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CAT 2021 Slot 1 — QA Question 7

Working AlternatelyEasy

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

Answer & solution

  • A

    8

  • B

    6

  • C

    5

  • 7

Solution

Easy

Take total work as the LCM of the times so each person's daily output is a whole number. Vinu works daily; Anu and Manu each work every other day on opposite parity. Compute work per 2-day block, then finish off the remainder day by day.

1

Set total work and efficiencies. Let total work =lcm⁡(15,12,20)=60=\operatorname{lcm}(15,12,20)=60 units.

Anu=6015=4,Vinu=6012=5,Manu=6020=3 units/day\begin{aligned} &\text{Anu}=\tfrac{60}{15}=4,\quad \text{Vinu}=\tfrac{60}{12}=5,\quad \text{Manu}=\tfrac{60}{20}=3 \ \text{units/day} \end{aligned}
2

Work in one 2-day block. Vinu works both days; Anu works on day 1 (odd days), Manu on day 2 (even days), so each contributes once per block.

per 2 days=2×5⏟Vinu+4⏟Anu+3⏟Manu=17 units\begin{aligned} &\text{per 2 days}=\underbrace{2\times 5}_{\text{Vinu}}+\underbrace{4}_{\text{Anu}}+\underbrace{3}_{\text{Manu}}=17\ \text{units} \end{aligned}
3

After 6 days. Three full blocks.

3×17=51 units done⇒ remaining=60−51=9 units\begin{aligned} &3\times 17=51\ \text{units done}\\ &\Rightarrow\ \text{remaining}=60-51=9\ \text{units} \end{aligned}
4

Day 7. Day 7 is odd, so Vinu and Anu work (Manu rests).

day 7=5+4=9 units=remaining⇒ work finishes exactly on day 7\begin{aligned} &\text{day 7}=5+4=9\ \text{units}=\text{remaining}\\ &\Rightarrow\ \text{work finishes exactly on day }7 \end{aligned}
Days needed=7(option (d))\text{Days needed}=7 \quad\text{(option (d))}
CAT 2021 Slot 1 QA Q7: Anu, Vinu and Manu can complete a work alone in 15 days, 12 days and 20 days, respectively. Vinu works everyda — Solution | TheCATExam