Question

Two numbers are in ratio 5 : 6. when 2 is added to first and 3 is added to second, the ratio becomes 4:5. Find the numbers.​

Answer 1

Step-by-step explanation:

Ratio in two numbers =5:6

Let first number =5x

Then second number =6x

Adding 2 in the first and 34 in the second

A=5x+2

B=6x+3

6x+3

5x+2

$\frac{5x + 2}{6x + 2} = \frac{4}{5}$

25x+10=24x+12

25x−24x=12−10

x=2

First number =5x=5×2=10

and second =6x=6×2=12

Answer 2

To find : numbers given in ratio

Solution :

given :  Two numbers are in ratio $5 : 6$

let, first number be :   $5x$

      second number be : $6x$

according to question we are given following conditions :

when,

condition (i) 2 is added to first number $5x$ i.e. $5x + 2$

condition (ii) 3 is added to second number  $6x$ i.e. $6x + 3$

then , ratio becomes $4 : 5$

i.e.          $\frac{5x + 2 }{6x + 3} = \frac{4}{5}$

solving further by cross multiplying terms

             $5 ( 5x + 2 ) = 4 ( 6x + 3 )$

             $25x + 10 = 24x + 12$

transfering like terms we get,

              $25x - 24x = 12 -10$

                            $x = 2$

Now substituting value of x in  numbers given in ratio :

first number :  $5x = 5 ( 2 ) = 10$

second number : $6x = 6 ( 2) = 12$

Hence 10 and 12 are the original numbers in ratio.