Question

Two numbers are in the ratio $5:6$. If $8$ is subtracted from each of the numbers, the ratio becomes $4:5$. Find the numbers.

• A. $35,21$
• B. $67,32$
• C. $40,48$
• D. $50,25$

Answer 1

The correct option is C $40,48$

Let the two numbers be $x$ and $y$.

It is given that two numbers are in the ratio 5:6 that is:

$\frac{x}{y}=\frac{5}{6}\Rightarrow 6x-5y=\mathrm{0............}\left(1\right)$

Also it is given that if 8 is subtracted from each of the numbers, the ratio becomes 4:5 that is:

$\frac{x-8}{y-8}=\frac{4}{5}\Rightarrow 5x-40=4y-32\Rightarrow 5x-4y=\mathrm{8............}\left(2\right)$

Multiplying equation 1 by $5$ and equation 2 by $6$ we get,

$30x-25y=0..........\left(3\right)$

$30x-24y=48..........\left(4\right)$

Now subtracting equation 3 from equation 4, we get

$-y=-48$

$\Rightarrow y=48$

Substitute the value of $y$ in equation 1 as follows:

$6x-(5\times 48)=0\Rightarrow 6x-240=0\Rightarrow 6x=240\Rightarrow x=40$

Hence, the numbers are $40$ and $48$..