Question

Arun , Bharath, Karthik can complete
a work separately in 24, 36 and 48
days. They started working together
but Karthik left after 4 days of start
and Arun left 3 days before
completion of the work. In how many
days will the work be completed?​

Answer 1

Answer:

Arun 28 Bharat 39

Explanation:

Arun 24+4=28

Bharat 36+3=39

Answer 2

The number of days taken to complete the total work = 12 3/5 days

Given:

Arun, Bharath, Karthik can complete a work in 24, 36 and 48 days. respectively

They started working together but Karthik left after 4 days of start and Arun left 3 days before completion of the work

To find:

In how many days will the work be completed?

Solution:

Given Arun can complete a work in 24 days

⇒ The work can be done by Arun in 1 day = 1/24

Bharath can complete a work in 36 days

⇒ The work can be done by Bharath in 1 day = 1/36

Karthik can complete a work in 48 days

⇒ The work can be done by Karthik in 1 day = 1/48

They started working together, and worked for 4 days

The done in 4 days = $4(\frac{1}{24} +\frac{1}{36} +\frac{1}{48} )$

= $4(\frac{6+4+3}{144} )$ = $4(\frac{13}{144} )$ = $\frac{13}{36}$  

Karthik left after 4 days of start,

Let's assume that after leaving Karthik,

Arun and Bharath worked for x days,

then work can be done by Arun and Bharath in x days

=  $x(\frac{1}{24} + \frac{1}{36})$  = $x(\frac{3+2}{72})$ = $\frac{5x}{72}$

Arun left 3 days before completion of the work, which means last 3 days work is done by Arun

The work done by Arun in last 3 days = 3(1/24) = 1/8

As we know total work will be equal to 1

⇒  $\frac{13}{36} + \frac{5x}{72}+ \frac{1}{8}$ = 1

⇒  $\frac{36+8}{72} + \frac{5x}{72} = 1$

⇒  $\frac{44}{72} + \frac{5x}{72} = 1$

⇒  $\frac{5x}{72} = 1 - \frac{44}{72}$

⇒  $\frac{5x}{72} = \frac{72 - 44}{72}$

⇒  5x = 72 - 44

⇒ 5x = 28

⇒  x = 28/5 = 5 3/5

Therefore, Arun and Bharath worked together for 5 3/5 days

The numbers of days taken to complete the total work = 4 + 5 3/5 + 3

= 12 3/5 days

Therefore,

The number of days taken to complete the total work = 12 3/5 days

#SPJ2