Math, asked by gyyd, 4 hours ago

Pratap and Prabhu together can paint an auditorium in 5 days. If Pratap alone can
paint this auditorium in 8 days in how many days can Prabhu alone paint it?

Answers

Answered by bhanuprakash814379
0

Step-by-step explanation:

work done by pratap in one day prabhu + pratap = 1/5

same work done by pratap alone = 1/8

prabhu alone can paint in = 1/5 -1/8 = 8-5/40 = 3/40

Answered by akshay0222
0

Given,

The complete work done by Pratap and Prabu\[ = 5\]

The complete work done by Pratap\[ = 8\]

Solution,

Assume that the complete work done in \[x\] days.

One day work of Pratap and Prabhu\[ = \frac{1}{5}\]

One day work of Pratap\[ = \frac{1}{8}\]

One day work of Prabhu\[ = \frac{1}{x}\]

Therefore,

\[\begin{array}{l} \Rightarrow \frac{1}{x} + \frac{1}{8} = \frac{1}{5}\\ \Rightarrow \frac{1}{x} = \frac{1}{5} - \frac{1}{8}\\ \Rightarrow \frac{1}{x} = \frac{{8 - 5}}{{40}}\end{array}\]

Solve further,

\[\begin{array}{l} \Rightarrow \frac{1}{x} = \frac{3}{{40}}\\ \Rightarrow x = \frac{{40}}{3}\end{array}\]

Hence, the work can be completed by Prabhu in \[\frac{{40}}{3}\]days.

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