Question

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

1) 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?

2) 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 6,400 bags.

Answer 1

Profit is denoted by a positive integer and loss is denoted by a negative integer.

1) Profit earned while selling 1 bag of white cement = Rs 8

Profit earned while selling 3000 bags of white cement = 8 × 3000

= 24000

Loss incurred while selling 1 bag of grey cement = −Rs 5

Loss incurred while selling 5000 bags of grey cement = −5 × 5000

= −25000

Total profit/loss earned = Profit + Loss

= 24000 + (−25000) = −1000

Therefore, a loss of Rs 1000 will be incurred by the company.

2) Loss incurred while selling 1 bag of grey cement = −Rs 5

Loss incurred while selling 6400 bags of grey cement = (−5) × 6400

= −32000

Let the number of bags of white cement to be sold be x.

Profit earned while selling 1 bag of white cement = Rs 8

Profit earned while selling x bags of white cement = x × 8

= 8x

In condition of no profit no loss,

Profit earned + Loss incurred = 0

8x + (−32000) = 0

8x = 32000

x = 4000

Therefore, 4000 bags of white cement must be sold.