` 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%