Lesson 5 Profit and Loss
Rajukanta bought a story book of cost Rs. 600 at a discount of 15%. How much amount does he have to pay to the shopkeeper?
SolutionHere, the marked price of story book (MP) = Rs. 600
Discount (D) = 15%
Selling price (SP) = ?
We know that,
Discount amount = 15% of Rs. 600
Selling Price (SP) = MP - Discount amount
= 600 - 90
= Rs. 510
Alternative methodLet the marked price (MP) = 100x
Discount (D) = 15x
Selling price (SP) = 85x
By the question,
MP = Rs. 600
or, 100x = 600
∴ x = 6
85x = 85 x 6
= Rs. 510
Hence, he has to pay Rs. 510 for the story books.
Example 2If Nabin buys a mobile at 8% discount and has to pay Rs. 22,080 to the shopkeeper, find the marked price of the mobile.
SolutionHere, Discount of mobile = 8%
Selling price (SP) = Rs. 22,080
Marked price (MP) = ?
Let, marked price (MP) = x
We know that,
SP = MP - discount % of MP
or, 22080 = x - 8/100 x
or, 22080 = x - 8x/100
or, 22080 = 100x - 8x/100
or, 22080 = 92x/100
or, x = 22080 x 100/92
Alternative methodHere,
Let, marked price (MP) = 100x
Discount (D) = 8x
Selling price (SP) = MP - discount amount
= 100x - 8x
= 92x
By the question,
SP = Rs. 22,080
or, 92x = 22,080
∴ x = 240
MP = 100x
= 100 x 240
= Rs. 24,000
Hence, the marked price of the mobile is Rs. 24,000.
Example 3Ujjwal buys a computer at Rs. 36,000. The marked price of the computer is 25% above the cost price. If he sells the computer at a 25% discount then,
(a) What is the marked price of the computer?
(b) What is the discount amount?
(c) What is the selling price of the computer?
(d) What is his profit or loss percent from that computer? Find it.
SolutionHere, cost price of computer (CP) = Rs. 36,000
By the question,
(a) Marked price (MP) = ?
Marked price (MP) = CP + 25% of CP
= 36000 + 36000 x 25/100
= 36000 + 9000
= Rs. 45,000
(b) Discount = ?
We know that,
Discount = discount % of MP
= 45000 x 25/100
= Rs. 11,250
(c) Selling price (SP) = ?
By formula,
SP = MP - Discount
= 45000 - 11250
= Rs. 33,750
(d) Profit or Loss percent = ?
Since the selling price of the computer is less than the cost price, there is a loss.
Loss = CP - SP
= 36,000 - 33,750
= Rs. 2,250
Loss percent = (Loss / CP) x 100
= 2250 / 36000 x 100
= 6.25%
Exercise 5.1
1. The following are the calculations to find the selling price (SP) for each item based on the given marked price (MP) and discount amount.
a. Books:
Marked Price (MP) = Rs 480
Discount = Rs 48
SP = MP - Discount
= 480 - 48
= Rs 432
b. Shoes:
Marked Price (MP) = Rs 1250
Discount = Rs 250
SP = MP - Discount
= 1250 - 250
= Rs 1000
c. Calculator:
Marked Price (MP) = Rs 750
Discount = Rs 50
SP = MP - Discount
= 750 - 50
= Rs 700
d. Shirt:
Marked Price (MP) = Rs 1500
Discount = Rs 300
SP = MP - Discount
= 1500 - 300
= Rs 1200
e. Mobile:
Marked Price (MP) = Rs 24500
Discount = Rs 480
SP = MP - Discount
= 24500 - 480
= Rs 240
2. The table below shows the marked price (MP) and selling price (SP) of different items. Calculate the discount amount and discount percentage for each item.
