A cement company earns a profit of Rs. 8 per bag of white cement sold and a loss of Rs. 5 per bag of grey cement sold.
(a) The company sells 3,000 bags of white cement and 5,000 bags of grey cement in a month. What is its profit or loss?
(b) What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey bags sod is 6,400 bags?
(a) In the question profit is denoted by a positive integer whereas loss is denoted by a negative integer
It is given in the question that:
Profit earned while selling 1 bag of white cement = Rs 8
Therefore,
Profit earned while selling 3000 bags of white cement = 8 × 3000
= Rs 24000
Also,
Loss during selling 1 bag of grey cement = Rs – 5
Therefore,
Loss during 5000 bags of grey cement = - 5 × 5000
= - 25000
Hence,
Total proft or loss earned by the company = Profit + Loss
= 24000 + (-25000)
= - 1000
Hence,
A loss of Rs 1000 is being incured by the company
(b) It is given in the question that,
Loss during selling 1 bag of grey cement = Rs – 5
Therefore,
Loss during 6400 bags of grey cement = - 5 × 6400
= - 32000
Let the number of bags of white cement to be sold be x
It is also given that,
Profit earned while selling 1 bag of white cement = Rs 8
Therefore,
Profit earned while selling x bags of white cement = x × 8
= 8x
For having a condition of no profit and no loss, we have:
Profit + Loss = 0
8x + (-32000) = 0
8x = 32000
x = 
= 4000
Therefore, 4000 bags of white cement must be sold