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:
58 comments Page 2 of 6.
Justin Varghese said:
2 months ago
P needs 12 days | 8hrs per day.
Q need 8 days | 10hrs per day.
Consider that Q works only 8hrs per day.
So,
day-1: Q works 8hrs (remain 2hrs pending).
day-2: Q works 8hrs (remain 4hrs pending).
day-3: Q works 8hrs (remain 6hrs pending).
.
.
.
day-8: Q works 8hrs (remain 16hrs pending).
Since, we considered that Q works only 8 hours per day.
So the 16 pending hours can be considered 2 days (hope you understood)
therefore.
Q need 10 days | 8hrs per day.
P -> 12 days.
Q -> 10 days.
By taking LCM.
60 => total work.
12 * 5 = 60 ie, efficiency of P = 5.
10 * 6 = 60 ie, efficiency of Q = 6.
P + Q works together with efficiency 5 + 6 =11,
Time = Work/Efficiency.
=> 60/11.
= 5 5/11 is the answer.
Q need 8 days | 10hrs per day.
Consider that Q works only 8hrs per day.
So,
day-1: Q works 8hrs (remain 2hrs pending).
day-2: Q works 8hrs (remain 4hrs pending).
day-3: Q works 8hrs (remain 6hrs pending).
.
.
.
day-8: Q works 8hrs (remain 16hrs pending).
Since, we considered that Q works only 8 hours per day.
So the 16 pending hours can be considered 2 days (hope you understood)
therefore.
Q need 10 days | 8hrs per day.
P -> 12 days.
Q -> 10 days.
By taking LCM.
60 => total work.
12 * 5 = 60 ie, efficiency of P = 5.
10 * 6 = 60 ie, efficiency of Q = 6.
P + Q works together with efficiency 5 + 6 =11,
Time = Work/Efficiency.
=> 60/11.
= 5 5/11 is the answer.
(1)
Rajan said:
6 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)
Mr. Mp said:
9 years ago
480/11 is the total hours taken to complete.
Now in days we want, and in a day only 8 hours is worked as said in question
so, (480/11) / 8 nothing but (480/11)*1/8.
Still confused look at this I complete the work in 40 hours, the company says I can work only 10 hours per day, so how many days it took. nothing but 40/10 or 40 * (1/10) = 4 days.
Now in days we want, and in a day only 8 hours is worked as said in question
so, (480/11) / 8 nothing but (480/11)*1/8.
Still confused look at this I complete the work in 40 hours, the company says I can work only 10 hours per day, so how many days it took. nothing but 40/10 or 40 * (1/10) = 4 days.
(1)
Saniya said:
10 years ago
Why did 1/8 is taken in ratio but not the above hours?
(1)
Srikanth said:
2 decades ago
Why should we take 11/480 as 480/11 ?
Henry said:
1 decade ago
What amount of work are they to complete?
Sagarika said:
2 decades ago
We can do this by taking up the lcm of both's working hours to complete the task i.e., of 96 and 80 which comes to be 480.
So if the whole work is considered to be 480parts then P can complete in 480/96=5 days and Q can in 480/80=6 days and if they work together then 480/(5+6) days.
If they work 8 hours each then
=(480/11*1/8) days
= 480/88
= 5.454545.. or 5(5/11)
So if the whole work is considered to be 480parts then P can complete in 480/96=5 days and Q can in 480/80=6 days and if they work together then 480/(5+6) days.
If they work 8 hours each then
=(480/11*1/8) days
= 480/88
= 5.454545.. or 5(5/11)
Tuhinaa said:
10 years ago
The explanation is a bit lengthy. Is there any shortcut to solve it.
Bhagyasri said:
9 years ago
1-hour work of p and q is(1/12*8+1/8*10) = 11/480.
8-hours of work is (11/480)*8 = 11/60.
For example, 1 day work is 1/x days then the total number of days is x.
Similarly, 8 hours of work is 11/60 then the total number of days is 60/11.
8-hours of work is (11/480)*8 = 11/60.
For example, 1 day work is 1/x days then the total number of days is x.
Similarly, 8 hours of work is 11/60 then the total number of days is 60/11.
Hariom pundir said:
9 years ago
25 men take 20 days to finish some work, after every 10 days 5 men leave the work, then in how many days will the work be finished? Explain the answer.
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