Question:
Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in 13 days, then how many men can finish the job in 13 days?
Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in 13 days, then how many men can finish the job in 13 days?
Updated On: Aug 21, 2024
- 10
- 12
- 13
- 14
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Assuming one machine completes 1 unit of work per day
Given that combined effort of two machines allows them to finish the job in 13 days.
Therefore, work = 2×1×13 = 26 units.
Let the daily work output of one man be denoted by 'm.'
From the given equation 3m + 8 × 1 = 2(8m + 3 × 1), we find that m = 2/13 units.
If 'x' represents the number of men required to complete the work in 13 days,
the equation xm × 13 = 26 units
This leads to the conclusion that x is equal to 13 men.
Given that combined effort of two machines allows them to finish the job in 13 days.
Therefore, work = 2×1×13 = 26 units.
Let the daily work output of one man be denoted by 'm.'
From the given equation 3m + 8 × 1 = 2(8m + 3 × 1), we find that m = 2/13 units.
If 'x' represents the number of men required to complete the work in 13 days,
the equation xm × 13 = 26 units
This leads to the conclusion that x is equal to 13 men.
Was this answer helpful?
0
0
Top Questions on Time and Work
- Two alarm clocks ring their alarms at regular intervals of 20 minutes and 25 minutes respectively. If they first beep together at 12 noon, at what time will they beep again together next time?
- CBSE Class X - 2024
- Mathematics
- Time and Work
- Two pipes A and B can fill a tank in 32 minutes and 48 minutes respectively. If both the pipes are opened simultaneously, after how much time B should be turned off so that the tank is full in 20 minutes?
- CUET (UG) - 2024
- Mathematics
- Time and Work
- Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been
- CAT - 2024
- Quantitative Aptitude
- Time and Work
- Two alarm clocks ring their alarms at regular intervals of 20 minutes and 25 minutes respectively. If they first beep together at 12 noon, at what time will they beep again together next time?
- CBSE Class X - 2024
- Mathematics
- Time and Work
- Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayana in the same job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayana on the second day, Mohit and Ayana on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is
- CAT - 2024
- Quantitative Aptitude
- Time and Work
View More Questions
Questions Asked in CAT exam
- The sum of all real values of $k$ for which $(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}$ is
- CAT - 2024
- Logarithms
- Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is
- CAT - 2024
- Profit and Loss
- The number of all positive integers up to 500 with non-repeating digits is
- CAT - 2024
- Number Systems
- A certain amount of water was poured into a 300 litre container and the remaining portion of the container was filled with milk. Then an amount of this solution was taken out from the container which was twice the volume of water that was earlier poured into it, and water was poured to refill the container again. If the resulting solution contains 72% milk, then the amount of water, in litres, that was initially poured into the container was
- CAT - 2024
- Mixtures and Allegations
- Consider the sequence\( t_1 = 1, t_2 = -1 and t_n = \left( \frac{n-3}{n-1} \right) t_{n-2} for n \ge 3. \)Then, the value of the sum \(\frac{1}{t_2}\) + \(\frac{1}{t_4}\) + \(\frac{1}{t_6}\) + ……. + \(\frac{1}{t_{2022}}\) + \(\frac{1}{t_{2024}}\), is
- CAT - 2024
- Sequence and Series
View More Questions