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 3 of 6.
Amritha said:
9 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).
Henry said:
1 decade ago
What amount of work are they to complete?
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.
Ash said:
9 years ago
Why 12*8 is taken? 12 days n 8 hrs =96hrs how it comes?
Please explain it.
Please explain it.
Justin Varghese said:
2 weeks 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.
Singham said:
8 years ago
If the equation is multiple with 1/8, then how could be possible that the is 5*5/11?
Supriya said:
8 years ago
We should take as 1/12 that means 1/n for every question noo. But in this question why we have taken as 12*8, why can't 1/12*8?
Anyone explain me.
Anyone explain me.
Hanmant said:
2 decades ago
How come 11/480?
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