Ramu lent ₹3,000 to Raju and a certain sum to Ravi at the same time and at the same rate of simple interest of 8% per annum. After 5 years, he received a sum of ₹1,600 from Raju and Ravi together as interest. Find the sum lent to Ravi.

Correct — A. Simple interest is additive, so take Raju's share out of the ₹1,600 first.

Interest from Raju = 3000 × 8 × 5 ⁄ 100 = ₹1,200
Interest from Ravi = 1600 − 1200 = ₹400

Invert the formula: P = SI × 100 ⁄ (R × T)
= 400 × 100 ⁄ (8 × 5) = 40000 ⁄ 40 = ₹1,000 → option (a).

Why the others are wrong

• (b)
  ₹1,250 — ₹1,250 at 8% for 5 years earns 1250 × 0.4 = ₹500. Added to Raju's ₹1,200 that is ₹1,700, above the ₹1,600 the question states.
• (c)
  ₹1,200 — ₹1,200 is Raju's interest, not Ravi's principal. It is the number you have just written down, placed on the option list for anyone who stops one line early.
• (d)
  ₹1,500 — ₹1,500 earns 1500 × 0.4 = ₹600 over the five years, making the pair's interest ₹1,800 — ₹200 more than the stated total.

SI = P × R × T ⁄ 100. The formula is linear in P, so several sums lent at one rate for one period contribute interests that simply add.

That linearity is what turns this into a subtraction rather than a pair of simultaneous equations. Work out the interest you can, subtract it from the total, and invert the formula on what is left.

The inversion is P = SI × 100 ⁄ (R × T). At R = 8 and T = 5 the factor R × T ⁄ 100 is 0.4, so over these five years every rupee lent returns 40 paise.

Key facts

• SI = P × R × T ⁄ 100, and it is linear in P.
• At 8% per annum for 5 years the interest is 40% of the principal.
• ₹3,000 at 8% for 5 years earns ₹1,200 in simple interest.

Common traps

• Reading ₹1,600 as Ravi's interest instead of the two borrowers' interest together.
• Applying the 8% for a single year and forgetting the five.
• Reporting the interest ₹400 as though it were the sum lent.

No directly related past PYQ was found.