Question

1. Two numbers are in the ratio 2: 3. TT 9 added to each of the numbers, the ratio
becomes 3:4. Find the numbers
find the value of x.​

Answer 1

Given :-  

• Two no.s are in ratio 2 : 3  

• If 9 is added to both the no.s the ratio becomes 3 : 4

 

To Find :-  

• The original no.s  

Solution :-  

~Here , firstly we will let the no.s according to the given ratios and then form an equation by the conditions given . By solving that equation we'll get the required answer .

Let the original no.s be  

‘ 2x ‘ and ‘ 3x ‘  

According to the given ratios  

Now , ATQ :  

$\sf \implies \dfrac{2x+9}{3x+9}= \dfrac{3}{4}$

• Cross multiply  

$\sf \implies 4(2x+9) = 3(3x+9)$

• By simplifying  

$\sf \implies 8x + 36 = 9x + 27$

• By transposing like terms on each side of the equation

 

$\sf \implies 9x - 8x = 36 - 27$

$\sf \implies x = 9$

Therefore ,  

The first no. = ‘ 2x ‘  

= 2(9) = 18  

The second no. = ‘ 3x ‘  

= 3(9) = 27  

The original no.s are 18 and 27

Answer 2

⠀⠀⠀⠀⠀⠀⠀${\rm{\purple{\underline{\underline{★Required \:Answer★}}}}}$

18 and 27

⠀⠀⠀⠀⠀${\rm{\pink{\underline{\underline{★Solution★}}}}}$

${\rm{\red{\underline{\underline{Given : }}}}}$

• The given numbers are in ratio of 2:3.
• If 9 is added to each, they will be in ratio of 3:4.

${\rm{\blue{\underline{\underline{To \: Find: }}}}}$

• The original value of the numbers.

${\rm{\green{\underline{\underline{ Let : }}}}}$

• Their common ratio be x.

${\rm{\orange{\underline{\underline{Calculations : }}}}}$

If their common ratio is x then the numbers will be 2x and 3x

After adding 9 to each we get :-

(2x + 9) and (3x + 9)

And their new ratio is :-

$\rm \: \frac{2x + 9}{3x + 9} = \frac{3}{4}$

Cross multiplying the terms, we get :-

$\longrightarrow\rm(2x + 9) \times 4 = (3x + 9) \times 3$

$\longrightarrow\rm8x + 36 = 9x + 27$

$\longrightarrow\rm8x - 9x = 27 - 36$

$\rm - x = - 9$

$\longrightarrow\rm \cancel - x = \cancel- 9$

$\longrightarrow\rm\purple{ x = 9}$

The numbers are :-

2x = 2 × (9) = 18

3x = 3 × (9) = 27

Hence, the numbers are 18 and 27.