A sum of ₹1,456, when invested for ten years, amounts to ₹2,366 on maturity. Find the rate of simple interest per annum that was to be paid on the sum invested.

Correct — B. The stem gives the amount, not the interest, so recover the interest first.

SI = 2366 − 1456 = ₹910
P = ₹1,456 and T = 10 years

R = (SI × 100) ÷ (P × T)
= (910 × 100) ÷ (1456 × 10)
= 91000 ÷ 14560 = 6.25

The rate is 6.25% per annum → option (b)
Check: 6.25% of ₹1,456 is ₹91 a year, and 91 × 10 = ₹910.

Why the others are wrong

• (a)
  5.75% — 5.75% earns ₹83.72 a year, ₹837.20 over ten years, and matures at ₹2,293.20 rather than ₹2,366.
• (c)
  6.15% — 6.15% earns ₹89.54 a year, ₹895.44 over ten years, and lands at ₹2,351.44 — ₹14.56 short.
• (d)
  6.5% — 6.5% earns ₹94.64 a year, ₹946.40 over ten years, and overshoots to ₹2,402.40.

Simple interest is paid on the original principal every year, so ten years earn exactly ten times one year's interest and the amount grows in a straight line.

SI = P × R × T ÷ 100 rearranges to give whichever of the four quantities is missing. Here that is R, and because the stem reports the maturity amount, the interest has to be extracted before the formula is any use.

Key facts

• Simple interest = Amount − Principal, so ₹2,366 − ₹1,456 = ₹910.
• R = (SI × 100) ÷ (P × T), with T in years when the rate is per annum.
• Under simple interest the base never changes, so total interest is T times one year's interest.
• 1% of ₹1,456 is ₹14.56, and ₹91 a year is 6.25% of the principal.

Common traps

• Putting ₹2,366 into the formula as the principal.
• Using the compound-interest formula, which the words simple interest rule out.
• Rounding 91000 ÷ 14560 to 6.2 and reaching for the nearest printed rate.

No directly related past PYQ was found.