2. Cost Price (C.P.):
The price at which an article is purchased, is called as its cost price.
Selling Price (S.P.):
The price at which an article is sold, is called its selling price.
Profit or Gain: If S.P. > C.P., the seller is said to have a profit or gain.
Loss: If S.P. < C.P., the seller is said to have incurred a loss.
Important Facts
5. In a certain store, the profit is 320 percentage of the cost. If the cost
increases by 25 percentage but the selling price remains constant,
approximately what percentage of the selling price is the profit?
Ans.
6. A vendor bought toffees at 6 for a rupee. How many for a rupee must he
sell to gain 20 percentage?
Ans.
7. If goods are purchased for Rs.900, one third of them sold at a profit 10
percentage, at what profit percent should the remaining be sold to obtain
a profit 15 percentage?
Ans.
1
3
× 10 +
2
3
× 𝑥 = 15
𝑥 = 15
8. The list price of an article is Rs. 2000. It is sold for Rs. 1666 after giving
three successive discounts. If two discounts are 10 and 50/9 percentages,
find the third discount percentage.
Ans.
10% 0f 2000 = 200 , after first discount price = 1800
50/9 % of 1800 = 100, after 1800 discount price = 1700
1700-1666= 34 & 34/ 1700= 2%
9. • Three successive discounts of 10, 10, and 5 percentages are equivalent
to a single discount percentage of
Ans. Initial value : 100
discounted value =
90
100
×
90
100
×
95
100
× 100 = 76.95
100-76.95 = 23.05
10. The cost price of 4 articles is same as the selling price of 3 articles. What is the loss or
gain percentage.
11. 8. Gowtham purchased a car for Rs 2,50,000 and sold it for Rs 3,48,000.
What is the percent profit the made on the car ?
Ans.
C.P. = 250000; S.P.=348000
Profit = 348000-250000=98000
Profit %=
98000
250000
× 100 % = 39.2%
12. 1. The cost price of 20 articles is the same as the selling price of x articles. If the
profit is 25 percentage, then the value of x is:
13. 2. If selling price is doubled, the profit triples. Find the profit percent:
14. 3. The percentage profit earned by selling an article for Rs. 1920 is equal to the
percentage loss incurred by selling the same article for Rs. 1280. At what price
should the article be sold to make 25% profit?
15. 4. A shopkeeper expects a gain of 22.5 percentage on his cost price. If
in a week, his sale was of Rs. 392, what was his profit?
Solution:
C.P + (22.5/100) C.P = S.P = 392
C.P= 392 Profit = 72
16. 5. Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each
one of them at the rate of Rs. 33. What was his percentage profit?
17. 6. A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at
Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
18. 7. On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The
cost price of a ball is:
19. 9. Three successive discounts of 10, 10, and 5 percentages are equivalent to a
single discount percentage of
Solution:
Let the price be 100
After 10% discount the price becomes 90
On this 90 again 10% discount the price becomes 81
On this 81 again 5% discount the price becomes 73.95
Equivalent to single discount percentage of (100-73.95) = 23.05
20. 10. A man sold two articles for Rs. 2880 each. On one he gains 20 percentage and
on the other he losses 20 percentage. Find the total loss in Rs.
Solution:
Total selling price= 2880+ 2880 = 5760
Cost price of first article = 2880 x (100/120) = 2400
Cost price of second article = 2880 x (100/80) = 3600
c.p of two articles = 6000
Loss = 6000 – 5760 = 240
4% loss
21. Ex 2.
A gold bracelet is sold for 14500 at a loss of 20 %. What is the cost price of the gold
bracelet?
Ans.
Given S.P.=14500
Loss % = 20
𝐶. 𝑃. =
100
(100 − 𝐿𝑜𝑠𝑠 %)
× 𝑆. 𝑃.
𝐶. 𝑃. =
100
80
× 14500 = 18125
22. Ex 3.
A trader expects a gain of 15 % on his cost price. If in a week his sale is of Rs. 580, then what is his
profit ?
Ans.
𝐶. 𝑃. =
100
(100 + 𝐺𝑎𝑖𝑛 %)
× 𝑆. 𝑃.
