Profit and loss questions with solutions

Profit and loss questions 

Let us first revise the basic concepts and formulas before solving the questions.

1. Cost Price = Buying price + Total overhead charges (if any)
2. Profit = Selling Price – Cost Price
3. Loss = Cost Price – Selling Price
4. \text{ Profit }(\text { in } \%)=\frac{\text { Profit }}{\text { Cost Price }} \times 100=\frac{\text { Selling price }-\text { Cost price }}{\text { Cost Price }} \times 100
5. \text { Loss }(\text { in } \%)=\frac{\text { Loss }}{\text { Cost Price }} \times 100=\frac{\text { Cost price }-\text { Selling price }}{\text { Cost Price }} \times 100
6. Marked Price = Selling price + Discount
7. \text {  Discount }(\text { in } \%)=\frac{\text { Discount }}{\text { Marked Price }} \times 100=\frac{\text { Marked Price }-\text {Selling Price }}{\text { Marked } \text { Price }} \times 100

Solved examples

1. Vickey brought 10 apples for Rs 80 and sold them at Rs 100. Find his profit percentage.

Solution:

Cost price of 10 apples = Rs 80

Selling price of 10 apples = Rs 100

Profit = Selling Price – Cost price = Rs 100 – Rs 80 = Rs 20

Profit percentage =\frac{\text { Selling price-Cost price }}{\text { Cost price }} \times 100=\frac{100-80}{80} \times 100=\frac{20}{80}\times 100=25 \%

Hence, Vickey got a profit of 25%.

2. A shopkeeper sold a TV for Rs 50,000. He gained a profit of Rs 5000. Find the cost price of the TV.

Solution:

Selling Price = Rs 50,000

Profit = Rs 5000

Cost price = Selling Price – Profit = 50,000-5000 = Rs 45000

Hence, the cost price of the Tv is Rs 45,000.

3. Mohit brought a second-hand motorcycle for Rs 20,000 and spent Rs 6,000 for repairing it. At what price should he sell the motorcycle to get a profit of 10%?

Solution:

Cost of the motorcycle brought by Mohit = Rs 20,000

Repairing charges = Rs 6000

Cost price = Rs 20,000 + Rs 6000 = Rs 26,000

Profit = 10% of Cost Price

= 10% of Rs 26,000

=\frac{10}{100} \times 26,000

= Rs 2600

Selling Price = Cost price + Profit = Rs 26000 + Rs 2600 = Rs 28600

Hence Mohit should sell the motorcycle at Rs 28600 to get a profit of 10%.

4. Priya brought a pair of shoes for Rs 1000. If the shopkeeper sold at 25% profit, Find the cost price of the shoes.

Solution:

Selling Price = Rs 1000

Profit percentage = 25 %

Let cost price be x.

Profit percentage =\frac{\text { Selling price-Cost Price }}{\text { Cost Price }} \times 100

\Rightarrow 25=\frac{1000-x}{x} \times 100

\Rightarrow \quad 25 x=100,000-100 x

\Rightarrow \quad 25 x+100 x=100,000

\Rightarrow \quad 125 x=100,000

\Rightarrow \quad x=800

Hence the cost price for the pair of shoes is equal to Rs 800.

5. A businessman brought an office for Rs 500,000. Find the selling price if he had 8% loss.

Cost Price = Rs 500,000

Loss Percentage = 8%

Loss = 8% of Rs 500,000

=\frac{8}{100} \times 500,000

= 8 × 5000

= 40,000

Selling price = Cost price – loss

= 500,000 – 40,000

= 460,000

Hence the selling price of the office is Rs 460,000.

6. A decorative piece was marked Rs 10,000. The shopkeeper offered a discount of 20%. Find the selling price of the decorative piece.

Solution:

Marked price = Rs 10,000

Let selling price be x. 

Discount = 20% of Marked Price

Marked price = Selling Price + discount

⇒ 10,000 = x + 2000

∴ x = 10,000 – 2000 = 8000

Hence the selling price of the decorative piece is equal to Rs 8000.

7. A shopkeeper sold a dress with a marked price of  Rs 800 after a discount of 5% but got a loss of Rs 100. Find the cost price of the dress.

Solution:

Marked Price = Rs 800

Discount Percentage = 5%

Loss = Rs 100

Discount = 5 % of marked price = 5% of Rs 800 =\frac{5}{100} \times 800=\text{Rs} 40

Selling Price = Marked Price – Discount

                       = Rs 800 – Rs 40

                       = Rs 760

Cost Price = Selling Price + loss

                   = Rs 760 + Rs 100

                   = Rs 860

Hence the cost price of the dress is Rs 860.

8. Priya brought two baskets for Rs 50 each. She sold 1 basket for Rs 60 and the other for Rs 45. Find profit or loss on both baskets. Also, find the total profit or loss.

Solution:

Basket 1

Cost Price = Rs 50

Selling Price = Rs 60

Since the cost price is less than the selling price, profit has occurred.

Profit = Selling price – Cost price

           = Rs 60 – Rs 50

           = Rs 10

Basket 2

Cost Price = Rs 50

Selling Price = Rs 45

Since the cost price is more than the selling price, loss has occurred.

Loss = Cost price – Selling price

         =Rs 50 – Rs 45

         = Rs 5

Total Cost Price = Rs 50 + Rs 50 = Rs 100

Total selling price = Rs 60 + Rs 45 = Rs 105

Total profit = Rs 105 – Rs 100 = Rs 5

Total profit percentage =\frac{\text { Total cost } \text { Price }}{\text { Total }} \times 100=\frac{5}{100} \times 100=5 \%

Hence Priya got a total profit of 5%.

9. Kavya bought 20 oranges for Rs 100 out of which 5 oranges turned bad. She sold the remaining at Rs 6. Find the profit or loss. 

Also, find the profit or loss if no oranges turn bad.

Solution:

The total cost price of 20 oranges = Rs 100

Number of oranges that turned bad = 5

Remaining number of oranges sold by Kavya = 20 – 5 = 15

The selling price of 1 orange = Rs 6

The total selling price of 15 oranges = Rs (6 × 15) = Rs 90

Since the total cost price (Rs 100) is less than the total selling price (Rs 90), Kavya had a loss.

Total Loss = Rs 100 – Rs 90 = Rs 10

Total Loss percentage =\frac{\text { Total loss }}{\text { Total cost price }} \times 100=\frac{10}{100} \times 100=10 \%