Question

a does half as much work as b, and c does half as much work as a&b together. if c alone can finish the work in 40 days, then all together will finish the work in?

Answer 1

40 is half of the work of a&b it means c have done half of the work of ab in 40 days, so we should add the work of a&b which is 40 bcoz its say a done the half work of b, so b ws 40 and b half ws 20 so a is 20, so total days is 80

Answer 2

Answer:

13.33

Step-by-step explanation:

Step -1: Finding the work done by A and B in a day.

                Let B takes a total of x days to complete the work alone.

                So as know that A takes 6 days less than B we can write that A takes

                 x - 6 days to complete the work alone.

                Work done by B in a day =  

x

1

​

                Work done by A in a day =  

x−6

1

​

Step -2: Finding x .

                As we know that A and B together complete the work in 4 days,we can write

                 

x

1

​

+

x−6

1

​

=

4

1

​

                Taking LCM and solving we get,

                 

x(x−6)

x−6+x

​

=

4

1

​

                 

x(x−6)

2x−6

​

=

4

1

​

                Cross - multiplying we get,

                8x−24=x

2

−6x

                x

2

−14x+24=0

                x

2

−12x−2x+24=0

                x(x−12)−2(x−12)=0

                x=2,12

                We will reject x=2 as x - 6 will become negative.

Hence, B takes 12 days to complete the work alone.