Question : If $x:y=3:4$, then $4x+5y:5x–2y=?$
Option 1: $7:32$
Option 2: $32:7$
Option 3: $4:3$
Option 4: $5:2$
Correct Answer: $32:7$
Solution :
Given: $x:y=3:4$ --------------------------------(1)
Or, $\frac{x}{y}=\frac{3}{4}$
Now, $(4x+5y):(5x–2y)$
Dividing by $y$ in the numerator and the denominator, we get,
$[4(\frac{x}{y})+5]:[5(\frac{x}{y})–2]$
= $[4(\frac{3}{4})+5:5(\frac{3}{4})–2]$ (Putting the value of $\frac{x}{y}$ from equation 1)
= $(3+5):(\frac{15}{4}–2)$
= $8:(\frac{15–8}{4})$
= $8:\frac{7}{4}$
= $32:7$
Hence, the correct answer is $32:7$.
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