‘A’ took a certain sum of money as loan from bank at the rate of 8% simple interest per annum. ‘A’…
Let the original principal sum be P. 'A' pays simple interest to the bank at 8% per annum and receives simple interest from 'B' at 12% per annum, earning a net gain of (12%…
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‘A’ took a certain sum of money as loan from bank at the rate of 8% simple interest per annum. ‘A’ lends the same amount to ‘B’ at 12% simple interest per annum. If at the end of five years, ‘A’ made profit of Rs. 800/- from the deal, how much was the original sum?
Answer and explanation
Correct answer B
Let the original principal sum be P. 'A' pays simple interest to the bank at 8% per annum and receives simple interest from 'B' at 12% per annum, earning a net gain of (12% - 8%) = 4% per annum. Over 5 years, the total profit is (P x 4 x 5) / 100 = 0.20 P. Given that the profit is Rs. 800/-, we have 0.20 P = 800, so P = 800 / 0.20 = 'Rs. 4,000/-'. (Verification: Interest paid = 4000 x 0.08 x 5 = Rs. 1,600/-; Interest received = 4000 x 0.12 x 5 = Rs. 2,400/-; Profit = 2,400 - 1,600 = Rs. 800/-.)
Option feedback
Option A
Incorrect. At a 4% annual simple interest differential over 5 years (20% total gain), a principal of Rs. 6,500/- would yield a profit of Rs. 1,300/-, not Rs. 800/-.
Option B
Correct. Net simple interest rate profit per annum = 12% - 8% = 4%. Over 5 years, total profit = P x (4 x 5) / 100 = 0.20 P. Setting 0.20 P = 800 gives P = Rs. 4,000/-.
Option C
Incorrect. A principal of Rs. 6,200/- would yield a 5-year simple interest profit of 20% of 6,200 = Rs. 1,240/-, not Rs. 800/-.
Option D
Incorrect. A principal of Rs. 6,000/- would yield a 5-year simple interest profit of 20% of 6,000 = Rs. 1,200/-, not Rs. 800/-.
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