Two numbers are such that the ratio between them is 3 : 5.
Question:

Two numbers are such that the ratio between them is 3 : 5. If each is increased by 10, the ratio between the new numbers so formed is 5 : 7. Find the original numbers.

Solution:

Let us consider x as the common multiple of both the number.

Then, first number = 3x

Second number = 5x

$\therefore \frac{3 x+10}{5 x+10}=\frac{5}{7}$

$\Rightarrow 7(3 x+10)=5(5 x+10) \quad$ (by cross multiplication)

$\Rightarrow 21 x+70=25 x+50$

$\Rightarrow 21 x-25 x=50-70$

$\Rightarrow-4 x=-20$

$\Rightarrow x=\frac{-20}{-4}=5$

Therefore, the common multiple of both the numbers is 5 .

First number $=3 x=3 \times 5=15$

Second number $=5 x=5 \times 5=25$