A certain amount invested at compound interest of 12% per annum, compounded annually, amounts to ₹3,136 in 2 years. What is 140% of the amount invested?

Correct — C. Undo two years of growth to find the sum invested, then take 140% of it.

Growth factor for 2 years = 1.12 × 1.12 = 1.2544
Sum invested = 3,136 ÷ 1.2544 = ₹2,500
Check: 2,500 × 1.2544 = ₹3,136

140% of the sum = 1.4 × 2,500 = ₹3,500 → option (c).

Why the others are wrong

• (a)
  ₹3,600 — ₹3,600 is 140% of ₹2,571.43, and that sum grows to 2,571.43 × 1.2544 ≈ ₹3,225.60 in two years, not ₹3,136.
• (b)
  ₹3,800 — ₹3,800 is 140% of ₹2,714.29, which grows to about ₹3,404.80 in two years at 12% — well above the ₹3,136 in the stem.
• (d)
  ₹3,000 — ₹3,000 is 140% of ₹2,142.86, which grows to only ₹2,688 in two years. It is 120% of the true ₹2,500, not 140%.

Compound interest multiplies the sum by (1 + r⁄100) once a year. Two years at 12% multiply it by 1.12 × 1.12 = 1.2544.

To go backwards, divide the amount by that factor.

Fractions keep it mental: 1.12 = 28⁄25, so the factor is 784⁄625. Then 3,136 ÷ 784 = 4, and 4 × 625 = ₹2,500.

Key facts

• Amount under annual compounding = P × (1 + r⁄100)ⁿ.
• At 12% for two years the factor is 1.12² = 1.2544, which is 784⁄625.
• Here the sum invested is ₹2,500 and the compound interest earned is ₹636.

Common traps

• Stopping at ₹2,500, the sum invested, and skipping the final step to 140%.
• Using the simple-interest factor 1.24: the sum becomes ₹2,529.03 and 140% of it about ₹3,540.65, which matches no option.
• Taking 140% of the amount ₹3,136 instead of the sum invested, which gives ₹4,390.40.

No directly related past PYQ was found.