Question

13. A can do a piece of work in 14 days, while B can do in 21 days. They begin together. But, 3 ,
before the completion of the work. A leaves off. Find the total number of days taken to complete the work.​

Answer 1

$\huge\underline{\underline{\mathfrak\red{Given::}}}$

$\text{A can do a piece of work in 14 days}, \\ \text{while B can do in 21 days.} \\ \text{ They begin together but, 3 days} \\ \text{ before the completion of the work a leaves off} \\ \text{Find the total \: number of days} \\ \text{ taken to complete the work.}$

$\huge\underline{\underline{\mathfrak\red{Solution::}}}$

$\bf{★ \: ( A \: and \: B)s \: work \: today} = \\ \\ \bf{ \frac{1}{14} + \frac{1}{21} } \\ \\ \bf{ \implies \frac{3 + 2}{42} } \\ \\ \bf{\implies \red { \frac{5}{42} } }$

$\bf{At \: the \: end, \: B \: works \: for \: 3 \: days } \\ \bf{so \: work \: done \: by \: B \: in \: 3 \: days} \\ \\ \bf{ = 3 \times \frac{1}{21} = \red{\frac{1}{7} }}$

$\bf{Remaining \: work \: 1− \frac{1}{7} = \frac{6}{7} } \\ \bf{which \: is \: to \: be \: done \: by \: A \: and \: B}$

$\bf{ \red { \frac{5}{42}} \: of \: work \: (A+B) \: can \: do \: in \: 1 \: days}$

$\bf{∴ \: \frac{6}{7} \: of \: work \: (A+B) \: can \: do \: in \: } \\ \bf{ \frac{1}{ \frac{5}{42} } \times \frac{6}{7} =\red{ 7 \frac{1}{5} \: days} }$

$\bf{∴ Time \: to \: complete \: the \: work \: } \\ \bf{ =3 + 7 \frac{1}{5} } \\\boxed{\mathfrak\pink{10 \frac{1}{5 \: } \: \: days} } \\ \\ \boxed{\mathfrak\green{hope \: it\: helps} }$