P works thrice as fast as Q, whereas P and Q together can work four times as fast as R. If P, Q and R together work on a job, in what ratio should they share the earnings?

Correct Option: 3 : 1 : 1

Step-by-step Explanation:

The share of earnings for individuals working together on a job is directly proportional to their rates of work (or work capacities per unit of time).

Let the work rate of Q be $q$.

According to the question, P works thrice as fast as Q. Therefore, the work rate of P, denoted as $p$, is:

$p=3q$

Next, we are given that P and Q together can work four times as fast as R. Let the work rate of R be $r$. We can express this condition as:

$p+q=4r$

Substitute $p=3q$ into the equation:

$3q+q=4r$

$4q=4r$

Dividing both sides by 4 gives:

$r=q$

Now, we can express the work rates of P, Q, and R in terms of $q$:

$p:q:r=3q:q:q$

Dividing throughout by $q$, we get the ratio of their efficiency and earnings share:

$p:q:r=3:1:1$

Thus, P, Q, and R should share the earnings in the ratio 3 : 1 : 1.