##### Two numbers are in the ratio 3:5. If 9 is subtracted from each, the new numbers are in the ratio 12:23 , find the numbers?

_{By Akshaya, Posted on 06/04/2021 - 3 Comments}

##### Answers (3)

_{ Posted by Hussaina on 08/04/2021 }

let 3:5 be 3x:5x

according to the question, 3x-9/5x-9 = 12/23,

cross-multiplication, 23(3x-9) = 12(5x-9)

69x-207 = 60x-108

9x = 99

x = 11

therefore, if x=11, 3x=33 and 5x=55

hence, 33-9/55-9 = 24/49

the numbers are 33:55 and 24:46

_{ Posted by Prasad Mahadeo Sonone on 07/04/2021 }

Let 2 bumbers be x and y

From condition 1

x/y = 3/5

i.e. 5x = 3y ....(1)

From condition 2

(x-9)/(y-9) = 12/23

i.e. 23x-207 = 12y-108

i.e. 23x = 12y + 99 .... (2)

Multiplying equation (1) × 4

i.e. 20x = 12y ....(3)

Subyracting equation (2) - (3)

3x = 99

i.e. x = 33

Substituting value of 'x' in equation (1)

5 × 33 = 3y

i.e. y = 5×33/3

i.e. y = 55

Hence numbers are 33 and 55

_{ Posted by Archana Sood on 07/04/2021 }

Suppose the numbers are x and y.

x/y = 3/5 hence 5x=3y and x = 3y/5

if 9 is subtracted from both numbers, the numbers are x-9 and y-9

Hence x-9/y-9 = 12/23

Putting the value of x in the equation, the equation becomes

3y/y = 21 hence y = 35

since 5x = 3y, value of x =21

So the numbers are 21 and 35

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