Question

If $\frac{a}{10}$ = $\frac{b}{4}$ = $\frac{c}{6}$ = $\frac{4a-3b+9c}{x}$. Find the value of $x.$

• A. 82

Answer 1

The correct option is A 82
$\frac{a}{10}$ = $\frac{b}{4}$ = $\frac{c}{6}$ = $\frac{4a-3b+9c}{x}$.

Multiply numerator and denominator of $\frac{a}{10}$ by 4, it becomes: $\frac{4a}{40}$ ....... (1)

Multiply numerator and denominator of $\frac{b}{4}$ by -3, it becomes$\frac{-3b}{-12}$ ...... (2)

Multiply numerator and denominator of $\frac{c}{6}$ by 9, it becomes: $\frac{9c}{54}$ ...... (3)

As per the theorem of equivalent ratio and using (1), (2) and (3),
Theorem used: $\frac{a}{b}=\frac{c}{d}$, then $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\frac{al+cm+dn}{bl+dm+en}$

$⟹$ $\frac{4a-3b+9c}{40-12+54}$= $\frac{4a-3b+9c}{x}$.

Hence, $x$ = 82.