An amount of Rs 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum. If the interests received from bank A and bank B are in the ratio 10 : 13, then the investment period, in years, in bank A is
Question:
An amount of Rs 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum. If the interests received from bank A and bank B are in the ratio 10 : 13, then the investment period, in years, in bank A is
An amount of Rs 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum. If the interests received from bank A and bank B are in the ratio 10 : 13, then the investment period, in years, in bank A is
Options
Answer: 6
Explanation:
Step 1: Define variables Principal in Bank A: P = 10000 Rate in Bank A: R₁ = 5% per annum Time in Bank A: t years → unknown Simple interest formula: SI = P × R × T / 100 Interest from Bank A: SI₁ = 10000 × 5 × t / 100 = 500t Total amount after Bank A: A₁ = Principal + SI = 10000 + 500t Step 2: Bank B deposit Total amount from Bank A deposited in Bank B Rate in Bank B: R₂ = 6% per annum Time in Bank B: 5 years Interest from Bank B: SI₂ = A₁ × 6 × 5 / 100 = (10000 + 500t) × 30 / 100 = 3000 + 150t Step 3: Use the ratio of interests Given: SI₁ : SI₂ = 10 : 13 SI₁ = 500t SI₂ = 3000 + 150t Set up ratio: 500t / (3000 + 150t) = 10 / 13 Cross multiply: 500t × 13 = 10 × (3000 + 150t) 6500t = 30000 + 1500t 6500t − 1500t = 30000 5000t = 30000 t = 6
Explanation:
Step 1: Define variables Principal in Bank A: P = 10000 Rate in Bank A: R₁ = 5% per annum Time in Bank A: t years → unknown Simple interest formula: SI = P × R × T / 100 Interest from Bank A: SI₁ = 10000 × 5 × t / 100 = 500t Total amount after Bank A: A₁ = Principal + SI = 10000 + 500t Step 2: Bank B deposit Total amount from Bank A deposited in Bank B Rate in Bank B: R₂ = 6% per annum Time in Bank B: 5 years Interest from Bank B: SI₂ = A₁ × 6 × 5 / 100 = (10000 + 500t) × 30 / 100 = 3000 + 150t Step 3: Use the ratio of interests Given: SI₁ : SI₂ = 10 : 13 SI₁ = 500t SI₂ = 3000 + 150t Set up ratio: 500t / (3000 + 150t) = 10 / 13 Cross multiply: 500t × 13 = 10 × (3000 + 150t) 6500t = 30000 + 1500t 6500t − 1500t = 30000 5000t = 30000 t = 6
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