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What is the value of R? Statement I: A sum at simple interest becomes ₹4800 in T years at R% and ₹5700 in 9 years at 10% rate. Statement II: The compound interest received after 2 years on ₹2000 at (T+8)% interest is ₹880.

1. I alone is sufficient
2. II alone is sufficient
3. I and II sufficient together
4. Either I or II alone is sufficient

Correct answer: I and II sufficient together

Solution

Statement I: P at 10% for 9 years = 5700. SI for 9 years = 5700-P. P×10×9/100 = 5700-P → 0.9P+P=5700 → P=3000. 3000+3000×R×T/100=4800 → 3000RT/100=1800 → RT=60. Can't find R alone without T. Statement II alone: 2000(1+(T+8)/100)²=2880 → (1+(T+8)/100)²=1.44 → (T+8)%=20% → T=12. Can't find R alone. Together: T=12 from II, R=60/12=5% from I.

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