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. How much he sells the white cement bag to have neither profit nor loss if the number of grey bags sold is 6,400.a)2000 bagsb)3000 bagsc)5000 bagsd)4000 bagsCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Given data:
Profit earned on selling 1 bag of white cement = Rs. 8
Loss incurred on selling 1 bag of grey cement = Rs. 5
Number of grey cement bags sold = 6,400

To find:
Number of white cement bags to be sold to have neither profit nor loss

Solution:
Let the cost price of 1 bag of white cement be x.
Selling price of 1 bag of white cement = cost price + profit
= x + 8
Selling price of 1 bag of grey cement = cost price - loss
= x - 5

Total cost price of 6,400 bags of grey cement = 6,400 * (x - 5)

For neither profit nor loss, the total selling price of white cement should be equal to the total cost price of grey cement.
Total selling price of white cement = number of white cement bags sold * selling price per bag
= n * (x + 8), where n is the number of white cement bags to be sold

Equating the total selling price of white cement to the total cost price of grey cement, we get:

n * (x + 8) = 6,400 * (x - 5)

nx + 8n = 6,400x - 32,000

nx - 6,392x = -32,000 - 8n

x(n - 6,392) = -32,000 - 8n

x = (-32,000 - 8n) / (n - 6,392)

Since x is the cost price of 1 bag of white cement, it should be a positive value. Therefore, we can assume that n > 6,392.

Now, we can check the options given and find the value of n that satisfies the condition n > 6,392 and gives a positive value of x.

(a) n = 2,000
x = (-32,000 - 8*2,000) / (2,000 - 6,392) = -72.67 (not possible)

(b) n = 3,000
x = (-32,000 - 8*3,000) / (3,000 - 6,392) = -29.33 (not possible)

(c) n = 5,000
x = (-32,000 - 8*5,000) / (5,000 - 6,392) = 80

(d) n = 4,000
x = (-32,000 - 8*4,000) / (4,000 - 6,392) = 20

Therefore, the correct option is (d) 4,000 bags of white cement should be sold to have neither profit nor loss.

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