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# g and h complete a work in 6 days. a alone can do it in 10 days. if both together can do the work in how many days?

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## [Solved] A and B complete a work in 6 days. If A alone can do the sam

Given: Time taken by A and B = 6 days Time taken by A = 10 days Formula used: Total work = Time taken × Efficiency Calculation: L.C.M of (6 and

Home Quantitative Aptitude Time and Work Work Efficiency

## A and B complete a work in 6 days. If A alone can do the same work in 10 days then B alone will do it in how many days?

8 days 12 days 16 days 15 days

None of the above/More than one of the above

Option 4 : 15 days Crack BPSC with

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## Detailed Solution

Given:

Time taken by A and B = 6 days

Time taken by A = 10 days

Formula used:

Total work = Time taken × Efficiency

Calculation:

L.C.M of (6 and 10) = 30 = Total work

Efficiency of A and B = 30/6 = 5 units/day

Efficiency of B = 30/10 = 3 units/day

Efficiency of B = (5 – 3) units/day

⇒ 2 units/day

Time taken by B = 30/2 days

⇒ 15 days

∴ B will complete the work in 15 days

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Last updated on Nov 23, 2022

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## More Work Efficiency 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. 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?Q3. 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?Q4. 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 :Q5. 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 :Q6. 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?Q7. 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 :Q8. 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?Q9. Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?Q10. 39 person can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work ?

## 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 :

स्रोत : testbook.com

## A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?

A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?

Home > Hindi > कक्षा 14 > Reasoning > Chapter > Work And Time >

A and B complete a work in 6 d...

A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?

Updated On: 27-06-2022

00 : 30

लिखित उत्तर A 4.75 4.75 days B 1.75 1.75 days C 2.75 2.75 days D 3.75 3.75 days Answer

उत्तर

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स्रोत : www.doubtnut.com

## B can complete a work in 6 days. A alone can do it in 10 days. If both work together, how many days will they take to complete the work?

Answer (1 of 7): Take the harmonic mean, divided by 2: \displaystyle\frac{1}{\frac{1}{6}+\frac{1}{10}}=\frac{15}{4}=3.75 They need 3.75 days to complete the work together. Why does that work? Convert the days into working speed (which is inversely proportional to the days each worker needs, we...

B can complete a work in 6 days. A alone can do it in 10 days. If both work together, how many days will they take to complete the work?

Sort Dipanjan Dey

Bachelor of Engineering from Savitribai Phule Pune University (SPPU) (Graduated 1993)Author has 239 answers and 196.7K answer views1y

Related

A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C, they completed the work in 2 days. In how many days can C, alone, do it?

Easiest way to do this problem

A does the work in 4 days. So A does 25% in a day.

B does work in 5 days, B does 20% in a day.

In 2 days A and B do 2*(25+20) = 90% of the work.

Remaining work is 10% for C which C does in 2 days or 5% per day.

Hence C would take 100/5= 20 days to do it alone.

Hope you found this useful.

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Louis M. Rappeport

B.S. from University of California, BerkeleyAuthor has 7K answers and 5.1M answer views4y

B does 1/6th of the work per day. A does 1/10th. Together, they do:

1/10 + 1/6=3/30 + 5/30=8/30=4/15

1/ 4/15=15/4 days working together

Studied at National Institute of Technology, Tiruchirappalli4y

We assume that work 30 units to complete.

B completes 5 units per day ~ 6 days to complete the work. Similarly A completes 3 units per day ~ 10 days to complete the work.

Together they complete 5+3=8 units per day. No of days required to complete the task is 30/8 days.

Thomas Schürger

Senior software architect at CGI Group (company)Author has 1.8K answers and 1.6M answer viewsUpdated 1y

Take the harmonic mean, divided by 2:

1 1 6 + 1 10 = 15 4 =3.75 116+110=154=3.75

They need 3.75 days to complete the work together.

Why does that work? Convert the days into working speed (which is inversely proportional to the days each worker needs, we use 1 as the proportionality factor here, i.e. a simple reciprocal). Clearly, the working speeds of the two can be added together to get their total speed. Take the reciprocal again to get the number of days they need when working together.

So: Convert each time to speed, add the speeds and convert the sum back to time.

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Shreyas Shetty

Software EngineerUpdated 2y

Work done in one day = Efficiency

Efficiency of A = 1/6

Efficiency of B = 1/10

Total Efficiency = Efficiency of A + Efficiency of B = 1/6 + 1/10 = 4/15.

Total Time = 1 / Efficiency = 15/4 = 3.75

Robert Diley

Studied at University of OxfordAuthor has 97 answers and 108.4K answer views3y

Related

A and b complete a work in 6 days. A alone can do it in 10 days. How many days does it take if both can do the work together?

You already state the answer. “A and b complete a work in 6 days”, fewer than A alone who takes 10. What are you asking?

Roger Austin

If it is software development, it would take 6 months to complete the work. The first 5+ months would be in meetings and developing work plans. Then, the annoyed boss would get rid of everyone but B and B would get the work done.

Read “The Mythical Man Month” by Fred Brooks.

If you are thinking some other field, it would take 6 days since the boss would fire A for being slow.

Vasudevan A.N.S.

Former Retired Professor of Chemistry. (1977–2014)Author has 7.8K answers and 8.9M answer views3y

Both A and B can complete the work in = (6 x 10)/(6+10)=60/16.- days

= 15/4- days. = 3.75- days. Saransh Goyal