ChandlerBong wrote:
A shopkeeper purchased 30 identical units of item X at $100 each. He sold some of the units at $p each and the remaining at $y each. What was the shopkeeper’s gross profit?
(A) If the cost price had been $10 less per unit of X, the gross profit would have been $2,700.
(B) If the selling price had been $2 more for all 30 units, the gross profit would have been $2,460.
- Let's assume that the number of items sold at $p = x
- Number of items sold at $y = 30 - x
- Cost Price of 30 items = 30*$100 = $3000
- Profit = Selling Price - Cost Price
= p*x + y(30-x) - 3000
= px + 30y - yx - 3000
Statement 1(A) If the cost price had been $10 less per unit of X, the gross profit would have been $2,700.New Cost Price of each item = $90
The selling price remains the same. So-
Selling Price = p*x + y(30-x)
Profit = p*x + y(30-x) - (90*30)
2700 = px + 30y - yx - 2700
Subtracting 300 on both sides of the equation we get
2400 = px + 30y - yx - 3000
Therefore shopkeeper’s gross profit was $2400.
The statement alone is sufficient and we can eliminate options B, C, and E.
Statement 2(B) If the selling price had been $2 more for all 30 units, the gross profit would have been $2,460Selling Price = (p+2)*x + (y+2)(30-x)
= px + 2x + 30y - yx + 60 - 2x
= px + 30y - yx + 60
Cost Price = $30*100 = $3000
Profit =px + 30y - yx + 60 - 3000
2460 =px + 30y - yx + 60 - 3000
Subtracting 60 from both sides of the equation
2400 =px + 30y - yx - 3000
Therefore shopkeeper’s gross profit was $2400.
This statement is also sufficient to find the profit.
Option D