A sum of Rs 10,000 is deposited in Bank P for some number of years at 5% simple interest per annum. On maturity, the entire amount is transferred to Bank Q for a further 5 years at 6% simple interest per annum. If the interest earned in Bank P and Bank Q are in the ratio 10:13, for how many years was the money deposited in Bank P?
Answer and solution
Correct answer: C
Solution
Answer: C — 6 years
1. Let the first deposit duration be t years. Interest in P=10000×0.05t=500t.
2. The full maturity amount 10000+500t goes into Q. Five years at 6% simple interest earns 30% of this amount.
3. Thus Q interest=3000+150t. Use 500t/(3000+150t)=10/13.
4. 6500t=30000+1500t, so t=6. Check interests 3000 and 3900, ratio 10:13. Answer C.
Why this method works:
BankQ’s principal includes the original₹10,000 plus all interest from BankP. The second interest is therefore 30% of the maturity amount, not 30% of₹10,000. The ratio 10:13 compares interest amounts, not final balances.
Independent check and common trap:
For t=6, BankP earns₹3,000 and transfers₹13,000. BankQ earns 13,000×6%×5=₹3,900. Their ratio 3,000:3,900 reduces to 10:13, confirming both the time and the correct principal for the second stage.
Apply: Bank Q earns 30% of its starting amount. If Bank P interest is I, use I/[0.3(10000+I)]=10/13 to get I=3000, then 3000/500=6 years.
Check: For t=6, BankP earns₹3,000 and transfers₹13,000. BankQ earns 13,000×6%×5=₹3,900. Their ratio 3,000:3,900 reduces to 10:13, confirming both the time and the correct principal for the second stage.
1. Let the first deposit duration be t years. Interest in P=10000×0.05t=500t.
2. The full maturity amount 10000+500t goes into Q. Five years at 6% simple interest earns 30% of this amount.
3. Thus Q interest=3000+150t. Use 500t/(3000+150t)=10/13.
4. 6500t=30000+1500t, so t=6. Check interests 3000 and 3900, ratio 10:13. Answer C.
Why this method works:
BankQ’s principal includes the original₹10,000 plus all interest from BankP. The second interest is therefore 30% of the maturity amount, not 30% of₹10,000. The ratio 10:13 compares interest amounts, not final balances.
Independent check and common trap:
For t=6, BankP earns₹3,000 and transfers₹13,000. BankQ earns 13,000×6%×5=₹3,900. Their ratio 3,000:3,900 reduces to 10:13, confirming both the time and the correct principal for the second stage.
G Strategy shortcut
Spot: Simple Interest.Apply: Bank Q earns 30% of its starting amount. If Bank P interest is I, use I/[0.3(10000+I)]=10/13 to get I=3000, then 3000/500=6 years.
Check: For t=6, BankP earns₹3,000 and transfers₹13,000. BankQ earns 13,000×6%×5=₹3,900. Their ratio 3,000:3,900 reduces to 10:13, confirming both the time and the correct principal for the second stage.
G Strategy: Spot: Simple Interest. Apply: Bank Q earns 30% of its starting amount. If Bank P interest is I, use I/[0.3(10000+I)]=10/13 to get I=3000, then 3000/500=6 years. Check: For t=6, BankP earns₹3,000 and transfers₹13,000. BankQ earns 13,000×6%×5=₹3,900. Their ratio 3,000:3,900 reduces to 10:13, confirming both the time and the correct principal for the second stage.