A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest per annum been 2% more, how much more interest would it have earned?a)Rs. 35b)Rs. 350c)Rs. 245d)cannot be determinedCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Solution:

Let's assume the principal amount as P and the rate of interest as R.

Given:
Principal amount = P
Rate of interest = R
Time = 7 years
Simple interest earned = Rs. 1750

Using the formula for simple interest:
Simple Interest = (Principal * Rate * Time)/100

1. Calculation of Principal amount:
1750 = (P * R * 7)/100
1750 * 100 = 7PR
175000 = 7PR
PR = 25000

2. Calculation of new rate of interest:
Let's assume the new rate of interest as R1.
According to the question, the new rate of interest is 2% more than the original rate of interest.
R1 = R + (2/100) * R
R1 = R + 0.02R
R1 = 1.02R

3. Calculation of new interest earned:
New interest = (Principal * New rate * Time)/100
New interest = (P * R1 * 7)/100
New interest = (P * 1.02R * 7)/100
New interest = (1.02PR * 7)/100
New interest = (1.02 * 25000 * 7)/100
New interest = (1.02 * 250 * 7)
New interest = 1785

4. Calculation of the difference in interest:
Difference in interest = New interest - Old interest
Difference in interest = 1785 - 1750
Difference in interest = 35

Therefore, if the interest per annum had been 2% more, the amount would have earned an additional interest of Rs. 35. Hence, the correct answer is option D.

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