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

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$\large\bold{\underline{\underline{Question:-}}}$

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?

$\large\bold{\underline{\underline{Answer:-}}}$

$\text{\large\underline{\red{Given:-}}}$

To numbers are in the ratio 3:5.

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

$\text{\large\underline{\purple{To \: Find:-}}}$

The original numbers

$\text{\large\underline{\green{Solution:-}}}$

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

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

According to the Question:-

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

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

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

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

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

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

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

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

Value of x is 5.

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Answer 2

${ \huge{ \underline{ \underline{ \frak{required \: answer:}}}}}$

◇Solution:

$\leadsto$x and y are 2 numbers..

$\leadsto$x : y = 3:5

$\leadsto$5x = 3y

$\leadsto$x = 3y / 5 $\implies$(1)

according to the problem given,

if each is increased by 10, the ratio between

the new numbers so formed is 5:7

$\leadsto$(x + 10 ): (y + 10 ) = 5:7

$\leadsto$7( x + 10 ) = (y + 10 ) 5

$\leadsto$7x + 70 = 5y + 50

$\leadsto$7x + 70 - 50 = 5y

$\leadsto$7x + 20 = 5y$\implies$(2)

substitute x value from equation (1) in (2)

$\leadsto$7x 3y/5 + 20 = 5y

$\leadsto$( 21y + 100 )/5 = 5y

$\leadsto$21y + 100 = 25y

$\leadsto$100 = 25y - 21y

$\leadsto$100 = 4y

$\leadsto$100 / 4 = y

$\leadsto$25 = y

Therefore,

$\leadsto$y = 25

put y = 25 in equation (1), we get

$\leadsto$x = 3 × 25 / 5

$\leadsto$x = 3 × 5

$\leadsto$x = 15

Original numbers are x and y

${\boxed{\bold{15\: and\: 25}}}$

◇Hence Proved...