x, y, z are painter. \( X \) paint wall of area \( A \) in \( 10 hrs ., Y \) paints wall of same area in \( 20 hrs . x, y, z \) work together and finishes wall 2 A in 8 hrs. how many hours \( z \) need to paint wall of area A

Work rates (area per hour): X = \(A/10\) Y = \(A/20\) X + Y + Z paint \(2A\) in 8 hours, so together = \(2A/8 = A/4\) Z = \(A/4 - A/10 - A/20 = 5A - 2A - A/20 = A/10\) So Z alone needs 10 hours to paint area A. Answer: (C) 10

x, y, z are painter. \( X \) paint wall... - Solved

Question 72

Mathematics Area Hard

x, y, z are painter. \( X \) paint wall of area \( A \) in \( 10 \mathrm{hrs} ., \mathrm{Y} \) paints wall of same area in \( 20 \mathrm{hrs} . \mathrm{x}, \mathrm{y}, \mathrm{z} \) work together and finishes wall 2 A in 8 hrs. how many hours \( z \) need to paint wall of area A

(A) 20

(B) 15

(C) 10

(D) 16

✓ Correct Answer: Option C Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

Work rates (area per hour):

X = \(\frac{A}{10}\)
Y = \(\frac{A}{20}\)
X + Y + Z paint \(2A\) in 8 hours, so together = \(\frac{2A}{8} = \frac{A}{4}\)

Z = \(\frac{A}{4} - \frac{A}{10} - \frac{A}{20} = \frac{5A - 2A - A}{20} = \frac{A}{10}\)

So Z alone needs 10 hours to paint area A.

Answer: (C) 10

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Question 72

📘 Step-by-Step Solution & Detailed Explanation:

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