Understanding the Machine Rate
The problem states that 7 machines take 7 minutes to produce 7 identical toys. This implies a direct relationship between machines, toys, and time.
From the given information, we can deduce the rate of production:
- If 7 machines make 7 toys in 7 minutes, then, on average, each machine makes 1 toy in those 7 minutes.
- This means the time required for a single machine to make a single toy is 7 minutes.
Calculating Time for 100 Machines
We need to find the time it takes for 100 machines to make 100 toys, assuming they work at the same rate.
Since each machine takes 7 minutes to make one toy, and we have 100 machines working simultaneously:
- Each of the 100 machines can work on one toy.
- Each machine will complete its toy in 7 minutes.
- Therefore, all 100 machines will finish their respective 100 toys in the same amount of time it takes one machine to finish one toy.
The calculation is as follows:
Rate of one machine = $\frac{1 \text{ toy}}{7 \text{ minutes}}$
Total rate of 100 machines = $100 \times \frac{1 \text{ toy}}{7 \text{ minutes}} = \frac{100}{7} \frac{\text{toys}}{\text{minute}}$
Time = $\frac{\text{Total Toys}}{\text{Total Rate}} = \frac{100 \text{ toys}}{\frac{100}{7} \frac{\text{toys}}{\text{minute}}} = 100 \times \frac{7}{100} \text{ minutes} = 7 \text{ minutes}$
Thus, it would take 7 minutes for 100 machines to make 100 toys.
Important Questions from Time and Work
A and B can do a piece of work in 18 days. B and C together can do it in 30 days. If A is twice as good a workman as C, find in how many days B alone can do the work?
Two men and 7 women can complete a work in 28 days, whereas 6 men and 16 women can do the same work in 11 days. In how many days will 5 men and 4 women, working together, complete the same work?
A man and a woman, working together can do a work in 66 days. The ratio of their working efficiencies is 3 ∶ 2. In how many days 6 men and 2 women together can do the same work?
Each one of five men independently can complete a work in 20 days. The work is started by one person. Next day one more person joins and every next day one more person joins. From the fifth day, five persons continued working as a team. In how many days, will the work be completed?
Numan does half the work as Gagan in 4/5 of the time. If together they take 16 days to complete a piece of work, then how long will it take Gagan to complete the work?
