Question

two numbers are in ratio 5:9 on subtracting 3 from each the ratio become 1:2 find the number

Answer 1

let numbers be 5x, 9x
subtracting 3 from each we get 5x-3,9x-3
5x-3/9x-3 =1/2
2(5x-3)=9x-3
10x-6=9x-3
10x-9x= -3+6
x=3
5x= 5(3)=15
9x=9(3)=27
15,27 are numbers

Answer 2

Ratio before subtraction →→ Number 1 : Number 2 = 5 : 9

Let x be the constant ratio.

Ratio before subtraction →→ Number 1 : Number 2 = 5x : 9x

Ratio after subtraction →→ Number 1 : Number 2 = 1 : 2

Let y be the constant ratio

Ratio after subtraction →→ Number 1 : Number 2 = 1y : 2y

Form the equations:

5x - 3 = y     --------------------- [ 1 ]

9x - 3 = 2y   --------------------- [ 2 ]

Substitute [ 1 ] into [ 2 ]:

9x - 3 = 2(5x - 3)

9x - 3 = 10x - 6

x = 3

Find the number:

5x = 5(3) = 15

9x = 9(3) = 27

The two numbers 15 and 27.