𝐶. 𝑃. =
100
(100 + 15)
× 580 = 504.35
Therefore,
𝑃𝑟𝑜𝑓𝑖𝑡 = 𝑆. 𝑃. −𝐶. 𝑃. = 580 − 504.35 = 75.65
23. Ex 4.
If a boy sells a book for Rs. 450 he gets a loss of 10 %, then find cost price. To gain 10 %, what should be the
selling price?
Ans.
Let C.P. of book = x and S.P. = Rs. 450
S.P. of book = C.P. – (10% of C.P.)
𝑆. 𝑃. = 𝐶. 𝑃. – (0.10 × 𝐶. 𝑃. )
450 = 0.9 × 𝐶. 𝑃.
𝐶. 𝑃. = 𝑅𝑠. 500
Now,
𝑆. 𝑃. =
110
100
× 500 = 550
24. Ex 5.
By selling 33 metres of cloth, one gains the selling price of 11 metres.
Find the gain percent ?
Ans.
(S.P. of 33 m)-(C.P. of 33 m) = Gain = S.P. of 11 m
S.P. of 22 m = C.P. of 33 m
Let C.P. of each metre be Rs. 1.
Therefore, 𝐺𝑎𝑖𝑛 % =
11
22
× 100 % = 50 %
25. Ex 6.
A vendor bought buttons at 6 for a rupee. How many for a rupee must he
sell to gain 20% ?
Ans.
C.P. of 6 buttons = Rs. 1
Gain = 20 %
S.P of 6 buttons=
120
100
× 1 =
6
5
For Rs.
6
5
, buttons sold = 6.
For Rs. 1, buttons sold = 6 ×
5
6
= 5
26. Ex 7.
A dealer marks price of all the goods at 30 % above the cost price and assumes that he will make a
profit of 15 % if he offers a discount of 15%. Find what will be his actual profit on sales?
Ans.
Let cost price goods be Rs. 100
Marked price (Selling Price) marked by the shopkeeper on goods = Rs. 130
He sells the goods at a discount of 15 %
Therefore,
Selling price = 85 % of Rs. 130 = Rs. 110.50
Gain = S.P. – C.P. = 110.5 – 100 = 10.50 %
27. Ex 8.
By selling an item for Rs. 15, a trader loses one sixteenth of what it costs him. The cost price of the item is?
Ans.
𝐶. 𝑃. −𝑆. 𝑃 =
1
16
𝐶. 𝑃
𝐶. 𝑃. −15 =
1
16
𝐶. 𝑃.
15
16
(𝐶. 𝑃. )=15
𝐶. 𝑃. = 16
28. Ex 9.
A manufacturer sells a pair shoes to a wholesale dealer at a profit of 20 %. Wholesaler sells them to retailer at
a profit of 25 %. The shoes are again sold to the customer for Rs. 50.50, there by earning a profit of 30 %. Find
the cost price of manufacturer?
Ans.
Profit earned by manufacturer = 20 %
Profit earned by wholesaler = 25 %
Profit earned by retailer = 30%
S.P. of shoes = Rs. 50
Therefore, 130% 𝑜𝑓 125% 𝑜𝑓 120% 𝑜𝑓 𝑥 = 50.50
𝑥 = 25.89
Cost price of shoes is 25.89
29. Ex 10.
John purchased a machine for Rs. 80,000. After spending Rs. 5000 on repair
and Rs. 1000 on transport he sold it with 25% profit. What price did he sell the
machine?
Ans.
𝐶. 𝑃. = 80000 + 5000 + 1000 = 86000
profit =25%
𝑆. 𝑃 = 86000 + 86000 ×
1
4
= 107500
30. Ex 11.
A man purchased two plots for Rs. 5,00,000. On one he gains 15 % while on the
other he losses 15%. Find how much does he gain or lose in the transaction ?
Ans.
Generally in such cases, there is always loss.
So always remember, when two materials are sold and if one material gets profit
and the other gets a loss, then use the trick shown below to calculate the loss.
𝐿𝑜𝑠𝑠 % =
𝐶𝑜𝑚𝑚𝑜𝑛 𝐿𝑜𝑠𝑠 𝑎𝑛𝑑 𝐺𝑎𝑖𝑛 %
10
2
=
𝑥
10
2
Therefore, here common loss and gain % = 15%
Hence,
𝐿𝑜𝑠𝑠 % =
15
10
2
= 2.25 %
31. Ex 12.
A train journey from P to D by an X-express has 4 classes of fares. The distance between P and D is 1100 km.
