The simple interest on a sum for 6 years is three-fifth of the sum. The rate of interest per annum is:

Correct — C. The principal is never given and never needed — it cancels the moment you write the simple interest formula.

SI = P × R × T ⁄ 100, and the stem says SI = 3P⁄5
3P⁄5 = P × R × 6 ⁄ 100
Cancel P on both sides: 3⁄5 = 6R⁄100
R = (3⁄5) × (100⁄6) = 300⁄30 = 10%

Check it forward: at 10% for 6 years the interest is 60% of the sum, and 60% is 3⁄5. That is option (c).

Why the others are wrong

• (a)
  3% — 3% is the numerator of three-fifth copied straight into the answer. At 3% for 6 years the interest is only 18% of the sum, nowhere near 60%.
• (b)
  7% — 7% for 6 years yields 42% of the sum. The stem needs 60%, and no rounding closes an 18-point gap.
• (d)
  5% — 5% for 6 years gives 30% of the sum, exactly half of what the stem requires. The rate that reaches 3⁄5 in six years is double it.

Simple interest is SI = P × R × T ⁄ 100, so the interest expressed as a fraction of the principal is just RT⁄100.

That single rearrangement is the whole question. Once the interest is quoted as a fraction of the sum, the principal disappears and you are solving one equation in one unknown.

Here RT⁄100 = 3⁄5, so RT = 60. With T = 6 the rate is 10% a year.

Any sum works — ₹500 grows by ₹300 in six years at 10%, and ₹5,000 grows by ₹3,000. Both are three-fifths.

Key facts

• Simple interest = P × R × T ⁄ 100, with R in percent per annum and T in years.
• Interest as a fraction of the principal equals RT⁄100, so the principal cancels whenever the interest is quoted that way.
• Here RT = 60 and T = 6, giving R = 10%.
• The same sentence with eight years in place of six would give R = 7.5%.

Common traps

• Treating three-fifth as the rate and answering 3%
• Solving RT = 60 and stopping there, reporting 60% instead of dividing by the six years
• Using the amount formula P(1 + RT⁄100) when the stem describes the interest alone

No directly related past PYQ was found.