Question

A cement company earns a profit of Rs \[9\] per bag of white cement sold and a loss of Rs \[5\] per bag of grey cement sold. What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey bags sold is\[5400\].

Answer 1

Hint: When the selling price is more than the cost price then we will get a profit and if the cost price is more than the selling price then we will incur a loss. A total profit or loss can be calculated by adding up the total profit earned and the total loss incurred. Here they have given that the company has to have zero total profit or loss.
Formula:
Total profit or loss\[ = \] total profit earned\[ + \] total loss incurred

Complete step-by-step solution:
It is given that the company gets Rs\[9\]on selling one white cement bag and loses Rs\[5\]on selling one grey cement bag. Let us represent profit as positive and loss as negative.
Therefore, Profit earned on selling one white cement bag \[ = Rs.9\]
Loss incurred on selling one grey cement bag \[ = - Rs.5\]
It is given that the number of grey cement bags is \[5400\].
Therefore, the loss incurred on selling \[5400\] grey cement bag \[ = 5400 \times ( - 5)\]
                                                                                                        \[ = - Rs.27000\]
Thus, the company has incurred \[Rs.27000\] of loss on selling \[5400\] grey cement bags.
We aim to find no. of white cement bags that the company has sold so that they will have neither a profit nor a loss.
Let \[x\]be the number of white cement bags that the company has to sell so that they will have neither a profit nor a loss.
We already know that the company has earned \[Rs.9\]on selling one white cement bag.
Therefore, the profit earned by selling \[x\]white cement bags \[ = Rs.9 \times x\]
                                                                                                                \[ = Rs.9x\]
The given condition is the company has to have neither a profit nor a loss that is the total profit/loss is zero.
We know that Total profit/loss\[ = \] total profit\[ + \] total loss
Therefore, Total profit/loss\[ = \] total profit\[ + \] total loss \[ = 0\]
The total profit that the company earned by selling white cement bags is \[Rs.9x\]and total loss incurred by selling grey cement bags is\[ - Rs.27000\]. Let us substitute it in the above formula.
Total profit/loss\[ = 9x + ( - 27000) = 0\]
Now let us simplify the above equation to find the value of\[x\].
\[ \Rightarrow 9x - 27000 = 0\]
\[ \Rightarrow 9x = 27000\]
\[ \Rightarrow x = \dfrac{{27000}}{9}\]
\[ \Rightarrow x = 3000\]
We know that \[x\]is the number of white cement bags sold by the company. Therefore, the company has to sell \[3000\]white cement bags to have neither a profit nor a loss.

Note: We can also check whether our answer is correct or not. Since we have found that the number of white bags sold is \[3000\]so profit earned by selling these will be\[Rs.27000\]. Thus, the total profit and the total loss have become the same so there won’t be any profit and loss.