P and Q can do a project in 25 and 50 days respectively. In how many days can they complete 18% of the project if they work together?
- A6 days
- B3 days
- C12 days
- D9 days
Solution & Step-by-step Explanation
Let total work be the LCM of 25 and 50, which is 50 units.
Efficiency of P =
25
50
=2 units/day
Efficiency of Q =
50
50
=1 unit/day
Total efficiency of P + Q = 2+1=3 units/day
We need to find the time taken to complete 18% of the total work:
Work to be done=18% of 50=
100
18
×50=9 units
Time taken by P and Q together:
Time=
Total efficiency
Work to be done
=
3
9
=3 days
Efficiency of P =
25
50
=2 units/day
Efficiency of Q =
50
50
=1 unit/day
Total efficiency of P + Q = 2+1=3 units/day
We need to find the time taken to complete 18% of the total work:
Work to be done=18% of 50=
100
18
×50=9 units
Time taken by P and Q together:
Time=
Total efficiency
Work to be done
=
3
9
=3 days