Anurag borrows a total sum of rupees 8,000 from two banks A and B. Bank A…
2025
Anurag borrows a total sum of rupees 8,000 from two banks A and B. Bank A lends at 12% per annum and Bank B lends at 10% per annum, both at simple rate of interest. After 2 years, he paid a total interest of Rs. 1,816. What sum did Anurag borrow from Bank A?
Answer: C. 5400 — Concept: Simple Interest (SI) = (Principal × Rate × Time) / 100. When a total sum is split between two lenders at different rates, the unknown split can be…
- A.
4400
- B.
5000
- C.
5400
- D.
5500
Attempted by 11 students.
Show answer & explanation
Correct answer: C
Concept: Simple Interest (SI) = (Principal × Rate × Time) / 100. When a total sum is split between two lenders at different rates, the unknown split can be found either by writing simultaneous equations for the two parts, or by the alligation (weighted-average) method, which compares each rate to the overall effective rate on the combined sum.
Application: Let the amount borrowed from Bank A be x, so the amount from Bank B is (8000 − x).
Total principal: x + (8000 − x) = 8000.
Total simple interest for 2 years: (x × 12 × 2)/100 + ((8000 − x) × 10 × 2)/100 = 1816.
Simplify: 0.24x + 0.20(8000 − x) = 1816 → 0.24x + 1600 − 0.20x = 1816.
Combine like terms: 0.04x = 216.
Solve: x = 216 / 0.04 = 5400.
Cross-check (alligation method): the overall interest rate on the combined sum is (1816 × 100)/(8000 × 2) = 11.35%. By alligation, the ratio in which the two rates (12% and 10%) combine to give 11.35% is (11.35 − 10) : (12 − 11.35) = 1.35 : 0.65 = 27 : 13. So the share from Bank A is 27/(27+13) × 8000 = 27/40 × 8000 = 5400 — confirming the same value obtained algebraically.
Anurag borrowed Rs. 5400 from Bank A.