Question

Two numbers are in the ratio 3:5 if 9 is subtracted from each then the ratio becomes 12:23. What is the smaller number

Answer 1

• As per the data given in the question, we have to find the value of the expression.

             Given data:- The Ratio is used for comparing two numbers $3:5.$

             To find:- smaller number.

             Solution:-

• The Ratio is used for comparing two numbers.

• Two numbers are compared using division.

         Therefore,

       Let the number be $3x$ and $5x.$

       According to question

        $\begin{array}{l}\Rightarrow(3 x-9) /(5 x-9)=12 / 23 \\\Rightarrow 23(3 x-9)=12(5 x-9) \\\Rightarrow 69 x-207=60 x-108 \\\Rightarrow 69 x-60 x=207-108 \\\Rightarrow 9 x=99 \\\Rightarrow x=11\end{array}$

         Now

        $3\times 11=33.$

           Hence the smaller number will be $33.$

Answer 2

To find : smaller number .

Given : two number are in ratio $3 : 5$

Solution :

• Let numbers be $3x$ and $5x$

• As per the given data , we write given condition as ,

                   $\frac{3x - 9}{5x - 9} = \frac{12}{23}$  

• Cross multiplying the terms

         $23 (3x - 9) = 12 ( 5x - 9 )$

             $69x - 207 = 60x - 108$

             $69x - 60x = 207 -108$

                         $9x = 99\\x = 11$

• first number , $3x = 3\times 11 = 33$
• Second number ,$5x = 5 \times 11 = 55$

Hence , smallest number is $33$.