Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers , the ratio becomes 4:5 find the numbers.

Problem : Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers , the ratio becomes 4:5 find the numbers.

Doubt by Ananya

Solution : Let the two numbers be x and y

ATQ

x/y = 5/6
6x = 5y
6x - 5y = 0 ----(1)

(x-8)/(y-8) = 4/5
5(x-8) = 4(y-8)
5x - 40 = 4y - 32
5x - 4y = -32 + 40
5x - 4y = 8 --- (2)

Eliminating Equation (1) and (2)

[ 6x - 5y = 0 ] × 4
[ 5x - 4y = 8 ] × 5

24 x - 20 y = 0
25 x - 20 y =40
-      +           -
----------------------
- x + 0  = - 40
----------------------

x = 40

Putting in eq (1)
 6(40) - 5y = 0
240 = 5y
y = 240/5
y = 48

∴ The required two numbers are 40 and 48.