A and B each borrowed equal sums for 3 years at a rate of 5% simple an

1.	A and B each borrowed equal sums for 3 years at a rate of 5% simple and compounded interest compounded annually, respectively. At the time of payment, B had to pay Rs. 427 more than A. The sum borrowed and the interest paid by B (in Rs.) were:1. Rs. 56,000; Rs. 8,4002. Rs. 48,000; Rs. 7,2003. Rs. 48,000; Rs. 7,5664. Rs. 56,000; Rs. 8,827
Answer» Correct Answer - Option 4 : Rs. 56,000; Rs. 8,827 Given: A and B borrow equal sum of money for 3 years at the rate of 5% for SI and CI respectively Difference between interest of A and B is 427 Formula Used: SI = (P × R × T)/100 CI = P (1 + R/100)^t - P Calculation: SI of A = (P × 3 × 5)/100 = 3P/20 ____(i) CI of B = P (1 + 5\100)³ - P ⇒ P × \(\frac{{21}}{{20}} × \frac{{21}}{{20}} × \frac{{21}}{{20}}\) - P ⇒ \(\frac{{9261P}}{{8000}}\) - 1 ⇒ 1261P/8000 ____(ii) According to question, ⇒ \(\frac{{1261P}}{{8000}} - \frac{{3P}}{{20}}\) = 427 ⇒ 61P/8000 = 427 ⇒ P = (427 × 8000)/61 ⇒ P = Rs.56000 Interest Paid by B = 56000 (1 + 5\100)3 - P ⇒ 56000 × \(\frac{{21}}{{20}} × \frac{{21}}{{20}} × \frac{{21}}{{20}}\) - P ⇒ 56000 × (9261/8000) - P ⇒ 64827 - P ⇒ 64827 - 56000 = Rs.8827 ∴ The sum borrowed is Rs.56,000 and interest paid by B is Rs.8827.

A and B each borrowed equal sums for 3 years at a rate of 5% simple and compounded interest compounded annually, respectively. At the time of payment, B had to pay Rs. 427 more than A. The sum borrowed and the interest paid by B (in Rs.) were:1. Rs. 56,000; Rs. 8,4002. Rs. 48,000; Rs. 7,2003. Rs. 48,000; Rs. 7,5664. Rs. 56,000; Rs. 8,827

Answer» Correct Answer - Option 4 : Rs. 56,000; Rs. 8,827

Given:

A and B borrow equal sum of money for 3 years at the rate of 5% for SI and CI respectively

Difference between interest of A and B is 427

Formula Used:

SI = (P × R × T)/100

CI = P (1 + R/100)^t - P

Calculation:

SI of A = (P × 3 × 5)/100 = 3P/20 ____(i)

CI of B = P (1 + 5\100)³ - P

⇒ P × \(\frac{{21}}{{20}} × \frac{{21}}{{20}} × \frac{{21}}{{20}}\) - P

⇒ \(\frac{{9261P}}{{8000}}\) - 1

⇒ 1261P/8000 ____(ii)

According to question,

⇒ \(\frac{{1261P}}{{8000}} - \frac{{3P}}{{20}}\) = 427

⇒ 61P/8000 = 427

⇒ P = (427 × 8000)/61

⇒ P = Rs.56000

Interest Paid by B = 56000 (1 + 5\100)3 - P

⇒ 56000 × \(\frac{{21}}{{20}} × \frac{{21}}{{20}} × \frac{{21}}{{20}}\) - P

⇒ 56000 × (9261/8000) - P

⇒ 64827 - P

⇒ 64827 - 56000 = Rs.8827

∴ The sum borrowed is Rs.56,000 and interest paid by B is Rs.8827.