Question

A and B complete a piece of work in 12 days B and C in 16 days a and c in 24 days how long will it take for a, b and c to do the work together​

Answer 1

Answer :-

A, B and C together can complete the work in 32/3 i.e 10 2/3 days.

Explanation :-

A and can complete a piece of work in 12 days

So A and B's 1 day work (A + B) = 1/12

B and C can complete the same work in 16 days

So B and C 1 day work (B + C) = 1/16

A and C can complete the same work in 24 days

So A and C's 1 day work (A + C) = 1/24

We know that

2(A + B + C) = (A + B) + (B + C) + (A + C)

⇒ 2(A + B + C) = (1/12) + (1/16) + (1/24)

Taking LCM

⇒ 2(A + B + C) = (4 + 3 + 2)/48

⇒ 2(A + B + C) = 9/48

⇒ A + B + C = (9/48) ÷ 2

⇒ A + B + C = (9/48) × (1/2)

⇒ A + B + C = 9/96

⇒ A + B + C = 3/32

i.e A , B and C's 1 day work = 3/32

So A, B and C together can complete the work in 32/3 i.e 10 2/3 days.

Answer 2

$\huge{\mathfrak{\green{S}}}{\mathfrak{o}}{\mathfrak {\orange {l}}}{\mathfrak{\red{u}}}{\mathfrak {\pink {t}}}{\mathfrak{\blue{i}}}{\mathfrak{\purple {o}}}{\mathfrak {\gray {n}}}$

$= > \frac{3}{32}$

Further Explanation

According to the given question:-

• A and B complete a piece of work in 12 days B and C in 16 days a and c in 24 days and We have to find that how long will it take for a, b and c to do the work together.

• 12 days is the A time taken to complete a piece of work.

• $A + B = 1/12$ is the A , B one day work

• 16 days is the B , C time taken to complete the same work and B + C = 1/16 for B , C day and finally the same same is complete by A , C in 24 days so, A + C = 1/24

$= > 2..A + B + C = A + B + B + C+ A + c \\ </p><p> = > 2(A + B + C) = \frac{1}{12} + \frac{1}{16} + \frac{1}{24}$

Therefore,

Now we take LCM

$= > 2..A + B + C = \frac{4 + 3 + 2}{48} \\ </p><p> = > 2..A + B + C = \frac{9}{48} \\ </p><p> = > A + B + C = \frac{9}{48} ÷ 2 \\ </p><p> = > A + B + C = \frac{9}{48} × \frac{1}{2} \\ </p><p> = > A + B + C = \frac{9}{96} </p><p> = > A + B + C = \frac{3}{32}$

3/32 is the time taken for A , B and C in 1 day frm 10 .2/3 days..