Question : A sum of money at simple interest amounts to Rs. 6,000 in 4 years and to Rs. 6,750 in 7 years at the same rate percent per annum of interest. The sum (in Rs.) is:
Option 1: 5,100
Option 2: 4,800
Option 3: 4,000
Option 4: 5,000
Correct Answer: 5,000
Solution :
The difference between the amounts after 7 years and 4 years = Rs. 6750 – Rs. 6000 = Rs. 750, is the simple interest for 3 years.
Therefore, the simple interest for 1 year = $\frac{750}{ 3}$ = Rs. 250
The simple interest for 4 years = Rs. 250 × 4 = Rs. 1000
We know that the amount (Rs. 6000) is the sum of the principal and the simple interest for 4 years.
Therefore, the principal = Rs. 6000 – Rs. 1000 = Rs. 5000
Hence, the correct answer is 5,000.
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