Question

a can build a wall in 12 days, b can do the same in 16 days and c can do in 24 days. totally 6 walls are to be built. 'a' does the work for first 16 days and 'b' continues the work for the next 12 days. how many days should c work?

Answer 1

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Answer 2

94 days is the number of days to complete the work by C.

Given:

A can build a wall in 12 days

B can build a wall in 16 days

C can build a wall in 24 days

To find:

The time taken by C to complete the left over work

Solution:

6 walls are built in total

A does the work for 16 days, so A completes one wall in 12 days.

In balance 4 days A completes, $\frac{4}{12}=  \frac{1}{3}$of the second wall.

Work done by A $= 1 wall + \frac{1}{3}$ of second wall

B works for next 12 days $=\frac{12}{16}=\frac{3}{4}$ of the wall

Total work done by A and B $=1+\frac{1}{3}+\frac{3}{4}$

Remaining walls $=3+\frac{2}{3}+\frac{1}{4}$

C can build a wall in 24 days

Hence it takes $24\times 3 =72$days to build 3 walls by C

To build $\frac{2}{3}$of the wall $=\frac{2}{3} \times 24=16 days$

To build $\frac{1}{4}$ of the wall $=\frac{1}{4} \times 24=6 days$

Total work done by C $= 72 + 16 + 6 = 94 days.$

Therefore, the total work done by C is 94 days.