Question : A group of workers can complete a piece of work in 50 days when they are working individually. On the first day one person works, on the second day, another person joins him, on the third day one more person joins them and this process continues till the work is completed. How many approximate days are needed to complete the work?
Option 1: 8 days
Option 2: 9 days
Option 3: 10 days
Option 4: 11 days
Correct Answer: 10 days
Solution : Let the total work be 50 units and let a man complete 1 piece of work in a day. Work done on 1st day = 1 man × 1 work/day = 1 unit of work Work done on 2nd day = 2 men × 1 work/day = 2 units of work Work done on 3rd day = 3 men × 1 work/day = 3 units of work Let the whole work will be completed in $N$ days. So, total work 1 + 2 + 3 + ..... + $N$ = 50 $\frac{N(N+1)}2=50$ ⇒ $N(N + 1) = 100$ ⇒ $N=10$ days(approx) Hence, the correct answer is 10 days.
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Question : A and B are equally efficient, and each can individually complete a piece of work in 36 days if none takes any holiday. A and B started working together on this piece of work, but A took a day off after every five days of work, while B took a day off after every seven days of work. If the duo had started work on 1 July 2021, on which date was the work completed?
Option 1: 22 July 2021
Option 2: 19 July 2021
Option 3: 21 July 2021
Option 4: 20 July 2021
Question : One man and one woman together can complete a piece of work in 8 days. A man alone can complete the work in 10 days. In how many days can one woman alone complete the work?
Option 1: $\frac{140}{9}$ days
Option 2: $30$ days
Option 3: $40$ days
Option 4: $42$ days
Question : A, B and C can do a piece of work in 20 days, 30 days and 60 days respectively. If A works daily and on every third day B and C also work with A, then in how many days, will the work be completed?
Option 1: 21
Option 2: 18
Option 3: 12
Option 4: 15
Question : If 10 men can complete a piece of work in 12 days by working 7 hours a day, then in how many days can 14 men do the same work by working 6 hours a day?
Option 1: 15
Option 2: 16
Option 3: 10
Option 4: 12
Question : A and B complete a work in 24 and 30 days, respectively, working 10 hours per day. The work is to be done in two shifts. The morning shift is for 6 hours and the evening shift is for 4 hours. On the first day, A works in the morning and B works in the evening, and they interchange their shifts every day. On which day did the work get completed?
Option 1: 21st day
Option 2: 24th day
Option 3: 30th day
Option 4: 27th day
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