Question

Two numbers are in the ratio $5:6$ and if $4$ is subtracted from each, they are reduced to $2:3$, then the greater number is

• A. $4$
• B. $12$
• C. $8$
• D. $10$

Answer 1

The correct option is C $8$

Let the largest number be $6x$ and smaller number be $5x$.

No according to problem, we have

$\frac{5x-4}{6x-4}=\frac{2}{3}$

$\Rightarrow 3(5x-4)=2(6x-4)$

$\Rightarrow 15x-12=12x-8$

$\Rightarrow 15x-12x=-8+12$

$\Rightarrow 3x=4$

$\Rightarrow x=\frac{4}{3}$

Therefore, the greater number is $6x=6\times \frac{4}{3}=8$.