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# 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 sold is $6,400$ bags.

Given:

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.

To do:

We have to find

(a) The profit or loss, if the company sells 3,000 bags of white cement and 5,000 bags of grey cement in a month.

(b) 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

Solution:

(a) Profit on white cement $= Rs.\ 8$

Loss on grey cement $=Rs.\ 5$

Profit on 1 bag of white cement $= Rs.\ 8$

Profit on 3000 bags of white cement $= Rs.\ 8 \times 3000 = Rs.\ 24000$

Loss on 1 bag grey cement $= Rs.\ 5$

Loss on 5000 bags grey cement $= Rs.\ 5 \times 5000$

$= Rs.\ 25000$

Total loss $=$ Total loss $-$ Total profit

$= 25000 - 24000$

$= Rs.\ 1000$

Therefore

**The total loss is $Rs.\ 1000$.**

(b) Loss on 1 bag grey cement $= Rs.\ 5$

Loss on 6400 bag grey cement $= Rs.\ 5 \times 6400$

$= Rs.\ 32000$

Let the number of bags of white cement $= x$

Profit on 1 bag white cement $= Rs.\ 8$

Profit on $x$ bags white cement $= Rs.\ 8x$

Now, Total profit $= 0$

Total profit $-$ Total loss $= 0$

$\Rightarrow 8x - (32000) = 0$

$\Rightarrow 8x = 32000$

$\Rightarrow x = \frac{32000}{8}$

$\Rightarrow x = 4000$

Therefore,

**The number of bags of white cement it must sell is $4000$ bags.**

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