Manish borrows a sum of Rs 54000 at 10% pa compound interest. He repa

1.	Manish borrows a sum of Rs 54000 at 10% pa compound interest. He repays a certain amount at the end of one year and the balance amount of Rs 32340 at the end of second year. What amount does he repay in the first year.1. Rs 300002. Rs 240003. Rs 294004. Rs 340005. None of these
Answer» Correct Answer - Option 1 : Rs 30000 Solution: Given: Sum Manish borrows = 54000 Amount repaid by Manish at the end of second year = 32340 Rate of interest = 10% Concept used: Amount at the end of second year = Amount at the end of first year {1 + (rate/100)} Calculation: Compound interest for first year = (54000 × 10)/100 ⇒ 5400 Amount at the end of first year = 54000 + 5400 ⇒ 59400 Let the amount repaid be Rs x Then, the sum at the beginning of the second year = 59400 – x Amount at the end of second year = (59400 – x) + [{(59400 – x) × 10}/100] ⇒ (59400 – x) + [{(59400 – x) × 10}/100] = 32340 ⇒ 59400 – x + 5940 – 0.1x = 32340 ⇒ 65340 – 1.1x = 32340 ⇒ 1.1x = 65340 – 32340 ⇒ 1.1x = 33000 ⇒ x = 30000 ∴ Amount repaid by Manish at the end of first year = 30000

Manish borrows a sum of Rs 54000 at 10% pa compound interest. He repays a certain amount at the end of one year and the balance amount of Rs 32340 at the end of second year. What amount does he repay in the first year.1. Rs 300002. Rs 240003. Rs 294004. Rs 340005. None of these

Answer» Correct Answer - Option 1 : Rs 30000

Solution:

Given: Sum Manish borrows = 54000

Amount repaid by Manish at the end of second year = 32340

Rate of interest = 10%

Concept used: Amount at the end of second year = Amount at the end of first year {1 + (rate/100)}

Calculation: Compound interest for first year = (54000 × 10)/100

⇒ 5400

Amount at the end of first year = 54000 + 5400

⇒ 59400

Let the amount repaid be Rs x

Then, the sum at the beginning of the second year = 59400 – x

Amount at the end of second year = (59400 – x) + [{(59400 – x) × 10}/100]

⇒ (59400 – x) + [{(59400 – x) × 10}/100] = 32340

⇒ 59400 – x + 5940 – 0.1x = 32340

⇒ 65340 – 1.1x = 32340

⇒ 1.1x = 65340 – 32340

⇒ 1.1x = 33000

⇒ x = 30000

∴ Amount repaid by Manish at the end of first year = 30000