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 $=5 x=5 \times 5=25$