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%
