A cement company earns a profit of ₹ 8 per bag of white cement sold and a loss of ₹ 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 sold is 6,400 bags.

Solution

We indicate profit in positive integer and loss in negative integer.

(a) Profit gained while selling 1 bag of white cement = Rs 8

Profit gained while selling 3000 bags of white cement = 8 × 3000= 24000

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

Loss suffered while selling 5000 bags of grey cement = −5 × 5000= −25000

Total profit/loss gained = Profit + Loss

= 24000 + (−25000) = −1000

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

(b) Loss suffered while selling 1 bag of grey cement = −Rs 5

The loss suffered while selling 6400 bags of grey cement = (−5) × 6400

= −32000

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

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

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

= 8x

In the condition of no profit no loss,

Profit gained + Loss suffered = 0

8x + (−32000) = 0

8x = 32000

x = 4000

Hence, 4000 bags of white cement must be sold.

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