<h3>A manufacturer sells an item to an agency at a profit of 25%. The agency sells the item to a shopkeeper at 10% profit and shopkeeper sells the item at a profit of 20%. If the selling price of the item is $594, find the manufacturing price.</h3>
Answer: $360
Step-by-step explanation:
Let Mp the manufacturing price.
First step:
Manufacturer sells at a profit of 25% = Mp + Mp·0.25 = Mp·1.25
Second step:
Agency sells at a profit of 10% = 1.25Mp + 1.25Mp·0.10 = Mp·1.375
Third step:
Shopkeeper sells at a profit of 20% = 1.375Mp + 1.375Mp·0.20 = Mp·1.65
Then the final price = 1.65·Mp
1.65Mp = $594
Mp = $594/1.65 = $360 ►Manufacturer price
Answer: $360
Verification
Manufacturer sells at a profit of 25% = 25/100 = 0.25:
$360 + $360·0.25 = $360(1 + 0.25) = $360 + $90 = $450
Agency sells at a profit of 10% = 10/100 = 0.10:
$450 + $450·0.10 = $450(1 + 0.10) = $450 + $45 = $495
Shopkeeper sells at a profit of 20% = 20/100 = 0.20
$495 + $495·0.20 = $495(1 + 0.20) = $495 + $99 = $594 Checked!