# Profit and Loss

 sample questions

examples:

1. John sold two smartphone for $3,000 each. On one he gains 20% and on the other he loses 20%. What percent does he gain on the whole transaction? Solution: For the first smartphone Gain = 20%. Let cost price (C.P.) =$100.

Therefore, selling price (S.P.) = $(100 + 20) =$120.

When selling price (S.P.) is $120, cost price (C.P.) is$100.

Therefore, when selling price (S.P.) is $300, cost price (C.P.) =$100/120 × 300

= $(100 × 300)/120 =$30000/120

= $2,500. Thus, cost price (C.P.) of the first smartphone=$2,500.

For the second smartphone

Loss = 20%

Let cost price (C.P.) = $100. Hence, selling price (S.P.) =$(100 – 20) = $80 When selling price (S.P.) is$80, the cost price (C.P.) is $100 Therefore, when selling price (S.P.) is$300, the cost price (C.P.)

= $100/80 × 300 =$30000/80

= $3,750. Therefore, cost price (C.P.) of the second smartphone =$3,750.

Thus, the total cost price (C.P.) of two smartphone= $2,500 +$3,750 = $6,250 Thomas bought a laptop for$8,000 and spent $500 on its spares. He later sold it for$9,500.

Find his gain or loss percent.

Workout Solution:

The C.P. = $8,000 +$500 = $8,500 and S.P. =$9,500

Since, S.P. > C.P., there is a profit

Profit = S.P. – C.P.

= $9,500 –$8500

= $1,000 Profit percent = profit/(C.P.) × 100 = 1000/8500 × 100 = 200/17 = 11 13/17 Thomas gain 11 13/%. We know, selling price is the price at which an article is sold and the seller makes a profit when the selling price is more than the cost price. Solved examples: 1. A vendor sold 600 quintals of wheat at a gain of 7%. If one quintal of wheat cost him$ 250 and his total overhead charges for transportation, etc., were $1,000, find his total profit and the selling price of 600 quintals of wheat. Solution: Cost of one quintal of wheat =$250

Therefore, cost of 600 quintals of wheat = $250 ×$600 = $150,000. Overhead charges =$ 1,000.

Hence, cost price (C.P.) = $150,000 +$1,000 = $151,000. gain = 7% Net profit = 7% of$151000

= $7/100 × 151,000 =$1057000/100

= $10,570 Selling price (S.P.) = cost price (C.P.) + gain =$(151,000 + 10,570)

= $161,570. Therefore, total gain is$10,570 and the selling price is $161,570. 2. Mike bought a Phone for$5000 and sold it at a profit of 105. Find the profit and the selling price of the laptop.

Solution:

Given, C.P. of a phone= $5000 and profit% of it = 10% Therefore, profit = profit% of C.P.; (we know, profit is always calculated on C.P.) = 10% ×$5000

= (10/100) × $5000 =$500

And, S.P. = C.P. + profit

= $5000 +$500

= $5500 Hence, profit is$500 and the selling price is $5500. Formula to find profit% = profit/C.P. × 100%. 1. By selling goods for$9000; a profit of $1000 is made. Find the profit percent. Solution: Given, selling price of goods =$9000 and profit made = $1000 Therefore, C.P. = S.P. – profit =$9000 – $1000 =$8000

And, profit% = (profit/cost price) × 100%

= (1000/8000) × 100%

= (1/8) × 100%

= 12.5%

Therefore, profit percent by selling goods is 12.5%.

By selling a machine at $240 a man gains 25%. How much would he gain in percent by selling the machine at$216?

Solution:

Let cost price (C.P.) = $100 Gain = 25% Selling price =$100 + $25 =$125

If selling price is $125, then cost price is$100.

If selling price is $1, then cost price is$(100/125)

If selling price is $240, then cost price is$100/125 × 240 = $192 Now, if the S.P. is$ 216, then gain = $216 –$192 = $24 Gain% = gain/cost Price (C.P.) × 100 = 24/192 × 100 = 25/2 = 12 1/2 Therefore, gain percent by selling a machine is 12 1/2%. 3. If the selling price of 20 textbooks is the same as the cost price of 21 textbooks. Find the profit percent. Solution: Let cost price of each textbook be$1

Cost price of 20 books = $1 × 20 =$20.

Selling price of 20 textbooks = cost price of 21 textbooks = $21. Profit = selling price – cost price =$21 – $20 =$1

Profits% = profit/cost price × 100

= 1/20 × 100

= 100/20

= 5

Therefore, profit percent is 5%.

Sasha bought an article for $1750 and sold it for$1680. Find her gain or loss percent.

Solution:

Cost price of the article = $1750 Selling price of the article =$1680

Since, C.P. > S.P. there is a loss

Loss = cost price – selling price

= $1750 –$1680

= $70 Loss% = (loss/cost price) × 100% = (70/1750) × 100% = 4% Therefore, the loss percent is 4%. Find the profit or loss as percent; when a car is bought for$25000 is sold for $28000. Solution: Given, cost price of car =$25000 and selling price of it = $28000 Therefore, profit =$28000 – $25000 =$3000

Profit percent = (profit/cost price) × 100%

= (3000/25000) × 100%

= 12%

Therefore, the profit percent is 12%.

4. Lauren purchases an article for $400 and sold it for$380. Calculate her gain or loss percent.

Solution:

Given, cost price of an article = $400 and selling price of it =$380

Therefore, loss = $400 –$380 = $20 Loss percent = (loss/cost price) × 100% = (20/400) × 100% = 5% Therefore, the loss percent is 5% Aaron bought an article for$120 is sold for $150. Find the gain or loss percent. Solution: Given, cost price =$120 and selling price = $150 Therefore, gain =$150 – $120 =$30

gain% = (gain/cost price) × 100%

= (30/120) × 100%

= 25%

Therefore, the gain percent is 25%

6. James bought a bike for $600 and is sold for$550. Find profit or loss percent.

Solution:

Given, cost price = $600 and selling price =$550

Therefore, loss = C.P. – S.P.

= $600 –$550

= \$50

loss percent = (loss/cost price) × 100%

= (50/600) × 100%

= 25/3%

= 8 1/3%