Question

two numbers are in the ratio 3:4; when 8 is subtracted from each, the ratio becomes 2:3.find the number

Answer 1

Let the no. be x
3x and 5x
3x/5x
3x-8/5x-8=2/3
3(3x-8)=2(5x-8)
9x-24 = 10x-16
9x-10x = 16-24
-x = -8
x = 8

Answer 2

Two numbers are 24 and 32

Given :

• Two numbers are in the ratio 3 : 4

• When 8 is subtracted from each, the ratio becomes 2 : 3

To find :

The numbers

Solution :

Step 1 of 2 :

Form the equation

Two numbers are in the ratio 3 : 4

Let the numbers are 3x and 4x

Now it is given that when 8 is subtracted from each, the ratio becomes 2 : 3

By the given condition

$\displaystyle \sf{ (3x - 8):(4x - 8) = 2:3 }$

Step 2 of 2 :

Find the numbers

$\displaystyle \sf{ (3x - 8):(4x - 8) = 2:3 }$

$\displaystyle \sf{ \implies \frac{3x - 8}{4x - 8} = \frac{2}{3} }$

$\displaystyle \sf{ \implies 9x - 24 = 8x - 16 }$

$\displaystyle \sf{ \implies 9x - 8x = 24 - 16 }$

$\displaystyle \sf{ \implies x = 8 }$

First number = 3x = 3 × 8 = 24

Second number = 4x = 4 × 8 = 32

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