Question

A man has Rs. 10,000. He lent a part of it at 15% simple interest and the remaining at 10% simple interest. The total interest he received after 5 years amounted to Rs. 6,500. The difference between the parts of the amounts he lent is:
1. Rs. 1,750
2. Rs. 2,500
3. Rs. 2,000
4. Rs. 1,500

Answer 1

Correct Answer - Option 3 : Rs. 2,000

Given:

Principal = Rs 10,000

Some part of money lent at 15%

Some part of it lent at 10%

Total interest earned = Rs. 6,500

Time = 5 years

Formula Used:

Interest = (Principal × Rate × Time)/100

Calculation:

Let the money lent at 15% be x

Then money lent at 10% be (10,000 - x)

6,500 = [(x × 15 × 5)/100] + [(10,000 - x) × 10 × 5]/100

⇒ 6,500 = (3x/4) + [(10,000 - x)/2]

⇒ 6,500 = (3x + 20,000 - 2x)/4

⇒ 26,000 = 20,000 + x

⇒ x = Rs 6,000

Then,

(10,000 - x) = (10,000 - 6,000) = Rs 4,000

Difference between the two sums lent = Rs 6,000 - Rs 4,000

⇒ Difference between the two sums lent = Rs 2,000

∴ The difference between the sums lent is Rs 2,000.