Assume that the train does not stop at any station unless otherwise indicated.
The running cost per kilometer: AC – Rs. 25; Non-AC – Rs. 10
What is the approximate profit for the railways if the X-express way runs at full occupancy on a particular
day ?
Ans.
Total fare collected at full occupancy = 8 × 72 × 300 + 2 × 64 × 898 + 2 × 45 × 1388 + 1 × 26 × 2691
= 482630
Total running cost = 25 × 5 × 1100 + 10 × 8 × 1100 = 225500
Profit = 482630 − 225500 = 257130
Class Price in Rs. No of Berths per boogie No of Bogies of Train
3 Tier 300 72 8
AC-3 Tier 898 64 2
AC-2 Tier 1388 45 2
AC- First Class 2691 26 1
32. Ex 13.
A train journey from P to D by an X-express has 4 classes of fares. The distance between P and D is 1100 km.
Assume that the train does not stop at any station unless otherwise indicated.
The running cost per kilometer: AC – Rs. 25; Non-AC – Rs. 10
Assuming full occupancy, a bogie of which class exhibits the highest profit margin?
Ans. Since,
Profit margin = Total fare collected – Total running cost
Profit margin exhibited by 3 tier = 8 × 72 × 300 − 8 × 10 × 1100 = 84800
Profit margin exhibited by AC 3 tier = 2 × 64 × 898 − 2 × 25 × 1100 =59944
Profit margin exhibited by AC 2 tier = 2 × 45 × 1388 − 2 × 25 × 1100 = 69920
Profit margin exhibited by AC First Class = 1 × 26 × 2691 − 1 × 25 × 1100 = 42466
Clearly, 3 Tier has the highest profit.
Class Price in Rs. No of Berths per bogie No of Bogies of Train
3 Tier 300 72 8
AC-3 Tier 898 64 2
AC-2 Tier 1388 45 2
AC- First Class 2691 26 1
33. Ex 14.
A train journey from P to D by an X-express has 4 classes of fares. The distance between P and D is 1100 km.
Assume that the train does not stop at any station unless otherwise indicated.
The running cost per kilometer: AC – Rs. 25; Non-AC – Rs. 10
The heist revenue for a journey from P to D will always be generated by?
Ans.
Revenue generated by 3 Tier = 8 × 72 × 300 =172800
Revenue generated by AC 3 Tier = 2 × 64 × 898 =114944
Revenue generated by AC 2 Tier = 2 × 45 × 1388 =124920
Revenue generated by AC First Class = 1 × 26 × 2691 =69966
Clearly, it is the highest for 3 Tier
Class Price in Rs. No of Berths per bogie No of Bogies of Train
3 Tier 300 72 8
AC-3 Tier 898 64 2
AC-2 Tier 1388 45 2
AC- First Class 2691 26 1
34. Ex 15.
A train journey from P to D by an X-express has 4 classes of fares. The distance between P and D is 1100 km.
Assume that the train does not stop at any station unless otherwise indicated.
The running cost per kilometer: AC – Rs. 25; Non-AC – Rs. 10
Assuming full occupancy in all the classes, for a journey between P and D, the profit margin (as a
percentage of running costs) of the class showing the lowest profit is approximately?
Ans.
The profit margin collected by AC First class is the lowest.
Required percentage =
42466
27500
× 100 % = 154.4%
Class Price in Rs. No of Berths per bogie No of Bogies of Train
3 Tier 300 72 8
AC-3 Tier 898 64 2
AC-2 Tier 1388 45 2
AC- First Class 2691 26 1
35. When a person sells two similar items, one at a gain of say,
𝑥% and the other at a loss of 𝑥%, then the seller always
incurs a loss given by:
𝐿𝑜𝑠𝑠 % =
𝐶𝑜𝑚𝑚𝑜𝑛 𝐿𝑜𝑠𝑠 𝑎𝑛𝑑 𝐺𝑎𝑖𝑛 %
10
2
=
𝑥
10
2
Important Formulae
