Question

Paul and Mathew are earning in the ratio of 3 : 4, and Mathew and Linda are earning in the ratio of 7 : m. If Linda earns $100 more than Mathew and $198 more than Paul, then what is the value of m?

• A. $7$
• B. $\frac{107}{56}$
• C. $9$
• D. $\frac{111}{14}$

Answer 1

The correct option is B $\frac{107}{56}$

Paul and Mathew earn in the ratio
of 3 : 4

Let's assume:
Paul earns = 3x
Mathew earns = 4x

Mathew and Linda earns in the ratio
of 7 : m

Let's assume:
Mathew earns = 7y
Linda earns = my

So, we can write, for Mathew's earning:

$4x=7y$
$\Rightarrow x=\frac{7y}{4}$

Linda earns $100 more than Mathew
$\text{m}y=100+7y\text{--- equation (i)}$

Linda earns $198 more than Paul
$\text{m}y=198+3x$
$\Rightarrow \text{m}y=198+3\times \frac{7y}{4}\text{-- equation (ii)}$

Equating equation (i) and (ii):

$100+7y=198+3\times \frac{7y}{4}$

$\Rightarrow 7y-\frac{21y}{4}=198-100$

$\Rightarrow \frac{28y-21y}{4}=98$

$\Rightarrow \frac{7y}{4}=98$

$\Rightarrow y=56$

Equation (i)
$\text{m}y=100+7y$
$\Rightarrow \text{m}=\frac{100}{56}+\frac{7}{56}$

$\Rightarrow \text{m}=\frac{25}{14}+\frac{1}{8}$

$\Rightarrow \text{m}=\frac{107}{56}$