10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank MCQs - Pair of Linear Equations in Two Variables

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

A) 48, 20

B) 40, 28

C) 40, 48

D) 20, 24

Correct Answer: C

Solution :

Let the two numbers be x and y.

Then, by first condition, ratio of these two numbers = 5 : 6

\[x:y\,=5\,:\,6\]

\[\Rightarrow \,\,\,\,\frac{x}{y}=\frac{5}{6}\,\,\Rightarrow y=\frac{6x}{5}\]

and by second condition, then, 8 is subtracted from each of the numbers, then ratio becomes 4:5.

\[\frac{x-8}{y-8}=\frac{4}{5}\]

\[\Rightarrow \,\,\,\,5x-40=4y-32\]

\[\Rightarrow \,\,\,5x-4y=8\] (ii)

Now, put the value of y in Eq. (ii), we get

\[5x-4\left( \frac{6x}{5} \right)=8\]

\[\Rightarrow \,\,\,25x-24x=40\]

\[\Rightarrow \,\,x=40\]

Put the value of x in Eq. (i), we get

\[y=\frac{6}{5}\times 40\]

\[=6\times 8=48\]

Hence, the required numbers are 40 and 48.