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Question

A man repays a loan of 3250 by paying 20 in the first month and then increase the payment by 15 every month. How long will it take him to clear the loan?


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Solution

Step1: Framing an equation for n.

The amount of the loan paid is in the form of an A.P. series, having first term as a=20 and common difference as d=15.

Let the loan is paid in n number of instalments.

Then, the total loan to be paid i.e.,3250 is the sum of n number of terms of the A.P.

The sum of n number of terms of an A.P. is given by Sn=n22a+(n-1)d, where a is the first term and d is a common difference.

Substitute the values of Sn,a and d in the formula Sn=n22a+(n-1)d to calculate the value of n.

3250=n22(20)+(n-1)15(Substitutingthevaluesofa,dandSn)6500=n40+15n-15(Multiplyingbothsidesby2)6500=n25+15n6500=25n+15n21300=5n+3n2(Dividingbothsidesby5)3n2+5n-1300=0(n20)(3n+65)=0(bysplittingmiddletermandfactorising)

Step2: Calculation of the value of n.

Equate both the factors to 0 to obtain the solution.

n-20=0n=203n+65=03n=-65(subtracting65frombothsides)n=-653(dividingbothsidesby3)

Since, the number of terms can not be negative, therefore, the correct value of n is 20.

Final Answer: The loan will be paid in 20 months.


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