# p can complete a work in 12 days working 10 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?

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## 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?

Click here👆to get an answer to your question ✍️ 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?

Question

## 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?

**A**5

11 5

**B**5

11 6

**C**6

11 5

**D**6

11 6 Medium Open in App

Updated on : 2022-09-05

Solution Verified by Toppr

Correct option is A)

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 =1/96

and Q's 1 hour's work =1/80

(P + Q)'s 1 hour's work =

W= 80 1 + 96 1 = 480 11

So, both P and Q will finish the work in480/11hrs.

W(8)= 11 480 8= 11 60 =5 11 5 Days Answer (A) 5 11 5 Days

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## Time and Work

This is the aptitude questions and answers with discussion section on "Time and Work" with explanation for various interview, competitive examination and entrance test. Solved examples with detailed answer description, explanation are given and it would be easy to understand - Discussion page for Q.398.

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## Aptitude :: Time and Work - Discussion

Home » Aptitude » Time and Work » General Questions - Discussion

### Discussion :: Time and Work - General Questions (Q.No.14)

Time and Work - Important Formulas

«« Time and Work - General Questions

Time and Work - Data Sufficiency 1

Time and Work - Data Sufficiency 2

Time and Work - Data Sufficiency 3

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?

[A]. 5 5 11 [B]. 5 6 11 [C]. 6 5 11 [D]. 6 6 11 Answer: Option A 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 Workspace Report

Hanmant said: (Jun 1, 2010)

How come 11/480?

Suresh said: (Jun 9, 2010)

How come 5 5/11 days from 60/11?

Deepak said: (Jun 16, 2010)

How come 11/480?

Manisha said: (Jun 30, 2010)

11/480 is the addition of 1/96+1/80

(1*5)/(96*5)+(1*6)/(80*6)=5/480+6/480=11/480

Asha said: (Jul 8, 2010)

When we divide 60 by 11 the quotient is 5 and the remainder is 5 11 is the divisor? so 5 5/11.

Nagu said: (Jul 12, 2010)

Hi all

we can write 60/11 = (5*11+5)/11

= (55+11)/11

it is same as 5 5/11 here first first 5 is quocient and senocd 5 is remainder and 11 is deviser

Neha said: (Aug 1, 2010)

Why multiplied by (1/8)?

Rani Maria said: (Aug 3, 2010)

Take the LCM of 96,80 then we get 480.

then 1/96 * 480 + 1/80 *480 = 5/480 + 6/480 = 11/480.

Chintan said: (Aug 7, 2010)

Neha. . They work to gather 8 hours in 1 day that is shown in que. So ans mult. By 1/8

Supriya said: (Aug 22, 2010)

How can we solve this 480/11 * 1/8..and how came the ans 60/11 ?

SrinivasaReddy said: (Aug 31, 2010)

P can do the work in 12days. He do per day 8 hours.

P can do work in total hours is:96.

Same as Q can do work in:80hours.

P's one day work is:1/96.

Q's one day work is:1/80.

P+q one day work is:1/96+1/80=11/480.

P+q work is:480/11.

P+q can done 8 hours per day:480/11*1/8.

Srikanth said: (Sep 7, 2010)

Why should we take 11/480 as 480/11 ?

Akila said: (Sep 17, 2010)

11/480 is the part of work completed in 1 hour.

If we reverse it we can get time.

Sagarika said: (Oct 3, 2010)

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)

Shridhar said: (Nov 26, 2010)

Sagarika your explaination is very nice.

Shekha said: (Dec 10, 2010)

Sagarika your explanation is very simple. And Rani maria thanks for thinking me simple.

Sikha said: (Dec 18, 2010)

Why multipled by 1/8 not 8?

Anshik said: (Jan 12, 2011)

Why multiplied by 1/8 and not 8 ?

Nagarjun said: (Jan 14, 2011)

@sikha,anshik

for 1 day they work 8hrs

for x days they work 480/11 hrs

so x=(480/11)*(1/8) thats it....

Sourya said: (Jul 18, 2011)

They worked 8 hours for 1 day

" " 1 " " 1/8 day

So, 480/11 " " (480/11)*1/8 day= 60/11 days= 5 5/11

Deeps said: (Aug 17, 2011)

Why should we take the reverse of 480/11 and multiply?

Why shouldnt we directly multiply?

Sush said: (Aug 26, 2011)

@Deeps

For 1hr-11/480th part of work is done.

So, to complete whole work it'll take 480/11hrs.

Eg:

For 1hr-1/4th f work

For xhr-1(whole) work..? x=4hrs.

Just take it to the l.h.s from r.h.s thats it.

Hope you are clear now...:)

Asha said: (Sep 16, 2011)

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.. :)

Jitendra Gupta said: (Mar 28, 2012)

We can simply do the following!

Convert both the person's work into days bringing the same hours/day so the Man Days remain unchanged!!

Where P works 8 hour/Day working 12 Days= Man Days 96

Where Q works 8 hours / Day working 10 days= Man days 80

Now 1/10 + 1/12

So 11/60 per day work by both

so 60/11 = 5 5/11

Baljeet said: (May 1, 2012)

Good jitendra.

Dileep said: (Aug 23, 2013)

## [Solved] P can complete a work in 12 days working 8 hours a day. Q ca

Given: 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. Both P and Q work togeth

Home Quantitative Aptitude Time and Work

## Question

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5611 5511 6611 6511

## Answer (Detailed Solution Below)

Option 2 : 5511

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## Detailed Solution

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**Given:**

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.

Both P and Q work together, working 8 hours a day.

**Concept Used:**

Total work = Number of days × Efficiency

**Calculation:**

Work done by P = 12 × 8 = 96 units.

Work done by Q = 8 × 10 = 80 units.

Total work = LCM of 96 and 80.

Total work = 480 units.

Efficiency of P = 480/96 = 5 unit.

Efficiency of Q = 480/80 = 6 unit.

Both P and Q work together, working 8 hours a day.

P and Q will finish the work in 480 / (5 + 6) × 8.

⇒ 480/88 ⇒ 60/11 = 5511 days.

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## More Time and Work Questions

**Q1.**A certain work was completed by A in 9 days, B in 12 days, C in 15 days, If A and C did work for 4 days and then leftt, then B will finishes rest work in how many days?

**Q2.**The efficiencies of A, B and C are in the ratio 2 ∶ 3 ∶ 4. They together can complete a piece of work in 6 days. In how many days A alone can complete that same piece of work?

**Q3.**A work may be completed in 10 days, if x, y and z work together. All three started work together. x left after 4 days, then y and z completed the remaining work by taking 10 more days. In how many days could x complete the whole work alone?

**Q4.**A takes 8 hours to copy a 50-page manuscript while B can copy the same manuscript in 6 hours. How many hours would it take them to copy a similar 100-page manuscript, if they work together?

**Q5.**15 men, 18 women and 12 boys working together earned ₹2070 in a day. If the daily wages of a man, a woman and a boy are in the ratio of 4 ∶ 3 ∶ 2, the daily wages (in ₹) of 1 man, 2 women and 3 boys are :

**Q6.**A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of work that is left, is :

**Q7.**A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?

**Q8.**A man and a boy together can do a certain amount of digging in 40 days. Their speeds in digging are in the ratio 8 ∶ 5. How many days will the boy take to complete the work if engaged alone?

**Q9.**A is twice as good a workman as B and together they finish a piece of work in 14 days less than B. Working together, they can do it in :

**Q10.**A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together?

Guys, does anyone know the answer?