Question

A can do a work in 12 days; B in 6 days and C in 3 days. A and B start
working together and after a day, C joins them. The total number of days
required to complete the work is​

Answer 1

Answer:

4 days because c joins them after a day and he can do it in 3 days so 1+3=4

Answer 2

The total number of days they need to work is 16/7.

Number of days A takes = $12 \ days$

Number of days B takes = $6 \ days$

Number of days C takes = $3 \ days$

According to the question, A and B start working together and C starts a day later.

Let the total number of days all three take to complete the work $=x \ days$

So A and B will work for x days and C will work for (x-1) days.

So,

$x(\frac{1}{12})+x(\frac{1}{6})+(x-1)\frac{1}{3}=1\\ \\ \implies \frac{x}{12}+ \frac{x}{6}+ \frac{x}{3}=1+\frac{1}{3} \\\\\implies \frac{x+2x+4x}{12}=\frac{4}{3} \\\\\implies \frac{7x}{12}=\frac{4}{3}\\ \\ \implies \frac{7x}{4}=\frac{4}{1}\\ \\ \implies x=\frac{16}{7}$

Hence the total number of days needed to complete the work together is $\frac{16}{7}=2\frac{2}{7}$ days.

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