Question

A, B and C can do a piece of work in 6, 8 and 12 hrs respectively. They started the work together and after 1 hr B left the work. In how much time will the remaining work be completely by A and C.
[Note: Answer should be in hours not days]​

Answer 1

Answer:

If B leaves one hour after the three of them works together, then A and C will complete the remaining work in 4 hours.

Step-by-step explanation:

Time taken by A to do the piece of work = 6 hours

Rate at which A can the piece of work / efficiency of A = $\frac{1}{6}$

Time taken by B to do the piece of work = 8 hours

Rate at which B can the piece of work / efficiency of B = $\frac{1}{8}$

Time taken by C to do the piece of work = 12 hours

Rate at which C can the piece of work / efficiency of C = $\frac{1}{12}$

A, B and C worked together for 1 hour.

Amount of work done = rate at which the work done × time taken

Since three people worked together, the combined rate at which the work is done / combined efficiency is the sum of their efficiencies.

So the amount of work they completed in that hour = $(\frac{1}{6} +\frac{1}{8}+ \frac{1}{12} ) \times 1$

                     = $\frac{3+4+2}{24}$

                     = $\frac{9}{24}$

                     = $\frac{3}{8}$

That is, $\frac{3}{8}$ of the work was completed when they worked for 1 hour.

B left after 1 hour.

Amount of work left to do = $1- \frac{3}{8}$

                                            = $\frac{5}{8}$

Now, $\frac{5}{8}$ of the work has to be completed by A and C alone.

Combined efficiency of A and C = $\frac{1}{6}+ \frac{1}{12}$

                                                      = $\frac{2+1}{12}$

                                                      = $\frac{3}{12}$

                                                      = $\frac{1}{4}$

Now the time taken for them to complete the work = 1 ÷ their combined efficiency

                                                                                      = $\frac{1}{\frac{1}{4} }$   = 4.

That is, the time taken for A and C to complete the remaining work is 4 hours.

                                       

Answer 2

A and C will take 2.5 hrs to complete remaining work if A, B and C can do a piece of work in 6, 8 and 12 hrs respectively and they started the work together and after 1 hr B left the work

Given:

• A can do a piece of work in 6 hrs
• B can do a piece of work in 8 hrs
• C can do a piece of work in 12 hrs
• A, B and C started the work together
• After 1 hr B left the work

To Find:

• How much time A and C will take to complete remaining work.

Solution:

Step 1:

Find work done by A , B and C in 1 hr

A's 1 hr wok  = 1/6

B's 1 hr work = 1/8

C's 1 h wok  = 1/12

Step 2:

Find work done by A , B and C together  in 1 hr

1/6 + 1/8 + 1/12

= (4 + 3 + 2)/24

= 9/24

= 3/8

Step 3:

Find remaining wok

1 - 3/8  = 5/8

Step 4:

Find work done by A  and C together  in 1 hr

1/6 +   1/12

= (2 + 1)/12

= 3/12

= 1/4

Step 5:

Find time taken  by A  and C together to complete remaining work

= (5/8) / ( 1/4)

= 5/2

= 2.5 hrs

A and C will take 2.5 hrs to complete remaining work

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