Question

A and B can do a picee of work in 30 days,while B and C can do the same work 24 days C and A in 20 days.if they all togther, in how many days will the work finish.​

Answer 1

Answer:

18 days will the work finish, If they work together.

Step-by-step explanation:

Given that :

A and B can do a piece of work in 30 days  :

$\sf \implies  \dfrac{1}{a} + \dfrac{1}{b} = \dfrac{1}{30}$

C and B can do the same work 24 days

[tex]\sf \implies \dfrac{1}{b} + \dfrac{1}{c} = \dfrac{1}{24} [/tex]

C and A can do the same work in 20 days  :

$\sf \implies \dfrac{1}{c} + \dfrac{1}{a} = \dfrac{1}{20}$

We have three equations now,

$\sf 1. \implies  \dfrac{1}{a} + \dfrac{1}{b} = \dfrac{1}{30}$

[tex]\sf 2. \implies \dfrac{1}{b} + \dfrac{1}{c} = \dfrac{1}{24} [/tex]

$\sf 3.\implies \dfrac{1}{c} + \dfrac{1}{a} = \dfrac{1}{20}$

Add these equations :

⇒ 2(1/a +1/b + 1/c) = 1/30 + 1/24 + 1/20 = (20+25+30)/600 = 75/600 = 1/8

⇒ 1/a + 1/b + 1/c = 1/16

When A, B and C work together

The amount of work done in one day is 1/16

⇒ (1/a + 1/b + 1/c) - (1/b + 1/c) = 1/16 - 1/24 = (3–2)/48 = 1/48

⇒ 1/a = 1/48

The work done by A in one day = 1/48

As we know :

A, B & C work together for 10 days,

Work done by them together for 10 days :

⇒ 10 * (1/16) = 10/16 = 5/8

The remaining work to be done by A alone :

⇒1 - 5/8 = 3/8

The number of days taken by A alone to complete the remaining work :

⇒ (3/8)/(1/48) = 18 days.

Hence, 18 days is the answer.

Answer 2

$\huge{\mathfrak{\underline{\underline{Answer}}}}$

$\huge{\sf{18 days}}$

$\huge{\mathfrak{\underline{\underline{Explanation}}}}$

$\large{\sf{2(A+B+C)'s \: 1 \: day \: work \: = \: 1/30 \: + \: 1/24 \: + \: 1/20 \: = \: 1/8}}$

=>$\large{\sf{(A+B+C)'s \: 1 \: day's \: work \: = \: 1/16}}$

$\large{\sf{work \: done \: by \: A,B \: and \: C \: in \: 10 \: days \: = \: 10/16 \: = \: 5/8}}$

$\large{\sf{Remaining \: work \: = \: 3/8}}$

$\large{\sf{A's \: 1 \: day's \: work \: = \: (1/16 - 1/24) \: = \: 1/48}}$

$\large{\sf{Now, \: 1/48 \: work \: is \: done \: by \: A \: in \: 1 \: day}}$

$\large{\sf{ So, \: 3/8 \: work \: will \: be \: done \: by \: A \: in \: = \: 48 x (3/8) \: = \: 18 days}}$

» 18 days