Question

Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
(a)648
(b)1800
(c)2700
(d)10800

Answer 1

Hint: Focus on the point that the work rate of machines is constant. Let the number of bottles produced by each machine be x bottles per minute and get the value of x using the data that 270 bottles are produced per minute by 6 machines.

Complete step-by-step answer:
To start with the solution, we let the number of bottles produced by a machine per minute be x bottles.
The number of bottles produced in k minutes is given by:
$k\times \sum{\left( \text{work capacity of each machine per minute} \right)\text{.}}$
Now, try to interpret the statement given in the question in mathematical terms using the above formula, we get:
$\text{Total number of bottles produced by 6 machines in 1 minute=6}\times x$ .
$\therefore \text{270=6}\times x$
$\Rightarrow x=45\text{ bottles per minute}\text{.}$
$\therefore \text{Total number of bottles produced by 10 machine in 4 minute=10}\times \text{4}\times x$
Now we will put the value of x from the above result. On doing so, we get
$\text{Total number of bottles produced by 10 machine in 4 minute=10}\times \text{4}\times 45=1800\text{ bottles}$
Therefore, 10 machines can produce a total of 1800 bottles in 4 minutes. Hence, the answer to the above question is option (b).

Note: Questions, including working capacities of machines, have two things to be wisely selected. One is the elements of the problem that we are treating as variables, and the other is the unit. We can either let work done per unit time of each machine as variables or let the total work done by 10 machines all together be the variable. The choice of unit and element for variable decides the complexity of solving.