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P works twice as fast as Q, whereas P and Q together can work three times as fast as R. If P, Q and R together work on a job, in what ratio should they share the earnings?
- a)2:1:1
- b)4:2:1
- c)4:3:2
- d)4:2:3
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
P works twice as fast as Q, whereas P and Q together can work three ti...
If P is taking 3 days to do some work, then Q takes 6 days to do the same work. Now, both of them will take 2 days to complete the work. So, R takes 6 days to complete the same work.
Hence, earning should be distributed in the ratio of their efficiency, i.e., 2 : 1 : 1.
Hence, earning should be distributed in the ratio of their efficiency, i.e., 2 : 1 : 1.
Most Upvoted Answer
P works twice as fast as Q, whereas P and Q together can work three ti...
To solve this problem, we can use the concept of work and efficiency. Let's assume that Q can complete the work in 'x' days, which means that P can complete the same work in 'x/2' days.
Let's calculate the work done by each person in a day:
- P's work per day = 1/(x/2) = 2/x
- Q's work per day = 1/x
- R's work per day = 1/(3(x/2)) = 2/3x
Now, let's calculate the combined work done by P, Q, and R together in a day:
- (P + Q + R)'s work per day = (2/x) + (1/x) + (2/3x) = (6 + 3 + 4)/3x = 13/3x
We know that (P + Q + R) together can complete 1 work in 1 day, so we can equate the combined work done by P, Q, and R to 1 and solve for 'x':
13/3x = 1
13x = 3
x = 3/13
Now, let's find the ratio in which they should share the earnings:
- P's share = (2/x) / [(2/x) + (1/x) + (2/3x)] = (2/(3/13)) / [(2/(3/13)) + (1/(3/13)) + (2/(9/13))] = (2 * 13/3) / [(2 * 13/3) + (1 * 13/3) + (2 * 13/9)] = (26/3) / [(26/3) + (13/3) + (26/9)] = (26/3) / (26/3 + 13/3 + 26/9) = (26/3) / (78/9 + 39/3 + 26/9) = (26/3) / (143/9) = (26/3) * (9/143) = 2/11
- Q's share = (1/x) / [(2/x) + (1/x) + (2/3x)] = (1/(3/13)) / [(2/(3/13)) + (1/(3/13)) + (2/(9/13))] = (1 * 13/3) / [(2 * 13/3) + (1 * 13/3) + (2 * 13/9)] = (13/3) / [(26/3) + (13/3) + (26/9)] = (13/3) / (78/9 + 39/3 + 26/9) = (13/3) / (143/9) = (13/3) * (9/143) = 1/11
- R's share = (2/3x) / [(2/x) + (1/x) + (2/3x)] = (2/(9/13)) / [(2/(3/13)) + (1/(3/13)) + (2/(9/13))] = (2 * 13/9) / [(2 * 13
Let's calculate the work done by each person in a day:
- P's work per day = 1/(x/2) = 2/x
- Q's work per day = 1/x
- R's work per day = 1/(3(x/2)) = 2/3x
Now, let's calculate the combined work done by P, Q, and R together in a day:
- (P + Q + R)'s work per day = (2/x) + (1/x) + (2/3x) = (6 + 3 + 4)/3x = 13/3x
We know that (P + Q + R) together can complete 1 work in 1 day, so we can equate the combined work done by P, Q, and R to 1 and solve for 'x':
13/3x = 1
13x = 3
x = 3/13
Now, let's find the ratio in which they should share the earnings:
- P's share = (2/x) / [(2/x) + (1/x) + (2/3x)] = (2/(3/13)) / [(2/(3/13)) + (1/(3/13)) + (2/(9/13))] = (2 * 13/3) / [(2 * 13/3) + (1 * 13/3) + (2 * 13/9)] = (26/3) / [(26/3) + (13/3) + (26/9)] = (26/3) / (26/3 + 13/3 + 26/9) = (26/3) / (78/9 + 39/3 + 26/9) = (26/3) / (143/9) = (26/3) * (9/143) = 2/11
- Q's share = (1/x) / [(2/x) + (1/x) + (2/3x)] = (1/(3/13)) / [(2/(3/13)) + (1/(3/13)) + (2/(9/13))] = (1 * 13/3) / [(2 * 13/3) + (1 * 13/3) + (2 * 13/9)] = (13/3) / [(26/3) + (13/3) + (26/9)] = (13/3) / (78/9 + 39/3 + 26/9) = (13/3) / (143/9) = (13/3) * (9/143) = 1/11
- R's share = (2/3x) / [(2/x) + (1/x) + (2/3x)] = (2/(9/13)) / [(2/(3/13)) + (1/(3/13)) + (2/(9/13))] = (2 * 13/9) / [(2 * 13
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