P & Q amounts equal that is Rs. 12,000. P invested half of the amount at 10% CI & remaining at 6% of SI for 2 years and Q invested (\frac{3}{4}) amount at 20% CI & remaining at 10% SI for 2 years. Find the interest received by P & Q both ?
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4650
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5460
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6450
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6540
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None of these
D
Correct answer
Explanation
P invests half (6000) at 10% CI for 2 years: 6000(1.1)² - 6000 = 6000 × 1.21 - 6000 = 7260 - 6000 = 1260. Remaining 6000 at 6% SI for 2 years: 6000 × 0.06 × 2 = 720. P's total interest = 1260 + 720 = 1980. Q invests 3/4 (9000) at 20% CI for 2 years: 9000(1.2)² - 9000 = 9000 × 1.44 - 9000 = 12960 - 9000 = 3960. Remaining 3000 at 10% SI for 2 years: 3000 × 0.10 × 2 = 600. Q's total interest = 3960 + 600 = 4560. Combined interest = 1980 + 4560 = 6540.