Question

Ravi can do some work in 20 days, which Sankar can do in 12 days. Sankar
worked at it for 9 days and left. In how many days can Ravi finish the remaining
work?​

Answer 1

Answer:

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Answer 2

Answer:

• Ravi = 20 Days
• Sankar = 12 Days
• Sankar worked at it for 9 day and left

Let Ravi take n days to finish remaining work

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf \dfrac{Days}{Ravi}+\dfrac{Days}{Sankar}=Total\:Work\\\\\\:\implies\sf \dfrac{(6+n)}{20}+\dfrac{6}{12}=1\\\\\\:\implies\sf \dfrac{(6+n)}{20}+\dfrac{1}{2}=1\\\\\\:\implies\sf \dfrac{(6+n)}{20} = 1 - \dfrac{1}{2}\\\\\\:\implies\sf \dfrac{(6+n)}{20} =\dfrac{1}{2}\\\\\\:\implies\sf \dfrac{(6+n)}{10} = 1\\\\\\:\implies\sf 6 + n = 10\\\\\\:\implies\sf n = 10 - 6\\\\\\:\implies\sf n = 4 \:Days$

⠀

$\therefore\:\underline{\textsf{Hence, Ravi will finish remaining work in \textbf{4 Days}}}.$

$\rule{200}{1}$

Important Formulae :

1. Let A can do a work in x days and B can do the same work in y days. They'll do the same work together in :

$\begin{aligned}\dashrightarrow\sf (A+B)=\dfrac{1}{x}+\dfrac{1}{y}=1\\\\\\\dashrightarrow\sf (A+B)=\dfrac{x+y}{xy}=1\\\\\\\dashrightarrow\sf (A+B)=\dfrac{xy}{x+y}\end{aligned}$

2. Let A, B and C can do a work in x, y and z days respectively. They'll do the same work together in :

$\begin{aligned}\dashrightarrow\sf (A+B+C)=\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=1\\\\\\\dashrightarrow\sf (A+B+C)=\dfrac{xy+yz+zx}{xyz}=1\\\\\\\dashrightarrow\sf (A+B+C)=\dfrac{xyz}{xy+yz+zx}\end{aligned}$

3. Let (A + B) can do a work in x days and A can do the same work in y days. B will do the same work in :

$\begin{aligned}\dashrightarrow\sf B=\dfrac{1}{x}-\dfrac{1}{y}=1\\\\\\\dashrightarrow\sf B=\dfrac{y-x}{xy}=1\\\\\\\dashrightarrow\sf B=\dfrac{xy}{y-x}\end{aligned}$