Aptitude - Time and Work - Discussion

P can complete work in 12 days. So for one day he completes 1/12 work. But for one day he works only for 8 hours.

Similarly Q can complete work in 8 days. So for one day he completes 1/8 work. Q works 10 hours a day.

in question they have asked in how many days P and Q can complete the work if they work for 8 hours a day.

So for P already the given work is 8 hours a day and for Q it is 10 hours a day.

So just convert Q's work into 8 hours a day. The conversion is as follows

Q for one day he works for 10 hours and can complete the work in 8 days.
Q= 1/8 for 10 hrs.

Then for one hour it is (1/8)/10.
Q=1/80 for 1 hour.

So for 8 hours it is (1/80)*8= 1/10.
Now P+Q= 1/12+1/10.

Total work is 11/60.

So they can complete the given work in 60/11 days or 5 5/11 days.

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.

The total amount work done is 480/11, but we can not divide it by 8. Because P works for 8 hours a day and Q works for 10 hours a day.

Instead we have to calculate the amount of work done by P per day + amount of work done by Q per day, The take the reciprocal.

If we do that we get:

P = 1/96*8 = 1/12 units of work per day.

Q = 1/80*10 = 1/8 units of work per day.

Amount of work done By P+Q per day = 1/8 + 1/12 = 5/24.

Therefore to complete the entire work it will take 24/5 days.

That's equal to 4 4/5 days.

Ok now look at the theorem. as per the theorem if A does a work in x days and B does the same work in y days then total no of days taken by A&B to complete the same work is xy/x+y

Now for the question the equation would be (12*8)*(8*10)/ 12*8+10*8= 480/11

The answer obtained is in hrs, to convert this in no of days divide it by 8 as A/B does the work 8hrs in a day, now the answer becomes 60/11 which is the required answer..

Hope this will clear all the doubts.. :)

P's total work in hours = 12 day*8 hour = 96 hr.
P's 1 hour work = 1/96.

Q's total work in hours = 8 days*10 hours = 80 hr.
Q's 1 hour work = 1/80.

Now Both work only for 8 hours a day.

P's 8 hr work = 8* (1/96) = 1/12 (P's 1 day work).
Q's 8 hr work = 8* (1/80) = 1/10 (Q's 1 day work).

Now if P and Q work together in how many days they can complete the task.

= 1/ (1/p + 1/q).
= 1/ (1/12 + 1/10).
= 1/ (11/60).
= 60/11.

= (5*11+5) /11 in mixed fraction.

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)

B works for 10 hrs a day i.e 2 hrs more than A.
In days he works for 16 hrs more than A.
It is equal to 2 days' work of A.

If B works for 8 hrs a days he would take 8+2=10 days to complete the same work.

Work done by A per day = 1/12.
Work done by B per day = 1/10.

Work done by A and B together in 1 day = (1/12+1/10).
= 11/60.

So number of days required will be 60/11.

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)

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.

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.