a. Watch:
Marked Price (MP) = Rs 2200
Discount = 15%
SP = MP - (Discount% of MP)
= 2200 - (15/100 × 2200)
= 2200 - 330
= Rs 1870
b. Bag:
Marked Price (MP) = Rs 1750
Discount = 12%
SP = MP - (Discount% of MP)
= 1750 - (12/100 × 1750)
= 1750 - 210
= Rs 1540
c. Cupboard:
Marked Price (MP) = Rs 30000
Discount = 25%
SP = MP - (Discount% of MP)
= 30000 - (25/100 × 30000)
= 30000 - 7500
= Rs 22500
d. Computer:
Marked Price (MP) = Rs 40000
Discount = 10%
SP = MP - (Discount% of MP)
= 40000 - (10/100 × 40000)
= 40000 - 4000
= Rs 36000
e. TV:
Marked Price (MP) = Rs 54500
Discount = 20%
SP = MP - (Discount% of MP)
= 54500 - (20/100 × 54500)
= 54500 - 10900
= Rs 43600
3. The following are the calculations to find the Marked Price (MP) for each item based on the given Selling Price (SP) and Discount Percentage (%).
a. Table:
Selling Price (SP) = Rs 2150
Discount % = 14%
Marked Price (MP) = SP / (1 - Discount % / 100)
= 2150 / (1 - 14 / 100)
= 2150 / 0.86
= Rs 2500
b. Sari:
Selling Price (SP) = Rs 1360
Discount % = 20%
Marked Price (MP) = SP / (1 - Discount % / 100)
= 1360 / (1 - 20 / 100)
= 1360 / 0.80
= Rs 1700
c. Coat:
Selling Price (SP) = Rs 4100
Discount % = 18%
Marked Price (MP) = SP / (1 - Discount % / 100)
= 4100 / (1 - 18 / 100)
= 4100 / 0.82
= Rs 5000
d. Computer:
Selling Price (SP) = Rs 28800
Discount % = 10%
Marked Price (MP) = SP / (1 - Discount % / 100)
= 28800 / (1 - 10 / 100)
= 28800 / 0.90
= Rs 32000
e. Laptop:
Selling Price (SP) = Rs 80750
Discount % = 5%
Marked Price (MP) = SP / (1 - Discount % / 100)
= 80750 / (1 - 5 / 100)
= 80750 / 0.95
= Rs 85000
4. The following are the calculations to find the selling price (SP) for each item based on the given marked price (MP) and discount percentage.
a. Iron:
Marked Price (MP) = Rs 1800
Discount = 15%
SP = MP - (Discount% of MP)
= 1800 - (15/100 × 1800)
= 1800 - 270
= Rs 1530
b. Telephone set:
Marked Price (MP) = Rs 2500
Discount = 12%
SP = MP - (Discount% of MP)
= 2500 - (12/100 × 2500)
= 2500 - 300
= Rs 2200
c. Motorcycle:
Marked Price (MP) = Rs 245000
Discount = 15%
SP = MP - (Discount% of MP)
= 245000 - (15/100 × 245000)
= 245000 - 36750
= Rs 208250
d. Watch:
Marked Price (MP) = Rs 3000
Discount = 10%
SP = MP - (Discount% of MP)
= 3000 - (10/100 × 3000)
= 3000 - 300
= Rs 2700
e. Printer:
Marked Price (MP) = Rs 30000
Discount = 13%
SP = MP - (Discount% of MP)
= 30000 - (13/100 × 30000)
= 30000 - 3900
= Rs 26100
5. (a) The marked price of a book is Rs. 250. What is the price of the book after a 12% discount?Solution:
Here, the marked price of the book (MP) = Rs. 250
Discount (D) = 12%
Selling price (SP) = ?
We know that,
Discount amount = 12% of Rs. 250
= 12x250/100
= 30
Selling Price (SP) = MP - Discount amount
= 250 - 30
= Rs. 220
(b) The marked price of a jacket is Rs. 2,250. What is the price of the jacket if the shopkeeper sells it after an 8% discount?Solution:
Here, the marked price of the jacket (MP) = Rs. 2,250
Discount (D) = 8%
Selling price (SP) = ?
