Question

two numbersare in the ratio 3:5.if each is increased by 10.the ratio formed so is 5:7. find the original numbers​

Answer 1

Solution:

Let x and y are two numbers,

According to question:

Two numbers are in the ratio 3:5. So,

=> x : y = 3 : 5

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

=> 5x = 3y

$\sf{\implies x = \dfrac{3y}{5}\;\;\;\;......(1)}$

Now, if each is increased by 10 the ratio formed so is 5:7.

=> (x + 10) : (y + 10) = 5 : 7

$\sf{\implies \dfrac{x+10}{y+10}=\dfrac{5}{7}}$

$\sf{\implies 7(x+10)=5(y+10)}$

$\sf{\implies 7x+70=5y+50}$

$\sf{\implies 7x+70-50=5y}$

$\sf{\implies 7x+20=5y\;\;\;.......(2)}$

Put the value of x in Equation (2) from Equation (1), we get

$\sf{\implies 7x+20=5y}$

$\sf{\implies 7\bigg(\dfrac{3y}{5}\bigg)+20=5y}$

$\sf{\implies \dfrac{21y}{5}+20=5y}$

$\sf{\implies \dfrac{21y+100}{5}=5y}$

$\sf{\implies 21y+100=25y}$

$\sf{\implies 100=25y-21y}$

$\sf{\implies 100=4y}$

$\sf{\implies \dfrac{100}{4}=y}$

∴ y  = 25

Now, put the value of y in Equation (1), we get

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

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

$\sf{\implies x = \dfrac{75}{5}}$

∴ x = 15

Hence, numbers are 15 and 25.

Answer 2

$\huge\sf{Answer:-}$

Let x,y be the numbers.

3 : 5 = x : y

Given Question:-

$\bf \frac{x}{y} = \frac{3}{5}$

$\bf (5x = 3y)$

$\bf x = \frac{3y}{5} - eq(1)$

5 : 7 = increased by 10

$\sf (x + 10):(y + 10) = 5:7 \\ \\ = \sf \frac{x + 10}{y + 10} = \frac{5}{7}$

$\sf= > 7(x + 10) = 5(y + 10) \\ \sf= > 7x + 70 = 5y + 50 \\ \sf= > 7x + 70 - 50 = 5y \\ \sf= > 7x + 20 = 5y - eq(2)$

Adding Values:-

$\bf= > 7x + 20 = 5y \\ \bf= > 7( \frac{3y}{5} ) + 20 = 5y$

Adding Values:-

$\bf= > x = \frac{3y}{5} \\ \bf= > x = \frac{3 \times 25}{5} \\ \bf = > x = \frac{75}{5} \\ \bf= > (x = 15)$

.•. 15 and 25 are numbers.

$\sf\color{red}{Nayan}$$\sf\color{blue}{Shreyas ....}$