Question

In the following question, two equations numbered I and II are given. Solve both the equations and mark the appropriate option:

I. $\frac{3x-2}{y}=\frac{3x+6}{y+16}$
II. $\frac{x+2}{y+4}=\frac{x+5}{y+10}$

• A. if x > y
• B. if x < y
• C. if x ≥ y
• D. if x ≤ y
• E. if x = y or definite relationship cannot be established between ‘x’ and ‘y’

Answer 1

The correct option is B if x < y

On cross-multiplying equation (i),we get
$3xy-2y+48x-32=3xy+6y\to 6x-y=4.....\left(iii\right)$
On cross-multiplying equation (ii),we get
$xy+2y+10x+20=xy+5y+4x+20\to 2x=y.....\left(iv\right)$
Substiuting (iv) in (iii), we get
$x=1y=2$
Hence, $x<y.$