Aptitude - Time and Work - Discussion

@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,

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.

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)

Hi @Joel.

How did you assume 10 days and 8 hours? Please explain.

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.

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.

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 = 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).

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.

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.