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Previous Year Question (PYQs)
3
$x, y, z$ 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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