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.

Answer 1

Let us consider x as the common multiple of both the number.
Then, first number = 3x
Second number = 5x


$$\begin{gathered} \therefore \frac{3x+10}{5x+10}=\frac{5}{7} \\ \Rightarrow 7(3x+10)=5(5x+10)(\mathrm{by}\mathrm{cross}\mathrm{multiplication}) \\ \Rightarrow 21x+70=25x+50 \\ \Rightarrow 21x-25x=50-70 \\ \Rightarrow -4x=-20 \\ \Rightarrow x=\frac{-20}{-4}=5 \end{gathered}$$

Therefore, the common multiple of both the numbers is 5.
First number = $3x=3\times 5=15$
Second number = $5x=5\times 5=25$