interest received from both Jaabir and Kabir is given as Rs.1,422.
So, we can write the equation: Interest from Jaabir + Interest from Kabir = 1,422
⇒ $\frac{(10800 ×3 × r)} {100}+\frac{(7500 ×2 × r)} {100}=1422$
⇒ $\frac{32400r+15000r}{100}=1422$
⇒ $r=\frac{1422}{474}$
⇒ $r=3$%
Hence, the correct answer is 3%.
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