Question

One-third of Mathew's money is equal to one-fourth of Linda's money. If both together have $600 less than Paul, who has thrice as much money as Mathew, what is the total money with Mathew and Linda?

• A. $1200
• B. $2100
• C. $1500
• D. $900

Answer 1

The correct option is B $2100

Let
Money with Mathew = x
Money with Linda = y

One-third of Mathew's money is equal to one-fourth of Linda's money.

So, we see:
$\frac{1}{3}\times x=\frac{1}{4}\times y$
$\Rightarrow y=\frac{4x}{3}$

Paul has thrice as much money as Mathew.

So,
Money with Paul = 3x

Now, both Mathew and Linda have $\$600$ less than Paul.

So, according to the condition, we get:
$3x–600=x+y$
$\Rightarrow 3x–600=x+\frac{4x}{3}$
$\Rightarrow 3x–600=\frac{7x}{3}$
$\Rightarrow 3x–\frac{7x}{3}=600$
$\Rightarrow \frac{2x}{3}=600$
$\Rightarrow x=\frac{600\times 3}{2}$
$\Rightarrow x=900$

And, value of y is:
$y=\frac{4\times 900}{3}$
$\Rightarrow y=1200$

So, the total money present with Mathew and Linda is
$=\$900+\$1200$
$=\$2100$