Question

Mr Kasam runs a small business of making earthen pots. He makes a certain number of pots on a daily basis. Production cost for each pot is Rs 40 more than 10 times the total number of pots he makes in one day. If the production cost of all pots per day is Rs 600, find the production cost of one pot and the number of pots he makes per day.

Answer 1

Hint:This problem is related to the Algebra. In the problem, it is very clear that there is only one variable, i.e.number of pot. All the conditions written are related to that variable; hence we have one equation with one variable.Solving that equation we get the required answer.

Complete step-by-step answer:
In the problem, it is clear that the quantity of pot produced per day is variable and is unknown. All the conditions are in terms of that variable.
Let us assume that the total number of pots produced per day is equal to $x$.
Inquisition they given , production cost for each pot is Rs 40 more than 10 times the total number of pots he makes in one day
Then, the production cost per pot
$ = 10x + 40$…………………….. (1)
Now, it is given that the production cost per day is Rs 600, therefore, mathematically, it can be expressed as
$ \Rightarrow (10x + 40).x = 600$
Rearranging and simplifying the above expression, we get
$
   \Rightarrow (10x + 40).x = 600 \\
   \Rightarrow 10{x^2} + 40x - 600 = 0 \\
   \Rightarrow {x^2} + 4x - 60 = 0 \\
 $
Now, factorising and simplifying the above expression, we get
$
   \Rightarrow {x^2} + 10x - 6x - 60 = 0 \\
   \Rightarrow x(x + 10) - 6(x + 10) = 0 \\
   \Rightarrow (x + 10)(x - 6) = 0 \\
 $
This expression will give two values of $x$as
$x = - 10,6$
Since, pots produced per day cannot be negative, therefore, $x = - 10$ will be rejected. With this, we have only one value of $x$ left, which is $x = 6$.
Thus the number of pots produced per day$ = x = 6$
And the production cost of one pot can be found by substituting value of $x$ in equation (1)
$
   = 10x + 40 \\
   = 10 \times 6 + 40 \\
   = 100 \\
 $
So, production cost of one pot is Rs.100 and total tumber of pots per day = x = 6 pots

Note:It is noted here that we have found out that there is one variable and the equation will be in that variable only. Sometimes, it is possible that when one variable is there, a linear equation can be formed with one variable which is easy to solve but the question was framed in such a way that a quadratic equation has been formed. So you should be very careful while reading the problem.