A man borrows Rs 2500 and agrees to repay with a total interest of rs 380 in 12 monthly instalment each installment being less than the preceding one by rs 20 find amount of the first and last installment
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Given, amount to be repaid = Rs 2500 + Rs 380 = Rs 2880
No. of installments = No. of terms in the A.P. (n) = 12
Let the first installment be of value Rs.x
So, value of the succeeding installment = Rs. (x-20)
A.P.: x, x-20, x-40, ... a = x, d = -20
Sum of the installments = 2880
i.e, 12/2{2x + (11 x -20)} = 2880
⇒ 6{2x - 220} = 2880
⇒2x - 220 = 480
⇒2x = 700 ⇒ x = 350
∴ Amount of first installment = Rs. 350
Amount of last installment = a12 = a + 11d = 350 -220 = Rs. 130
No. of installments = No. of terms in the A.P. (n) = 12
Let the first installment be of value Rs.x
So, value of the succeeding installment = Rs. (x-20)
A.P.: x, x-20, x-40, ... a = x, d = -20
Sum of the installments = 2880
i.e, 12/2{2x + (11 x -20)} = 2880
⇒ 6{2x - 220} = 2880
⇒2x - 220 = 480
⇒2x = 700 ⇒ x = 350
∴ Amount of first installment = Rs. 350
Amount of last installment = a12 = a + 11d = 350 -220 = Rs. 130
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