Home
Class 14
MATHS
A can do a job in 12 days and B can do t...

A can do a job in 12 days and B can do the same job in 6 days, in how many days working together they can complete the job?

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of how many days A and B can complete the job together, we can follow these steps: ### Step 1: Determine the work done by A and B individually. - A can complete the job in 12 days. - B can complete the job in 6 days. ### Step 2: Calculate the efficiency of A and B. - The efficiency of A (work done per day) = Total work / Time taken by A = 1 job / 12 days = 1/12 jobs per day. - The efficiency of B (work done per day) = Total work / Time taken by B = 1 job / 6 days = 1/6 jobs per day. ### Step 3: Find the combined efficiency of A and B. - Combined efficiency = Efficiency of A + Efficiency of B - Combined efficiency = (1/12) + (1/6) ### Step 4: Find a common denominator to add the efficiencies. - The common denominator for 12 and 6 is 12. - Convert (1/6) to (2/12) so that we can add: - Combined efficiency = (1/12) + (2/12) = 3/12 = 1/4 jobs per day. ### Step 5: Calculate the time taken to complete the job together. - Time taken = Total work / Combined efficiency - Total work = 1 job - Combined efficiency = 1/4 jobs per day - Time taken = 1 job / (1/4 jobs per day) = 4 days. ### Conclusion: A and B, working together, can complete the job in **4 days**. ---
Promotional Banner

Topper's Solved these Questions

  • TIME AND WORK

    ARIHANT SSC|Exercise EXERCISE(LEVEL 1)|100 Videos

  • TIME AND WORK

    ARIHANT SSC|Exercise EXERCISE(LEVEL 2)|55 Videos

  • THEORY OF EQUATIONS

    ARIHANT SSC|Exercise EXERCISE(LEVEL 2)|20 Videos

  • TIME, SPEED AND DISTANCE

    ARIHANT SSC|Exercise SPEED TEST (TSD)|10 Videos

Similar Questions

Explore conceptually related problems

P can do a job in 12 days and Q can do the same job in 6 days, in how many days working together they can complete the job?

A can do a job in 10 days, B can do the same job in 12 days and C can do the same job in 15 days. In how many days they will finish the work together?

A can do a work in x days while B can do the same work in y days then in how many days will they complete the work, working together?

A and B together can do a job in 15 days and A alone could do the same job in 20 days how many days would B take to do half the job if he worked alone

A and B working together can do a piece of work in 12 days, B and C can do it in 15 days nd C and A can do the same work in 20 days b. How long would each of them take to complete the job?

A and B together can do a piece of work in 12 days, B and C can do it in 15 days and C and A can do the same work in 20 days. How long would each of them take to complete the job?

A can do a job in 16 days and B can do the same job in 12 days. With the help of C, they can finish the job in 6 days only. Then, C alone can finish it in

If A can do a piece of work in 4 days, B can do the same work in 8 days and C can do the same work in 12 days , then working together , how many days will they take to complete the work ?