p alone can finish a job in 12 days while q can do so in 16 days. with the help of R they have finished the job in 4 days for a contract price of Rs 1200.How much should R get out of it?
Answers
Answer:
P can do a work in 12 days, therefore P can do 1/12 part of the work in one day and in 9 days P would complete...
1/12 x 9 = 9/12 or 3/4 part of the work.
The remaining part of the work is...
1 - 3/4 = 1/4 part or quarter of the whole work.
Now Q can do the whole work in 16 days, so Q can do 1/16 part of the work in 1 day.
The remaining part of work is 1/4, and to help P, to complete this portion of the work Q should join P, at certain points in time.
Q would take to complete 1/4 part of the work is.... 1/4 divided by 1/16 = 4 days.
Since P completes 3/4 part of the work in 9 days and Q can complete the balance work in 4 days, Q should join (9–4) 5 days after P had started the work.
5 days is the answer.
hope it helps
Given :-
- P alone can finish job in = 12 days.
- Q alone can finish in = 16 days.
- With the help of R, they have finished the job in 4 days for a contract price of 1,200.
To Find :-
- How much should R get out of it ?
Solution :-
LCM of 12 and 16 = 48 units = Let total work
so,
→ Efficiency of P = (Total work)/(Total days) = 48/12 = 4 units/day.
and,
→ Efficiency of Q = (Total work)/(Total days) = 48/16 = 3 units/day.
Now, Let us assume that , Efficiency of R is x units/day.
then,
→ 4(4 + 3 + x) = 48 units
→ 4 + 3 + x = 12
→ x = 12 - 7
→ x = 5 units/day .
Therefore, we can conclude that, they will get amount in the ratio of their efficiency .
hence,
→ Share of R = (5/12) * 1200 = Rs.500 (C) (Ans.)
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