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.
![]() |
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 |
![]() |
![]() |
480 | x | 1 | ![]() |
= | 60 | days = 5 | 5 | days. |
11 | 8 | 11 | 11 |
Discussion:
57 comments Page 1 of 6.
SARAN KUMR said:
4 weeks ago
@Nav Raj Bhatta.
To make it easy to calculate, we can divide both by 8.
Now P = 96/8 = 12,
and Q=80/8=10,
To make it easy to calculate, we can divide both by 8.
Now P = 96/8 = 12,
and Q=80/8=10,
Ravalisai Enugandula said:
1 year ago
P->1day work=1/12, 8 hrs per day.
Q->1day work=1/8, 10 hours per day.
Now they are working together for 8 hours per day.
So Q will have extra 2 hours which becomes=8*2.
Now Q can finish work in 10 days, 8 hours per day.
Q->1 day work = 1/10.
Now 1/12 + 1/10 = 11/60.
So, they finish it in 60/11 days to finish the work if they work 8 hours per day.
Q->1day work=1/8, 10 hours per day.
Now they are working together for 8 hours per day.
So Q will have extra 2 hours which becomes=8*2.
Now Q can finish work in 10 days, 8 hours per day.
Q->1 day work = 1/10.
Now 1/12 + 1/10 = 11/60.
So, they finish it in 60/11 days to finish the work if they work 8 hours per day.
(2)
Nav Raj Bhatta said:
4 years ago
Total time taken by P = 12 * 8 = 96 hrs.
Total time taken by Q = 8 * 10 = 80 hrs.
To make easy to calculate we can divide both by 8.
now P=96/8=12,
and Q=80/8=10,
The time is taken by P and Q together =p*q/p+q=120/22 = 5(10/22) = 5(5/11).
Another method;
p = 12
q = 10.
LCM of 10 and 12 = 60 (total work).
Per day work of P = 60/12 = 5.
And Q = 60/10 = 6.
per day work of P and Q = 5+6 = 11.
Required time = 60/11 = 5(5/11)
Total time taken by Q = 8 * 10 = 80 hrs.
To make easy to calculate we can divide both by 8.
now P=96/8=12,
and Q=80/8=10,
The time is taken by P and Q together =p*q/p+q=120/22 = 5(10/22) = 5(5/11).
Another method;
p = 12
q = 10.
LCM of 10 and 12 = 60 (total work).
Per day work of P = 60/12 = 5.
And Q = 60/10 = 6.
per day work of P and Q = 5+6 = 11.
Required time = 60/11 = 5(5/11)
(17)
Akshal said:
4 years ago
Hi @Joel.
How did you assume 10 days and 8 hours? Please explain.
How did you assume 10 days and 8 hours? Please explain.
(3)
Joel said:
4 years ago
Easy method I will explain.
p --- 12 days ---- 8 hours
q --- 8 days ---- 10 hours.
q will do work in 10 days working for 8 hours. Got it?????
If working hours decreased days will increase.
so if hours decreased from 10 to 8=2 hours decreased
so he needs extra 2 hours to complete the remaining.
so, q-----10 days---8 hours.
Now total days are 12 days and 10 days.
taking lcm of these,
60 units of total work.
P -- one day's work is 60/12=5 units.
q----one day's work is 60/10=6 units.
p+q one days work = 11 units.
So they complete work in 60/ 11 days,
=5(5/11)days.
p --- 12 days ---- 8 hours
q --- 8 days ---- 10 hours.
q will do work in 10 days working for 8 hours. Got it?????
If working hours decreased days will increase.
so if hours decreased from 10 to 8=2 hours decreased
so he needs extra 2 hours to complete the remaining.
so, q-----10 days---8 hours.
Now total days are 12 days and 10 days.
taking lcm of these,
60 units of total work.
P -- one day's work is 60/12=5 units.
q----one day's work is 60/10=6 units.
p+q one days work = 11 units.
So they complete work in 60/ 11 days,
=5(5/11)days.
(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)
Swapnil phulari said:
5 years ago
P = 1/12 Q = 1/10.
P + Q = 1/12 + 1/10 = 11/60 i.e 1Day work.
And n day work = 60/11 = 5 5/11.
P + Q = 1/12 + 1/10 = 11/60 i.e 1Day work.
And n day work = 60/11 = 5 5/11.
(19)
Jaydeep Lalakiya said:
5 years ago
P = 12 days = 8 hours, hence P = 1/12 --> (i)
Q = 8 days = 10 hours.
So Q works 10 hours for 8 days so how many days he will take if he works for 8 hours only?
=8*10/8 = 10 days hence Q = 1/10--> (ii)
So now if both work together 1/12+1/10 = 11/60, (5 * 5/11 would be the answer).
Q = 8 days = 10 hours.
So Q works 10 hours for 8 days so how many days he will take if he works for 8 hours only?
=8*10/8 = 10 days hence Q = 1/10--> (ii)
So now if both work together 1/12+1/10 = 11/60, (5 * 5/11 would be the answer).
(5)
Ashwini said:
6 years ago
1/12+1/10 = 11/60.
Total work done in 60/11 days.
60/11 = 5 5/11.
No need to consider hours directly can solve by considering no.of days worked.
Total work done in 60/11 days.
60/11 = 5 5/11.
No need to consider hours directly can solve by considering no.of days worked.
(4)
Jakrik said:
6 years ago
p to complete eating chocolate(12*8)=96hrs (work=chocolate).
q to complete eating chocolate(10*8)=80 hrs.
LCM of 96&80=480.
p->5 chocolates/hr(480/96).
Q->6 chocolates/hr(480/80).
In 1 hour = 5+6 = 11 chocolates.
8 hour =11 * 8 = 88(in one day)
Total chocolates = 480.
Days taken to complete = 480/88 = 60/11 = 5 5/11.
q to complete eating chocolate(10*8)=80 hrs.
LCM of 96&80=480.
p->5 chocolates/hr(480/96).
Q->6 chocolates/hr(480/80).
In 1 hour = 5+6 = 11 chocolates.
8 hour =11 * 8 = 88(in one day)
Total chocolates = 480.
Days taken to complete = 480/88 = 60/11 = 5 5/11.
(22)
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