Single correct option
₹12,300 is divided into two parts. The first part is lent at 10% per annum simple interest for 2 years and the second at 10% per annum compound interest (compounded annually) for 2 years. If the interest earned on the two parts is equal, what is the first part?
- A. ₹5,700
- B. ₹6,000
- C. ₹6,150
- D. ₹6,300
Show answer and solution
Answer: (D) ₹6,300
SI on x for 2 years at 10% = 0.20x.
CI on (12,300 − x) for 2 years at 10% = (1.21 − 1)(12,300 − x) = 0.21(12,300 − x).
Setting them equal: 0.20x = 2,583 − 0.21x → 0.41x = 2,583 → x = ₹6,300.
Check: 0.2 × 6,300 = 1,260 and 0.21 × 6,000 = 1,260 ✓.
Tip: Parts are in the inverse ratio of their interest factors: x : (12,300 − x) = 0.21 : 0.20 = 21 : 20, so x = 21/41 × 12,300.
CI on (12,300 − x) for 2 years at 10% = (1.21 − 1)(12,300 − x) = 0.21(12,300 − x).
Setting them equal: 0.20x = 2,583 − 0.21x → 0.41x = 2,583 → x = ₹6,300.
Check: 0.2 × 6,300 = 1,260 and 0.21 × 6,000 = 1,260 ✓.
Tip: Parts are in the inverse ratio of their interest factors: x : (12,300 − x) = 0.21 : 0.20 = 21 : 20, so x = 21/41 × 12,300.
Saved on this device. Sign in or create a free account to keep it on every device.