Question

Two numbers are in the ratio 5 : 9 on subtracting 3 form each of the numbers, the ratio becomes 2 : 3 fund the number. ​

Answer 1

Answer:

Numbers = -5 and -9

Step-by-step explanation:

Given :

Number are in ratio = 5:9

Number are in ratio after subtracting by 3 = 2:3

To find :

The numbers

Taken :

Let the number be x

So , to find the numbers use this equation -:

$\boxed{\rm{\dfrac{5x-3}{9x-3}=\dfrac{2}{3}}}$

After finding the value of x multiply the value of x with the ratio .

Solution :

$:\Rightarrow\rm{\dfrac{5x-3}{9x-3}=\dfrac{2}{3}}$

Cross multiply the numbers

$:\Rightarrow\rm{3(5x-3)=2(9x-3)}$

$:\Rightarrow\rm{15x-9=18x-6}$

$:\Rightarrow\rm{-9+6=18x-15x}$

$:\Rightarrow\rm{-3=3x}$

$:\Rightarrow\rm{\cancel{\dfrac{-3}{3}}=x}$

$:\Rightarrow\rm{-1=x}$

Numbers -:

First number :

$:\Rightarrow\rm{5(-1)}$

$:\Rightarrow\rm{-5}$

Second number :

$:\Rightarrow\rm{9(-1)}$

$:\Rightarrow\rm{-9}$

So , the numbers are -5 and -9 .

Extra -:

After subtracting numbers are -:

First number :

$:\Rightarrow\rm{-5-3}$

$:\Rightarrow\rm{-8}$

Second number :

$:\Rightarrow\rm{-9-3}$

$:\Rightarrow\rm{-12}$

Answer 2

$\begin{gathered}\bf{\underline{\underline{Given :-}}}\\\end{gathered}$

★ Two numbers are in the ratio 5 : 9 on subtracting 3 form each of the numbers, the ratio becomes 2 : 3 fund the number.

$\begin{gathered}\bf{\underline{\underline{To\:find : - }}}\\\end{gathered}$

★ Numbers.

$\large{\boxed{\boxed{\sf{Solution : - }}}}$

• Let x be the common variable.

So , the first ratio can be written as 5x and 9x.

$\large{\boxed{\boxed{\sf{According \ to \ the \ question :- }}}}$

• On substracting 3 from 5 : 9 it becomes 2 : 3

So ,

5x - 3 / 9x - 3 = 2 / 3

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

15x - 9 = 18x - 6

- 9 + 6 = 18x - 15x

- 3 = 3x

x = - 3 / 3

x = - 1

Therefore , the old numbers will be.

5x = 5 x ( - 1 ) = - 5

9x = 9 x ( - 1 ) = - 9

New numbers will be :-

2x = 2 x ( - 1 ) = - 2

3x = 3 x ( - 1 ) = - 3

$\bf\red{Required \ Numbers :-}$

★ 9x - 3 = - 9 - 3 = - 12

★ 5x - 3 = - 5 - 3 = - 8