$A$ can do a piece of work in $14$ days while $B$ can do it in $21$ days. They began together and worked at it for $6$ days. Then , $A$ fell and $B$ had to complete the remaining work alone. In how many days was the work completed?

Open in App

Solution

We know that,
Number of days $A$ required to do piece of work $= 14$ days
Number of days $B$ required to do piece of work $= 21$ days

$∴$ We can calculate, work done by $A$ in $1$ day $= 1 / 14$
Work done by $B$ in $1$ day $= 1 / 21$
Work done by $A, B$ together in a one day $= 1 / 14 + 1 / 21 = 5 / 42$
$∴$ they can work together in $42 / 5$ days.

$A$ and $B$ work for $6$ days So, the work completed by $A$ and $B$ in $6$ days $= 6 \times 5 / 42 = 5 / 7$
$∴$ work left $= 1 - 5 / 7 = 2 / 7$

Number of days taken by $B$ to complete the left over work $= 2 / 7 \times 21 = 6$ ( $21$ is used because $21$ is the days required by $B$ to complete a piece of work )
Tame taken to complete the work $= 6 + 6 = 12$ days

$∴$ Total time taken to complete the work $= 12$ days.

Suggest Corrections

Similar questions

A can do a piece of work in $14$ days while B can do it in $21$ days. They began together and worked at it for $6$ days. Then, A fell ill and B had to complete the remaining work alone. In how many days was the work completed?

Q. A can do a pieces of work in

14 d a y s

while

B

can do it in

21 d a y s

. They began together and worked for

7 d a y s

. Then, A fell ill and

B

has to complete the work. In how many days was the work completed?

Q. A can do a piece of work in 14 days which B can do in 21 days. They begin together and work at it for 7 days. Then, A fell ill and B had to complete the work. In how many days, the work was completed?

Q. A alone can do a piece of work in 10 days and B alone can do the same work in 15 days. They started working together. After two days, both of them left the work. If C alone can complete the remaining work in 5 days, then in how many days can C alone complete the work?

Q. A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. In how many days can the two of them complete the work together ?

Join BYJU'S Learning Program

A can do a piece of work in 14 days while B can do it in 21 days. They began together and worked at it for 6 days. Then , A fell and B had to complete the remaining work alone. In how many days was the work completed?

$A$ can do a piece of work in $14$ days while $B$ can do it in $21$ days. They began together and worked at it for $6$ days. Then , $A$ fell and $B$ had to complete the remaining work alone. In how many days was the work completed?