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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Question : A and B together can complete a work in 20 days. B and C together can complete the same work in 15 days. If A, B, and C all work together, then the same work gets completed in 10 days. How many days will A and C together take to complete the same work?
Option 1: 8 days
Option 2: 10 days
Option 3: 15 days
Option 4: 12 days
Question : Disha takes 12 hours to copy a 75-page manuscript, while Mohit can copy the same manuscript in 10 hours. How many hours will it take for them to copy a 150-page manuscript if they work together?
Option 1: $10 \frac{10}{11}$ hours
Option 2: $9 \frac{9}{11}$ hours
Option 3: $8 \frac{9}{11}$ hours
Option 4: $11 \frac{8}{11}$ hours
Question : A can do $\frac{7}{8}$ of work in 28 days, and B can do $\frac{5}{6}$ of the same work in 20 days. The number of days they will take to complete if they do it together is:
Option 1: $15\frac{3}{7}$ days
Option 2: $17\frac{3}{5}$ days
Option 3: $14\frac{5}{7}$ days
Option 4: $13\frac{5}{7}$ days
Question : A can finish a work in 7 days. B can finish the same work in 9 days. The number of days required to finish the same work by both of them together is:
Option 1: $1\frac{15}{16}$
Option 2: $2\frac{15}{16}$
Option 3: $3\frac{15}{16}$
Option 4: $4\frac{15}{16}$
Question : Rahul alone can complete a work in 10 days and Sonu alone can complete the same work in 15 days. If they work together for 4 days, then what part of total work is left?
Option 1: $\frac{2}{3}$
Option 2: $\frac{1}{5}$
Option 3: $\frac{1}{3}$
Option 4: $\frac{2}{5}$
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