Gaurav invested Rs. ‘x’ in a scheme offering 10% compound interest for three years. Prem invested Rs. 18,000 in a scheme offering 15% simple interest for four years. Find the interest earned by Gaurav if the interest earned by Prem is Rs. ‘2x – 1,200’.
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Correct answer: D
Explanation
Given:
Gaurav's investment = Rs. x
Rate = 10%
Time = 3 years (compound interest)
Prem's investment = Rs. 18,000
Rate = 15%
Time = 4 years (simple interest)
Prem's interest = 2x − 1200
By formula:
Simple interest = PRT / 100
Prem's simple interest = 18,000 × 15 × 4 / 100 = 10,800
10,800 = 2x − 1200
2x = 12,000
x = 6,000
Compound interest = P[(1 + r/100)³ − 1]
Gaurav's compound interest = 6,000[(1.10)³ − 1]
= 6,000(1.331 − 1)
= 6000 × 0.331
= 1986
Interest earned by Gaurav = Rs 1986.