Question

At a simple interest a sum amounts to rs 1012 in 2.5 yr and becomes rs 1057.54 in 4 yr what is the rate of interest.

Answer 1

let the principal be P and rate be r%
ATQ
$1012 - p =\frac{ pr \times 2.5 }{100} \\ 101200 - 100p = 2.5pr \\ 101200 = 2.5pr + 100p \\ 101200 = p(2.5r + 100) \\ p = \frac{101200}{2.5r + 100} \\ \\ \\ \\ \\ 1057.54 - p = \frac{ pr \times 4 }{100} \\ 105754 - 100p = 4pr \\ 105754 = p(4r + 100) \\ 105754 = \frac{101200}{2.5r + 100} \times (4r + 100) \\ 264385r + 10575400 = 404800r + 10120000 \\404800r - 264385r = 10575400 - 10120000 \\ 140415r= 455400 \\ r = \frac{455400}{140415} = 3.24$