P takes 10 days and Q takes 24 days to complete a work. With the help of R, they all work together and finish it in 6 days. Find the payment they receive out of a total remuneration of Rs.1000.

Correct option is C

Given:

P's time to complete the work = 10 days
Q's time to complete the work = 24 days
Together with R, they complete the work in 6 days
Total remuneration = Rs. 1000

Formula Used:

The amount of work done per day by each person is the reciprocal of the number of days they take to complete the work.
Work done by P per day = 1/10
Work done by Q per day = 1/24
Let R's work done per day be 1/x.
Total work done per day by P, Q, and R together = 1/6.

Solution:

Set up the equation for their combined work

.$$\frac{1}{10} + \frac{1}{24} + \frac{1}{x} = \frac{1}{6} \\\ \\\frac{12}{120} + \frac{5}{120} + \frac{1}{x} = \frac{20}{120} \\\ \\\Rightarrow \frac{17}{120} + \frac{1}{x} = \frac{20}{120} \\\ \\\Rightarrow \frac{1}{x} = \frac{20}{120} - \frac{17}{120} \\\ \\\Rightarrow \frac{1}{x} = \frac{3}{120} \\\ \\\Rightarrow x = 40$$​​

So, R takes 40 days to complete the work alone.

the total work done by each person in 6 days.
P's work = (1/10) × 6 = 0.6
Q's work = (1/24) × 6 = 0.25
R's work = (1/40) × 6 = 0.15

the payments based on the work done.
Total work done = 0.6 + 0.25 + 0.15 = 1

P's share of the payment = 0.6 × 1000 = Rs.600

Q's share of the payment = 0.25 × 1000 = Rs.250
R's share of the payment = 0.15 × 1000 = Rs.150

P receives Rs.600, Q receives Rs.250, and R receives Rs.150.

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