How much simple interest will ₹6,700 earn in 13 months at a 12% interest rate per annum?

Correct — A. Simple interest is P × R × T ⁄ 100, with T measured in years.

13 months = 13⁄12 year.

SI = 6700 × 12 × (13⁄12) ⁄ 100
The 12 in the rate cancels the 12 in the time, leaving
SI = 6700 × 13 ⁄ 100 = ₹871 → option (a).

Cross-check: one year at 12% is ₹804, one month is ₹67, and 804 + 67 = 871.

Why the others are wrong

• (b)
  ₹889 — ₹889 is one year's ₹804 plus ₹85, but the thirteenth month is worth ₹67. Nothing in the question lifts the rate above 12% per annum.
• (c)
  ₹821 — ₹821 leaves the thirteenth month worth only ₹17. At 12% per annum on ₹6,700 a single month is worth ₹67, so ₹821 falls short.
• (d)
  ₹813 — ₹813 prices the extra month at ₹9, which would need a rate near 1.6% per annum rather than 12%. The correct extra is ₹67.

Simple interest is charged only on the original principal, so the interest per unit time never changes: SI = P × R × T ⁄ 100.

The one thing that reliably breaks candidates is the unit of T. When the rate is per annum, a period in months must become a fraction of a year — 13 months is 13⁄12 of a year, not 13.

Here the rate is 12%, which cancels the 12 in the denominator, so the interest reduces to P × 13 ⁄ 100. That cancellation is why SSC picked 12% rather than 10%.

Key facts

• Simple interest = P × R × T ⁄ 100, with T in years whenever R is per annum.
• 12% per annum on ₹6,700 is ₹804 a year, so ₹67 a month.
• At a rate of exactly 12% per annum, the interest for m months is simply P × m ⁄ 100.

Common traps

• Taking T as 13 years and computing 6700 × 12 × 13 ⁄ 100 = ₹10,452.
• Rounding 13 months down to one year and answering ₹804.
• Reading 13 months as one year and three months and using 15⁄12, which gives ₹1,005.

No directly related past PYQ was found.