Question

Two numbers are in the ratio 7:5. If 2 is subtracted from each of them, the ratio becomes 3:2. Find the numbers.

Answer 1

Explanation:

Ratio = 7 : 5

Numbers are 7x , 5x

`(7x-2)/(5x-2)=(3)/(2)\\\\\\`

Cross multiply,

2*(7x - 2) = 3*(5x -2)

2*7x - 2*2 = 3*5x - 3*2

14x - 4 = 15x - 6

14x - 4 + 6 = 15x {Add 6 to both sides}

14x + 2 = 15x

2 = 15x - 14x {Subtract '4x' from both sides}

x = 2

7x = 7*2 = 14

5x = 5*2 = 10

Numbers are 14 , 10