Question : Aditya can complete a grill painting job in 20 hours, while Vinay can complete the same work in 15 hours. If Aditya and Vinay both work together, then in how many hours will the painting work be completed?
Option 1: $10 \frac{2}{3}$ hours
Option 2: $10$ hours
Option 3: $12$ hours
Option 4: $8 \frac{4}{7}$ hours
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Correct Answer: $8 \frac{4}{7}$ hours
Solution :
Given: Aditya can complete a grill painting job in 20 hours.
Vinay can complete the same work in 15 hours.
Let the total work be LCM of (20, 15) = 60 units
⇒ Efficiency of Aditya = $\frac{60}{20} = 3$ units/hour
⇒ Efficiency of Vinay = $\frac{60}{15} = 4$ units/hour
⇒ Efficiency of Aditya + Vinay = 3 + 4 = 7 units/ hour
If they work together, time taken = $\frac{60}{7} = 8\frac{4}{7}$
Hence, the correct answer is $8 \frac{4}{7}$ hours.
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