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 3000 bags of white cement and 5000 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 sold is 6400 bags?

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

Profit earned  by selling 1 bag of white cement is = rs 8 

Loss incurred by selling 1 bag of grey cement = -5

 (a) Profit earned by selling 3000 bags of white cement = 8 × 3000 =rs 24000 

Loss incurred by selling 5000 bags of grey cement = -5 ×5000

 = - 25000 RS 

Total profit/loss earned = profit + loss 

=24000 +( - 25000)

= -1000 

therefore a loss of rs 1000 will be incurred by the company.

(B)

Loss incurred while selling 6400 bags of grey cement = - 5 × 6400 = - 32000

Let the number of the bags of white cements to be sold be X.

 Profit earned by selling X bags of white cement = 8 × X = 8 X

In condition of no profit no loss profit earned+ loss incurred=0

8 X + (- 32000 ) = 0

 8 X = 32 000 

x = 4000

 Therefore 4000 bags of white cement must be sold.