Question

A B and C can do a piece of work individually in 8, 12 and 15 days, respectively. A and B start working together, but A
quits after working for 2 days. After this, C joins and works till the completion of work in how many days will the work
be completed?​

Answer 1

$\Large\underline\bold{Question:-}$

A, B, C can do a piece of work individually in 8,10 and 15 days respectively. A and B start working by A quits after working for 2 days. After this, C joins B till the completion of work. In how many days will the work be completed?

$\Large\underline\bold{Solution:-}$

$\sf\ Work\:done\:by\:A\:in\:1\:day= \frac{1}{8}$

$\sf\ Work\:done\:by\:B\:in\:1\:day= \frac{1}{10}$

$\sf\ Work\:done\:by\:C\:in\:1\:day= \frac{1}{15}$

$\sf\ Work\:done\:by\:A\:and\:B\:together\:in\:1\:day$

$\sf\ = \frac{1}{8} + \frac{1}{10}$

$\sf\ = \frac{5+4}{40}$

$\sf\ = \frac{9}{40}$

$\sf\ Therefore,\: In\:2\: days\: A\:and\:B\: complete$

$\sf\ 2× \frac{9}{40}$

$\sf\ = \frac{9}{20}$

$\sf\ Work\: remaining= 1- \frac{9}{20}= \frac{11}{20}$

$\sf\ Work\:done\:by\:A\:and\:C\:together\:in\:1\:day$

$\sf\ = \frac{1}{10} + \frac{1}{15}$

$\sf\ = \frac{3+2}{30} = \frac{5}{30} =\frac{1}{6}$

$\sf\ Let\: Number\:of\:days\:be\:n$

$\sf\ Therefore,\: n× \frac{1}{6} = \frac{11}{20}$

$\sf\ n× \frac{11}{20}×6 = \frac{33}{10} days$

$\sf\ Total\: number\:of\:days= (2+\frac{33}{10})$

$\Large\underline\bold\red{=\frac{53}{10}.}$

Answer 2

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