Ravi can do a piece of work in $15$ hours while Raman can do it in $12$ hours. How long will both take to do it, working together?

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Solution

We know that,
Number of hours Ravi required to do a piece of work $= 15$ hours
Number of hours Raman required to do a piece of work $= 12$ hours
$∴$ Work done by Ravi in $1$ hour $= \frac{1}{15}$

And, Work done by Raman in $1$ hour $= \frac{1}{12}$

Now, work done by both ravi and raman together in $1$ hour $= \frac{1}{15} + \frac{1}{12} = \frac{9}{60} = \frac{3}{20}$

$∴$ They can do work together in $\frac{20}{3}$ hours $= 6 \frac{2}{3}$ hours $= 6$ hours $40$ minutes
[ $∵ \frac{2}{3} \times 60$ minutes $= 40$ minutes ]

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Ravi can do a piece of work in 15 hours while Raman can do it in 12 hours. How long will both take to do it, working together?

Ravi can do a piece of work in $15$ hours while Raman can do it in $12$ hours. How long will both take to do it, working together?