Question

Arun and Varun harvest in 6hours, Varun and Naveen harvest the same field in 8 hours while Arun and Naveen harvest in 12 hours. How long would they take working together to harvest the same field .​

Answer 1

Arun and Varun harvest in 6hours, Varun and Naveen harvest the same field in 8 hours while Arun and Naveen harvest in 12 hours. How long would they take working together to harvest the same field .

Answer 2

Answer:

$\boxed{\bf \frac{16}{3} \: \:days}$

$\tt{Given}\begin{cases}\tt{Arun\: and \:varun=6\:hour} \\ \tt{varun \:and \:naveen \:=8\:hour } \\\tt{arun \:and\: Naveen =12 \:hour}\end{cases}$

$\large\underline\textsf{ To Find }$

$\small\textsf{ How long would they take working}$

$\small\textsf{ together to harvest the same field? }$

$\huge\underline\textsf{Explantion:- }$

____________________________________

$\boxed{\sf arun \: + \: varun = \frac{1}{6} hour}$

$\boxed{\sf varun + naveen = \frac{1}{8}hour }$

$\boxed{\sf arun \: + naveen = \frac{1}{12}hour}$

_____________________________________

$\small\underline\textsf{ We have to add Now, :- }$

$\small\mathtt{[varun+arun]+[varun+naveen]+[arun+naveen] }$

$\huge\underline\textsf{in One day :- }$

$\implies\boxed{\sf \frac{1}{6} + \frac{1}{8} + \frac{1}{12}}$

$\large\underline\textsf{\red{Again} }$

$\implies\sf \frac{4 + 3 + 2}{24}$

$\implies\sf \frac{9}{25} \times 2$

$\implies\sf\frac{\cancel9}{\cancel{48}}$

$\implies\sf \frac{3}{16}$