Question

Two numbers are in the ratio $1\frac{1}{2}:2\frac{2}{3}$.When each one of these is increased by $15$, their ratio becomes $1\frac{1}{2}:2\frac{1}{2}$. The larger of the numbers is

• A. $60$
• B. $90$
• C. $160$
• D. $164$

Answer 1

Answer: (C)

$160$

Let the numbers be $\frac{3}{2}a;\frac{8}{3}a$.

When they are increased by $15$, their ratio is $\frac{3}{2}:\frac{5}{2}$
$\Rightarrow \frac{\frac{3}{2}a+15}{\frac{8}{3}a+15}=\frac{3}{2}:\frac{5}{2}$

$\Rightarrow \frac{\frac{3a+30}{2}}{\frac{8a+45}{3}}=\frac{3}{2}:\frac{5}{2}$

$\Rightarrow \frac{\left(3\right)(3a+30)}{2(8a+45)}=\frac{3}{5}$

$\Rightarrow \frac{(3a+30}{2(8a+45)}=\frac{1}{5}$

$\Rightarrow 15a+150=16a+90$

$\Rightarrow a=60$
So, the numbers are $\frac{3}{2}\times 60;\frac{8}{3}\times 60=90;160$.

Hence the answer is $160$.