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CAT 2019 Slot 2 — QA Question 15

Working in ShiftsEasy

Anil alone can do a job in 20 days while Sunil alone can do it in 40 days. Anil starts the job, and after 3 days, Sunil joins him. Again, after a few more days, Bimal joins them and they together finish the job. If Bimal has done 10% of the job, then in how many days was the job done?

Answer & solution

Correct answer: 13

  • 13

  • B

    12

  • C

    15

  • D

    14

Solution

Easy

Work in one-day rates. Anil works alone for the first 3 days; then Anil + Sunil work together; Bimal contributes a fixed 10%10\% of the job. The part Anil + Sunil must cover is the whole job minus Anil's head start minus Bimal's share — and that pair's combined rate gives the remaining days.

1

Rates and Anil's head start. Anil does 120\tfrac{1}{20} of the job per day, Sunil 140\tfrac{1}{40} per day. In the first 3 days Anil works alone.

Anil (3 days)=3×120=320Anil+Sunil rate=120+140=340 per day\begin{aligned} &\text{Anil (3 days)}=3\times\frac{1}{20}=\frac{3}{20}\\ &\text{Anil}+\text{Sunil rate}=\frac{1}{20}+\frac{1}{40}=\frac{3}{40}\ \text{per day} \end{aligned}
2

Work left for Anil + Sunil. Bimal does 10%=11010\%=\tfrac{1}{10} of the job. Subtract Anil's head start and Bimal's share from the whole.

Anil+Sunil share=1−320−110⇒ =1−320−220(common denominator)⇒ =20−520=1520=34\begin{aligned} &\text{Anil}+\text{Sunil share}=1-\frac{3}{20}-\frac{1}{10}\\ &\Rightarrow\ =1-\frac{3}{20}-\frac{2}{20} \quad\text{(common denominator)}\\ &\Rightarrow\ =\frac{20-5}{20}=\frac{15}{20}=\frac{3}{4} \end{aligned}
3

Days the pair work, then total. The pair must finish 34\tfrac{3}{4} at rate 340\tfrac{3}{40} per day. Add to the initial 3 days.

pair days=3/43/40=34×403=10⇒ total=3+10=13 days\begin{aligned} &\text{pair days}=\frac{3/4}{3/40}=\frac{3}{4}\times\frac{40}{3}=10\\ &\Rightarrow\ \text{total}=3+10=13\ \text{days} \end{aligned}
Job done in 13 days\text{Job done in }13\ \text{days}

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CAT 2019 Slot 2 QA Q15: Anil alone can do a job in 20 days while Sunil alone can do it in 40 days. Anil starts the job, and after 3 da — Solution | TheCATExam