Question

A and B can finish a piece of work in 6 days and 4 days, respectively, working alone.
A started the work. After 2 days, he was joined by B. Find the time taken to finish the
remaining work.​

Answer 1

Step-by-step explanation:

Given that A can finish a piece of work in 6 days,

So, in one day A will do 1/6 th of work,

Given that B can finish a piece of work in 4 days,

So, in one day B will do 1/4 th of work,

Given that initially A has worked for 2 days,

So A will complete 2*1/6 = 1/3 rd of work

Remaining Work = 2/3 rd of work.

If A and B works together,

In 1 day, bot A and B could do = (1/6 + 1/4) of work

= 5/12 th of work

So, 2/3 rd of work requires 2/3*1/(5/12)

= 8/5 days,

Total time , to finish the work

= Time A working alone an Time taken when both A and B are

working together

= 2 + 8/5

= 18/5 days

Hope, it helps !

Answer 2

Answer:

${\huge{\underline{\bold{\red{Given:-}}}}}$

that A can finish a piece of work in 6 days,

${\huge{\underline{\bold{\green{so,}}}}}$

in one day A will do 1/6 th of work,

${\huge{\underline{\bold{\red{Given:-}}}}}$

that B can finish a piece of work in 4 days,

${\huge{\underline{\bold{\green{so,}}}}}$

in one day B will do 1/4 th of work,

${\huge{\underline{\bold{\red{Given:-}}}}}$

that initially A has worked for 2 days,

${\huge{\underline{\bold{\green{so,}}}}}$

A will complete 2$×$1/6 = 1/3 rd of work

${\huge{\underline{\small{\bold{\pink{remaining\:work:-}}}}}}$

2/3 rd of work.

$⇒$If A and B works together,

$⇒$In 1 day, bot A and B could do = (1/6 + 1/4) of work

$⇒$ 5/12 th of work

${\huge{\underline{\bold{\pink{So,}}}}}$

2/3 rd of work requires 2/3$×$1/(5/12)

$⇒$ 8/5 days,

${\huge{\underline{\small{\bold{\red{total\:time,\:to\: finish\:the\:work:-}}}}}}$

$⇒$Time A working alone an Time taken when both A and B are

${\huge{\underline{\small{\bold{\pink{working\: together:-}}}}}}$

$⇒$ 2 + 8/5

$⇒$ 18/5 days

${\huge{\underline{\small{\bold{\blue{hope\:help \:u:)}}}}}}$