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?
5 5
11
5 6
11
6 5
11
6 6
11
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 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,

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.
(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)
(17)

Akshal said:   4 years ago
Hi @Joel.

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.
(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.
(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).
(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.
(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.
(22)


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