Question

Two numbers are such that the ratio between them is 3:5 if each is increased by 10, the ratio between the new numbers so formed is 5:7. find the original number ​

Answer 1

Given :

• Two numbers are in the ratio 3:5.
• If each number is increased by 10 then the ratio of the new numbers is 5:7.

To Find :

• Original Numbers.

Solution :

$\longmapsto\tt{Let\:the\:first\:no.\:be=3x}$

$\longmapsto\tt{Let\:second\:no.\:be=5x}$

A.T.Q :

• If each number is increased by 10 then the ratio of the new numbers is 5:7.

$\longmapsto\tt{\dfrac{3x+10}{5x+10}=\dfrac{5}{7}}$

$\longmapsto\tt{7(3x+10)=5(5x+10)}$

$\longmapsto\tt{21x+70=25x+50}$

$\longmapsto\tt{21x-25x=50-70}$

$\longmapsto\tt{-4x=-20}$

$\longmapsto\tt{x=\cancel\dfrac{-20}{-4}}$

$\longmapsto\tt\bold{x=5}$

Value of x is 5...

Therefore :

$\longmapsto\tt{First\:No.=3(5)}$

$\longmapsto\tt\bold{15}$

$\longmapsto\tt{Second\:No.=5(5)}$

$\longmapsto\tt\bold{25}$

So , The original numbers are 15 and 25...

Answer 2

Given :-

• Two numbers are such that the ratio between them is 3 : 5

• If each is increased by 10, the ratio between the new numbers so formed is 5 : 7

To Find :-

• The original Numbers

Solution :-

Let the first number be = '3x'

Let the second number be = '5x'

★ According to the question :-

$:\implies\sf{\dfrac{3x+10}{5x+10}=\dfrac{5}{7}} \\ \\ :\implies\sf{7(3x+10)=5(5x+10)} \\ \\ :\implies\sf{21x+70=25x+50} \\ \\ :\implies\sf{21x-25x=50-70} \\ \\ :\implies\sf{\cancel-4x = \cancel-20} \\ \\ </p><p>:\implies\sf{x=\dfrac{\cancel{20}}{\cancel{4}}} \\ \\ :\implies\boxed{\sf\bold{x=5}}$

$\blue{\therefore\underline{\tt Value \: of \: x \: is \: 5}}$

Therefore :-

• First Number = 3(5) = 15.
• Second Number = 5(5) = 25.

So, The original numbers are 15 and 25.