Question

The difference of two numbers is 1660. if 7.5% of one number is equal to 12.5% of the other number, find the larger numbers​

Answer 1

let the numbers be x and y

x - y = 1660

7.5%x = 12.5% y

$\frac{7.5}{100} x = \frac{12.5}{100} y \\ \frac{7.5x}{100} - \frac{12.5y}{100} = 0 \\ 7.5x - 12.5y = 0 \\ multiple \: (x - y = 1660)with \: 7.5 \\ 7.5x - 12.5y = 5450 \\ \: \: \: equ \: (2) \\ equ \: 2 \: - \: equ \: 1 \\ \: we \: get \\ 5y = 5450 \\ y = \frac{5450}{5} = 1090 \\ substitute \: in \: equ \: 1 \\ x - y = 1660 \\ x - 1090 = 1660 \\ x = 2750$

hence the larger number is 2750