Question

Two numbers are in the ratio $3:5$. When each of these numbers is increased by $10$, their ratio becomes $5:7$. Find the greater number.

• A. $27$
• B. $15$
• C. $20$
• D. $25$

Answer 1

Answer: (D)

$25$

$\Rightarrow$ Let the first number is $x$, the second is $y$.Then $\frac{x}{y}=\frac{3}{5}$ , $3y=5x$

On the other hand $\frac{x+10}{y+10}=\frac{5}{7}$,hence $7(x+10)=5(y+10)$

We get that $3y=5x,7x+70=5y+50$

$3y=5x,5y=7x+20$

$y=\frac{5x}{3},y=\frac{7x+20}{5}$

$\therefore$ $\frac{5x}{3}=\frac{7x+20}{5}$

$25x=3(7x+20)$

$25x=21x+60$

$4x=60$

$\therefore$ $x=15$

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

$\therefore$ $x=15,y=25$

$\therefore$ The greater number is $25$.