Question

Anu, Vinu and Manu can complete a work alone in 15 days, 12 days and 20 days,respectively. Vinu works everyday. Anu works only on alternate days starting from the first day while Manu works only on alternate days starting from the second day. Then, the number of days needed to complete the work is

• A. 8
• B. 6
• C. 5
• D. 7

Answer 1

The Correct Option is D

Let's assume that the total amount of work is 60 units. Anu, Vinu, and Manu contribute 4, 5, and 3 units of work per day, respectively.

On the first day, Anu and Vinu are working together, completing 9 units of work. On the second day, Manu and Vinu join forces and accomplish 8 units of work. This pattern continues, alternating between Anu and Vinu, and Manu and Vinu.

Step 1: Work Done in the First Six Days

In the first six days, the work done is as follows: - Day 1: Anu and Vinu together complete \(9\) units of work. - Day 2: Manu and Vinu together complete \(8\) units of work. - Day 3: Anu and Vinu again complete \(9\) units of work. - Day 4: Manu and Vinu together complete \(8\) units of work. - Day 5: Anu and Vinu again complete \(9\) units of work. - Day 6: Manu and Vinu together complete \(8\) units of work. The total work done in the first six days is: \[ 9 + 8 + 9 + 8 + 9 + 8 = 51 \text{ units}. \]

Step 2: Work Done on the Seventh Day

On the seventh day, Anu and Vinu team up again to finish the remaining 9 units of work. Thus, they complete the entire task in 7 days.

Final Answer:

The entire task is completed in \( \boxed{7} \) days.