Question

the ratio of two numbers is 2:3 if 30th is added to both the numbers then ratio is 3:4 find the sum of numbers​

Answer 1

ANSWER :

$\large\underline{\boxed{\mathsf{Sum \: = 150}}}$

Step-by-step explanation:

Given :

Ratio of two numbers is 2:3 if 30 is added to both the numbers then ratio is 3:4.

Now we need to find the sum of the numbers

Answer :

Let x Be the constant of the ratio then ,

we have >>

• First Number = 2x

and

• Second Number = 3x

Now ATQ

When we add 30 to both numbers then ratio becomes 3:4 that is

• First number after adding 30 = 2x + 30

and

• 2nd number after adding 30 = 3x + 30

Then from question we know

$\mathsf{\dfrac{First \: number \:after \: adding\:30}{2nd \: number\: after\: adding\: 30}\: = \: \dfrac{3}{4}}$

Thus we have

$\mathsf{\dfrac{2x + 30}{3x + 30}\: =\: \dfrac{3}{4}}$

Now by cross multiplication we have

$\mathsf{4(2x + 30) \: =\: 3(3x + 30)}$

$\mathsf{= 8x + 120) \: =\: 9x + 90)}$

Now taking variable in LHS and Consant in RHS we have

$\mathsf{ -x \: =\: -30)}$

That is

$\mathsf{ x \: =\: 30)}$

Now Putting value of X in above taken variable numbers we have

1st number = 2x = 2(30) = 60

2nd number = 3x = 3(30) = 90

Therefore sum of both number

= 60 + 90 = 150

Thus Required answer =

$\large \boxed{\mathsf{Sum \: = 150}}$

Answer 2

Let the -

• one number be 2M
• another number = 3M

If 30 is added to both the numbers the ratio becomes 3:4.

$\bold{If\:30\:is\:added} \begin{cases} \text{One number = 2M + 30} \\ \text{Another number = 4M + 30} \end{cases}$

According to the question,

=> $\sf{\dfrac{2M\:+\:30}{3M\:+\:30}\:=\:\dfrac{3}{4}}$

=> $\sf{4(2M\:+\:30)\:=\:3(3M\:+\:30)}$

=> $\sf{8M\:+\:120\:=\:9M\:+\:90}$

=> $\sf{8M\:-\:9M\:=\:90\:-\:120}$

=> $\sf{-M\:=\:-30}$

=> $\sf{M\:=\:30}$

So,

One number = 2(30)

=> 60

Another number = 3(30)

=> 90

Now,

Sum of numbers = One number + Another number

=> 60 + 90

=> 150

•°• Sum of numbers is 150