Profit, loss and discount questions with answers

Questions

1. Question 1Selling price from a profit or loss %

   A shopkeeper buys a school bag for $150 and sells it at a loss of 15%. Find the selling price.

   Show the worked solution

   1. Step 1: Write the selling price as a percentage of the price it is based on$100\% - 15\% = 85\%$
   2. Step 2: Multiply (in dollars)$\text{Selling price} = \dfrac{85}{100} \times 150$$= 127.50$The selling price is $127.50.
2. Question 2Percentage profit or loss (on the cost price)

   A trader bought a fan for $80 and sold it for $120. Find the percentage profit.

   Show the worked solution

   1. Step 1: Profit = selling price − cost price (in dollars)$\text{Profit} = 120 - 80$$\phantom{\text{Profit}} = 40$
   2. Step 2: Percentage profit: divide by which price, then multiply by 100%?$\text{Percentage profit} = \dfrac{40}{80} \times 100\%$$= 50\%$
3. Question 3Selling price after a discount

   A rice cooker has a marked price of $80. It is sold at a discount of 30%. Find the selling price.

   Show the worked solution

   1. Step 1: Write the selling price as a percentage of the price it is based on$100\% - 30\% = 70\%$
   2. Step 2: Multiply (in dollars)$\text{Selling price} = \dfrac{70}{100} \times 80$$= 56$The selling price is $56.
4. Question 4Percentage discount (on the marked price)

   The marked price of a pair of earphones is $40. During a sale it is sold for $34. Find the percentage discount.

   Show the worked solution

   1. Step 1: Discount = marked price − selling price (in dollars)$\text{Discount} = 40 - 34$$\phantom{\text{Discount}} = 6$
   2. Step 2: Percentage discount: divide by which price, then multiply by 100%?$\text{Percentage discount} = \dfrac{6}{40} \times 100\%$$= 15\%$
5. Question 5Discount, then profit on the cost price

   A shop buys a sofa for $300 and marks it at $525. During a sale it is sold at a discount of 10%. Find the percentage profit.

   Show the worked solution

   1. Step 1: Find the selling price after the discount (in dollars)$\text{Selling price} = \dfrac{90}{100} \times 525$$\phantom{\text{Selling price}} = 472.50$
   2. Step 2: Profit = selling price − cost price$\text{Profit} = 472.50 - 300$$\phantom{\text{Profit}} = 172.50$
   3. Step 3: Percentage profit: divide by which price, then multiply by 100%?$\text{Percentage profit} = \dfrac{172.50}{300} \times 100\%$$= 57.5\%$
6. Question 6Work backwards to the cost or marked price

   The marked price of a dining table is $600. A shop sells it at a discount of 10% and still makes a profit of 50% on the cost price. Find the cost price of the dining table.

   Show the worked solution

   1. Step 1: The selling price: (100% − the discount) of the MARKED price$\text{Selling price} = \dfrac{90}{100} \times 600$$\phantom{\text{Selling price}} = 540$
   2. Step 2: The selling price is (100% + the profit) of the COST price: work backwards$100\% + 50\% = 150\%$$\text{Cost price} = \dfrac{540}{150} \times 100$$\phantom{\text{Cost price}} = 360$The cost price is $360.