Question

A and B can finish a piece of work in 16 days and 12 days respectively a started the work and worked at it for 2 days. then join by B. find the total time taken to finish the work.​

Answer 1

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⭐ A and B can finish a piece of work in 16 days and 12 days respectively a started the work and worked at it for 2 days. then join by B. find the total time taken to finish the work.

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✒ The total time taken to finish the work is 8 days.

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Let whole work be W.

⇒ Work done by A in one day = w/16

Work is done by B in one day = w/12

⇒ A worked for 2 days =2× w/16

= w/8

A and B worked for x days ( let )

⇒ w/8 + x(w/16 + w/12)

⇒ x × 7/48 =7/8

⇒ x = 7/8×48/7

⇒x = 48/8

⇒x=6 days.

If A and B work together they finish the remaining work in 6 days

ATQ,

A worked alone 2 day

So total work = A + A & B

=> 6+2= 8 days

✌ Sᝪ Tᕼᗴ TᝪᎢᗩᏞ ᎢᏆᗰᗴ ᎢᗩᏦᗴᑎ Ꮖᔑ 8 ᗞᗩᎩᔑ.

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Answer 2

Given:-

A can finish his work in 16 days

•1 day work of A = 1/16

B can find the piece of work in 12 days

• 1 day work of B = 1/12

To find :-

◆ We have to find how much time taken by both A and B to finish the work

Now ,

• So , A alone can do work for two days then B joined !

• Find the two day work of A

• Extra work done by A compare to B

1 day work of A = 1/16

2 days = 2×1/16= 1/8

• Remaining work ?

• Let total work = 1

• $\sf 1- \dfrac{1}{8} =\dfrac{8-1}{8} =\dfrac{7}{8}$

• Now caluculate the time taken by both to finish the given work !

One day work of A and B

$\longrightarrow\sf 1 \ day\ work \ of \ (A+B)= \dfrac{1}{16}+\dfrac{1}{12}\\ \\ \longrightarrow\sf \dfrac{3+4}{48}\\ \\ \longrightarrow\sf \dfrac{7}{48}\\ \\ \longrightarrow \sf A+B= \dfrac{48}{7}\ days$

If A and B work together they finish work in 48/7 days

Now find how much time they both take to finish the remaining work

$\longrightarrow\sf Time = \dfrac{\cancel7}{\cancel8}\times \dfrac{\cancel{48}}{\cancel7} \\ \\ \longrightarrow\sf 6 days$

If A and B work together they finish the remaining work in 6 days and It is given that A do 2 days Alone

So total work is calucuted by 2 days Alone work of A + Remaining work done by A and B together

=> 6+2= 8 days

$\bigstar{\boxed{\sf{ Total \ time \ taken\ (A+B) =8 days }}}$