Question

two numbers are such that the ratio between them is 3:5.if each is increased by 5,the ratio between the new numbers so formed is 2:3.Find the original number

step by step please do it a proper answer ​

Answer 1

Given:-

• Ratio of two numbers = 3 : 5

• If each is increased by 5, the ratio between the new numbers so formed = 2 : 3.

To Find:-

• The original number

Solution:-

Let the two numbers be x and y.

As given,

$\sf :\implies\:x : y= 3 : 5$

$\sf :\implies\:\dfrac{x}{y}= \dfrac{3}{5}$

$\sf :\implies\:x= \dfrac{3y}{5}$ ___ {1}

Each number increased by 5,

$\sf :\implies\:x+5 : y+5 = 2 : 3$

$\sf :\implies\:\dfrac{x+5}{y+5}= \dfrac{2}{3}$

$\sf :\implies\:3(x+5)= 2(y+5)$

$\sf :\implies\:3x+15= 2y+10$

$\sf :\implies\:3x-2y=10-15$

$\sf :\implies\:3x-2y= -5$

Putting value of x,

$\sf :\implies\:3\times \dfrac{3y}{5}-2y= -5$

$\sf :\implies\: \dfrac{9y}{5}-2y= -5$

$\sf :\implies\: \dfrac{9y-10y}{5}= -5$

$\sf :\implies\: \dfrac{-y}{5}= -5$

$\sf :\implies\: -y= -5\times 5$

$\sf :\implies\: -y= -25$

$\sf :\implies\: y= 25$

Putting value of y in {1},

$\sf :\implies\:x= \dfrac{3\times 25}{5}$

$\sf :\implies\:x= 3\times 5$

$\sf :\implies\:x= 15$

Hence, The two numbers are 15 and 25.

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Answer 2

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