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Previous Year Question (PYQs)



$x, y, z$ are painters. X paints wall of area A in 10 hrs. Y paints the same wall in 20 hrs. Together, X, Y, and Z finish 2A in 8 hrs. Find how many hours Z alone will take to paint wall A.





Solution

Work done per hr: $X = \dfrac{1}{10},\quad Y = \dfrac{1}{20}$ Together with Z: $\dfrac{2}{8} = \dfrac{1}{4} = \dfrac{1}{10} + \dfrac{1}{20} + \dfrac{1}{z}$ $\Rightarrow \dfrac{1}{z} = \dfrac{1}{4} - \dfrac{3}{20} = \dfrac{1}{10}$ $\Rightarrow z = 10$ hours.


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