Question

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

Answer 1

A] Let the two numbers be x,y

$\frac{x}{y}=\frac{3}{5}$

$\Rightarrow x=\frac{3}{5}y$

$\frac{x+10}{y+10}=\frac{5}{7}$

$=7x+70=5y+50$

$=7x+20=5y$

$=7x+20=5y=0$

$=7\left(\frac{3}{5}\right)y+20-5y=0$

$=21y+100-25y=0$

$=100-4y=0$

$=100=4y$

$\therefore y=25$

$x=\frac{3}{5}\times 25=15$

Thus numbers are 15,25