Question

A,B and a can do a piece of work in 6, 8 and 12 hours respectively they started the work together and after one hour we left the work .in how much time will the remaining work be completed by A and C?​

Answer 1

Answer:

A do his work in 6 hours

C do his work in 12 hours

B do his work in 8 hours

total time to do the work is 6+12+8 = 26 hours

A and C need to complete the work 26/2=13 hours.

Answer 2

Answer:

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 3 people worked together, the combined rate at which the work  done / combined efficiency =sum of their efficiencies.

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

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

                                                                                      = $\frac{9}{24}$

                                                                                      = $\frac{3}{8}$

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

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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

∴ The time taken for A and C to complete the remaining work is 4 hours.

Special Thanks to a Brainly Expert @navanithishere.