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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Updated on: 10-Oct-2022

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