Question

two number are in ratio 5:6 when 2 is added to first and 3 is added to second ,they are in ration 4:5. find the number

Answer 1

Hi there !!
Here's your answer.


Let the common factor be x
1st number = 5x
2nd number = 6x

Given,
when 2 is added to first and 3 is added to second ,they are in ration 4:5

so, we have the following equation


$\frac{5x + 2}{6x + 3} = \frac{4}{5}$
Cross multiplying, we have,


$5(5x + 2) = 4(6x + 3)$
removing and multiplying the brackets,
we have

$25x + 10 = 24x + 12$


$25x - 24x = 12 - 10$

$x = 2$


So,

1st number = 5x = 5 × 2 = 10
2nd Number = 6x = 6 × 2 = 12


Thus ,


The numbers are 10 and 12

Answer 2

let the first number be 5x
another number be 6x
A.T.Q.
5x+2/6x+3=4/5
By cross multiplication;
5 (5x+2)=4 (6x+3)
25x+10=24x+12
transposing 24
25x-24x=12-10
x=2
first number=5x=5×2=10
second number=6x= 6×2=12