Aptitude - Time and Work - Discussion
Discussion Forum : Time and Work - General Questions (Q.No. 14)
14.
P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?
Answer: Option
Explanation:
P can complete the work in (12 x 8) hrs. = 96 hrs.
Q can complete the work in (8 x 10) hrs. = 80 hrs.
 P's1 hour's work = |
1 | and Q's 1 hour's work = | 1 | . |
| 96 | 80 |
| (P + Q)'s 1 hour's work = |  |
1 | + | 1 |  |
= | 11 | . |
| 96 | 80 | 480 |
| So, both P and Q will finish the work in | |
480 | |
hrs. |
| 11 |
| Number of days of 8 hours each = |
|
480 | x | 1 | |
= | 60 | days = 5 | 5 | days. |
| 11 | 8 | 11 | 11 |
Discussion:
57 comments Page 2 of 6.
Rajan said:
5 years ago
I want to know they work 8 hrs a day together, what it means they individual work for 8-8 hrs or their combined work is 8 hrs a day? Please, anyone, tell me.
(1)
James Bond said:
1 decade ago
P's total work in hours = 12 day*8 hour = 96 hr.
P's 1 hour work = 1/96.
Q's total work in hours = 8 days*10 hours = 80 hr.
Q's 1 hour work = 1/80.
Now Both work only for 8 hours a day.
P's 8 hr work = 8* (1/96) = 1/12 (P's 1 day work).
Q's 8 hr work = 8* (1/80) = 1/10 (Q's 1 day work).
Now if P and Q work together in how many days they can complete the task.
= 1/ (1/p + 1/q).
= 1/ (1/12 + 1/10).
= 1/ (11/60).
= 60/11.
= (5*11+5) /11 in mixed fraction.
P's 1 hour work = 1/96.
Q's total work in hours = 8 days*10 hours = 80 hr.
Q's 1 hour work = 1/80.
Now Both work only for 8 hours a day.
P's 8 hr work = 8* (1/96) = 1/12 (P's 1 day work).
Q's 8 hr work = 8* (1/80) = 1/10 (Q's 1 day work).
Now if P and Q work together in how many days they can complete the task.
= 1/ (1/p + 1/q).
= 1/ (1/12 + 1/10).
= 1/ (11/60).
= 60/11.
= (5*11+5) /11 in mixed fraction.
Avinash said:
1 decade ago
Why we are taking (12*8) instead of (1/12*8)? As though taken in previous sums.
Deepak Patgar said:
1 decade ago
B works for 10 hrs a day i.e 2 hrs more than A.
In days he works for 16 hrs more than A.
It is equal to 2 days' work of A.
If B works for 8 hrs a days he would take 8+2=10 days to complete the same work.
Work done by A per day = 1/12.
Work done by B per day = 1/10.
Work done by A and B together in 1 day = (1/12+1/10).
= 11/60.
So number of days required will be 60/11.
In days he works for 16 hrs more than A.
It is equal to 2 days' work of A.
If B works for 8 hrs a days he would take 8+2=10 days to complete the same work.
Work done by A per day = 1/12.
Work done by B per day = 1/10.
Work done by A and B together in 1 day = (1/12+1/10).
= 11/60.
So number of days required will be 60/11.
Nabil said:
1 decade ago
No need to take hours in picture because number of hours are same.
Simple ab/a+b.
Where a=12 & b=10.
Thank you.
Simple ab/a+b.
Where a=12 & b=10.
Thank you.
Mishi said:
1 decade ago
P 12 days, 8 hours = 96. Q = 8 days, 10 hours, = 80.
P works 12 days in 8 days.
Q = 80/8 = 10 days.
= 1/12+1/10 = 60/11.
P works 12 days in 8 days.
Q = 80/8 = 10 days.
= 1/12+1/10 = 60/11.
Anjali sharma said:
1 decade ago
Very easy question no any doubt.
ARCHANA said:
1 decade ago
I could not understand this question can anyone explain it please.
Nagesh G S said:
1 decade ago
The total amount work done is 480/11, but we can not divide it by 8. Because P works for 8 hours a day and Q works for 10 hours a day.
Instead we have to calculate the amount of work done by P per day + amount of work done by Q per day, The take the reciprocal.
If we do that we get:
P = 1/96*8 = 1/12 units of work per day.
Q = 1/80*10 = 1/8 units of work per day.
Amount of work done By P+Q per day = 1/8 + 1/12 = 5/24.
Therefore to complete the entire work it will take 24/5 days.
That's equal to 4 4/5 days.
Instead we have to calculate the amount of work done by P per day + amount of work done by Q per day, The take the reciprocal.
If we do that we get:
P = 1/96*8 = 1/12 units of work per day.
Q = 1/80*10 = 1/8 units of work per day.
Amount of work done By P+Q per day = 1/8 + 1/12 = 5/24.
Therefore to complete the entire work it will take 24/5 days.
That's equal to 4 4/5 days.
Amritha said:
8 years ago
@Ash
For 1 day P works for 8hours, then for 12 days (Since P completes the work in 12days.), the total no of hours is 96 hours(12 * 8).
For 1 day P works for 8hours, then for 12 days (Since P completes the work in 12days.), the total no of hours is 96 hours(12 * 8).
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