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A man took a loan of Rs. 78000 at a simple interest of 5% per annum of 3 years. After some time, he took another loan of Rs. 44000 at simple interest for 2 years. If he cleared his both debts by paying a total amount of Rs. 138980, at what rate of interest did he took the second loan?

A man took a loan of Rs. 78000 at a simple interest of 5% per annum of 3 years. After some time, he took another loan of Rs. 44000 at simple interest for 2 years. If he cleared his both debts by paying a total amount of Rs. 138980, at what rate of interest did he took the second loan? Correct Answer 6%

∵ Simple interest (SI) = (Principal × Rate × Time)/100 & Amount = Principal + SI

For first loan, Principal = Rs. 78000, Rate = 5%, Time = 3 years

⇒ SI = (78000 × 5 × 3)/100 = Rs. 11700

⇒ Amount to clear first loan = 78000 + 11700 = Rs. 89700

But, total amount paid = Rs. 138980

⇒ Amount to clear second loan = 138980 – 89700 = Rs. 49280

For second loan, Principal = Rs. 44000, Time = 2 years

⇒ SI = (44000 × Rate × 2)/100 = 49280 – 44000

⇒ 880 × Rate = 5280

⇒ Rate = 5280/880 = 6%

∴ He took the second loan at 6% p.a.

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