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.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?

Dear Student

We denote profit in positive integer and loss in negative integer,
From the question,
Cement company earns a profit on selling 1 bag of white cement =₹8 per bag
Let the number of white cement bags be x.
Then,
Cement company earns a profit on selling x bags of white cement = (x) ×₹8
Loss on selling 1 bag of grey cement = -₹5 per bag
Then,
Loss on selling 6400 bags of grey cement = 6400 × -₹5
= -₹32000
According to the question,
Company must sell to have neither profit nor loss.
= Profit + loss = 0
= 8x + (-32000) =0
By sending -32000 from LHS to RHS it becomes 32000
= 8x = 32000
= x = 32000/8
= x = 4000
Hence, the 4000 bags of white cement have neither profit nor loss

Thanks