Question

A and B can do a job together in 25 days. after 15 days of working together, B leaves. if A completes remaining part of job in 20 days, how long would each take to complete the job, working separately??
answer is given in the book; A:50days and B : 50 days .
plz explain me the process.......
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Answer 1

Answer:

• A + B = 25 Days
• (A + B) work together = 15 Days
• A Alone work = 20 Days to finish it

$\underline{\bigstar\:\boldsymbol{According\:to\:the\:Question :}}$

$:\implies\sf \dfrac{Days}{(A+B)}+\dfrac{Days}{A}=Total\:Work\\\\\\:\implies\sf \dfrac{15}{25}+\dfrac{20}{A}=1\\\\\\:\implies\sf \dfrac{3}{5}+\dfrac{20}{A} =1\\\\\\:\implies\sf \dfrac{20}{A} = 1 - \dfrac{3}{5}\\\\\\:\implies\sf \dfrac{20}{A} = \dfrac{2}{5}\\\\\\:\implies\sf 20 \times \dfrac{5}{2} = A\\\\\\:\implies\sf 10 \times 5 = A\\\\\\:\implies\underline{\boxed{\sf A = 50\:Days}}$

$\rule{180}{2}$

$\underline{\bigstar\:\sf{When\:they\:both\:works\: together :}}$

$\dashrightarrow\sf\:\:(A+B)=\dfrac{A \times B}{A+B}\\\\\\\dashrightarrow\sf\:\:25 = \dfrac{50 \times B}{50 + B}\\\\\\\dashrightarrow\sf\:\:1 = \dfrac{2 \times B}{50 + B} \\\\\\\dashrightarrow\sf\:\:50 + B = 2B\\\\\\\dashrightarrow\sf\:\:50 = 2B - B\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf B = 50\:Days}}$

⠀

$\therefore\:\underline{\textsf{A \& B both can alone do work in \textbf{50 Days}}}.$