A, B, and C are capable of completing a job in 30, 45, and 90 days, respectively. A works every day, while B and C join A every f…

Question

A, B, and C are capable of completing a job in 30, 45, and 90 days, respectively. A works every day, while B and C join A every fifth day. How long will it take to finish the task?

1. A. 25 days (Correct answer)
2. B. 18 days
3. C. 16 days
4. D. 12 days

Correct Answer

Option A — 25 days

Detailed Solution & Explanation

The correct answer is 25 days.

Key Points

• Take the LCM of 30, 45 and 90 as the total work: 90 units. Then A does 3 units/day, B does 2 and C does 1.
• In each five-day cycle A works all five days (15 units) and B and C join on the fifth day (+3), so a cycle completes 18 units.
• $90 \div 18 = 5$ cycles, and each cycle is 5 days, so the job takes 25 days.

Additional Information

• The LCM method turns fractions into whole units and is almost always faster than working with 1/30 + 1/45 + 1/90.
• Check the ending: after 5 full cycles exactly 90 units are done, so the work finishes precisely on day 25 with no partial day.
• When a cycle does not divide the total evenly, complete as many whole cycles as possible and then count the remaining days individually.

प्रश्न (हिन्दी में)

A, B और C किसी काम को क्रमशः 30, 45 और 90 दिनों में पूरा कर सकते हैं। A हर दिन काम करता है, जबकि B और C हर पाँचवें दिन A के साथ जुड़ते हैं। काम पूरा करने में कितना समय लगेगा?

1. A. 25 दिन
2. B. 18 दिन
3. C. 16 दिन
4. D. 12 दिन