Question

A and b can do piece of work in 15 days b and c can do it in 12 days c and a can do it in 20 days how long they will take to finish the work working together also find the number of days taken by each of the same work working alone

Answer 1

Solutions :-

Given :
A and B can do piece of work in 15 days.
(A + B)'s one day work = 1/15

B and C can do it in 12 days.
(B + C)'s one day work = 1/12

C and A can do it in 20 days.
(C + A)'s one day work = 1/20


Find the (A + B + C)'s one day work :-

=> (A + C) + (B + C) + (C + A) = 1/15 + 1/12 + 1/20
=> 2(A + B + C) = (4 + 5 + 3)/60
=> A + B + C = 12/(60 × 2) = 1/10


A's one day work = (A + B + C) - (B + C)
= 1/10 - 1/12
= (6 - 5)/60
= 1/60

B's one day work = (A + B + C) - (A + C)
= 1/10 - 1/20
= (2 - 1)/20
= 1/20

C's one day work = (A + B + C) - (A + B)
= 1/10 - 1/15
= (3 - 2)/30
= 1/30


Hence,
A, B and C working together can do the work in 10 days.
A, B and C can do the work in 60 days, 20 days and 30 days respectively.

Answer 2

$\huge\underline{\bold{\red{Answer\::}}}$

A and B do a piece of work in 15 days.

Work done by (A + B) in 1 day = $\dfrac{1}{15}$ days ___(1)

B and C do a piece of work in 12 days.

Work done by (B + C) in 1 day = $\dfrac{1}{12}$ days. ___(2)

A and C do that work in 20 days.

Work done by (A + C) in 1 day = $\dfrac{1}{20}$ days ___(3)

Now

Work done by (A + B + C) together.. I that what we have to find.

Add eq. (1), (2) and (3)

(A + C) + (B + C) + (C + A) = $\dfrac{1}{15}$ + $\dfrac{1}{12}$ + $\dfrac{1}{20}$

On taking LCM of 15, 12 and 20 we get; 60

2 (A + B + C) = $\dfrac{4\:+\:5\:+\:3}{60}$

(A + B + C) = $\dfrac{12}{60}$ × $\dfrac{1}{2}$

$\textbf{(A + B + C)}$ = $\dfrac{1}{10}$ days

Now;

Work done by A alone itself = Work done by three (A + B + C) together - Work done by (B + C)

= (A + B + C) - (B + C)

= $\dfrac{1}{10}$ - $\dfrac{1}{12}$

= $\dfrac{6\:-\:5}{60}$

= $\dfrac{1}{60}$ days

Work done by B alone = (A + B + C) - (A + C)

= $\dfrac{1}{10}$ - $\dfrac{1}{20}$

= $\dfrac{2\:-\:1}{20}$

= $\dfrac{1}{20}$ days

Work done by C alone = (A + B + C) - (A + B)

= $\dfrac{1}{10}$ - $\dfrac{1}{15}$

= $\dfrac{3\:-\:2}{30}$

= $\dfrac{1}{30}$ days

$\textbf{Work done by (A + B + C) is}$ $\textbf{\red{ 10 days}}$

$\textbf{Work done by A alone is}$ $\textbf{\red{ 60 days}}$

$\textbf{Work done by B alone is}$ $\textbf{\red{ 20 days}}$

$\textbf{Work done by C alone is}$ $\textbf{\red{ 30 days}}$