A person invested ₹8,000 in one scheme at 6% simple interest and ₹5,000 in another scheme at 8% simple interest for the same duration. If he received a total interest of ₹1,760 from both investments, what was the duration (time period) of the investments?

Correct — B.
One year on ₹8,000 at 6%: 8000 × 6 ÷ 100 = ₹480
One year on ₹5,000 at 8%: 5000 × 8 ÷ 100 = ₹400
Add them: 480 + 400 = ₹880 a year

Divide the total interest by one year's interest: 1760 ÷ 880 = 2

So the duration is 2 years → option (b)

Why the others are wrong

• (a)
  1 year — One year earns only ₹880 from both schemes together, which is half of the ₹1,760 received.
• (c)
  2.5 years — 2.5 years earns 880 × 2.5 = ₹2,200, which is ₹440 more than the ₹1,760 received.
• (d)
  3 years — 3 years earns 880 × 3 = ₹2,640, one and a half times the ₹1,760 received.

When several sums earn simple interest for the same time, the time is a common factor: total SI = (P₁R₁ + P₂R₂) × T ÷ 100.

So find one year's interest from all the sums together, then divide the total interest by it to get the number of years.

Here one year brings ₹880, and ₹1,760 is exactly two years' worth.

Key facts

• Simple interest grows in step with time: two years earn twice one year's interest
• For sums invested for the same time, total SI = (P₁R₁ + P₂R₂) × T ÷ 100
• ₹8,000 at 6% and ₹5,000 at 8% earn ₹880 a year together

Common traps

• Averaging 6% and 8% to 7% on the whole ₹13,000. The sums are unequal, so the blended rate is 880 ÷ 13,000 ≈ 6.77%, not 7%

No directly related past PYQ was found.