We know that,
Discount amount = 8% of Rs. 2,250
Selling Price (SP) = MP - Discount amount
= 2,250 - 180
= Rs. 2,070
6. (a) If the price of a colour television after 10% discount is Rs. 13,950. What is the marked price of television?Solution:
Here, the selling price of the television (SP) = Rs. 13,950
Discount (D) = 10%
Marked price (MP) = ?
We know that,
SP = MP - Discount amount
Discount amount = 10% of MP
So, 13,950 = MP - (10% of MP)
13,950 = MP - 0.10 x MP
13,950 = 0.90 x MP
MP = 13,950 / 0.90
MP = Rs. 15,500
(b) If the price of a sweater after 14% discount is Rs. 1,075. What is the marked price of sweater?Solution:
Here, the selling price of the sweater (SP) = Rs. 1,075
Discount (D) = 14%
Marked price (MP) = ?
We know that,
SP = MP - Discount amount
Discount amount = 14% of MP
So, 1,075 = MP - (14% of MP)
1,075 = MP - 0.14 x MP
1,075 = 0.86 x MP
MP = 1,075 / 0.86
MP = Rs. 1,250
7. A shopkeeper bought a torchlight for Rs. 1,400. The marked price of the torch is 40% above the cost price. If the shopkeeper sold the torch after 20% discount, thenSolution:
Here, the cost price (CP) of the torch = Rs. 1,400
Marked price (MP) = 40% above the cost price
MP = CP + 40% of CP
MP = 1,400 + (40/100) x 1,400
MP = 1,400 + 560
MP = Rs. 1,960
(a) What is the marked price of the torchlight?The marked price of the torchlight = Rs. 1,960
(b) What is the discount amount for the customer?Discount amount = 20% of Rs. 1,960
Discount amount = (20/100) x 1,960 = Rs. 392
(c) What is the selling price of the torch?Selling price (SP) = MP - Discount amount
SP = 1,960 - 392
SP = Rs. 1,568
(d) What is the profit of the shopkeeper after selling the torch?Profit = Selling price (SP) - Cost price (CP)
Profit = 1,568 - 1,400
Profit = Rs. 168
8. The cost price of a mobile is Rs. 21,000. The marked price of the mobile is 30% above the cost price. If the shopkeeper sold the mobile after a 20% discount then,Solution:
Here, the cost price (CP) of the mobile = Rs. 21,000
Marked price (MP) = 30% above the cost price
MP = CP + 30% of CP
MP = 21,000 + (30/100) x 21,000
MP = 21,000 + 6,300
MP = Rs. 27,300
(a) What is the marked price of the mobile?The marked price of the mobile = Rs. 27,300
(b) What is the discount amount for the customer?Discount amount = 20% of Rs. 27,300
Discount amount = (20/100) x 27,300 = Rs. 5,460
(c) What is the selling price of the mobile?Selling price (SP) = MP - Discount amount
SP = 27,300 - 5,460
SP = Rs. 21,840
(d) What is the profit of the shopkeeper after selling the mobile?Profit = Selling price (SP) - Cost price (CP)
Profit = 21,840 - 21,000
Profit = Rs. 840
9. Ramhari bought a computer for Rs. 45,000. The marked price of the computer is 30% above the cost price. If Ramhari sold the computer after a 30% discount then,Solution:
Here, the cost price (CP) of the computer = Rs. 45,000
Marked price (MP) = 30% above the cost price
MP = CP + 30% of CP
MP = 45,000 + (30/100) x 45,000
MP = 45,000 + 13,500
MP = Rs. 58,500
(a) What is the marked price of the computer?The marked price of the computer = Rs. 58,500
(b) What is the discount amount?Discount amount = 30% of Rs. 58,500
Discount amount = (30/100) x 58,500 = Rs. 17,550
(c) What is the selling price of the computer?Selling price (SP) = MP - Discount amount
SP = 58,500 - 17,550
SP = Rs. 40,950
(d) What is his profit or loss with that computer?Profit = Selling price (SP) - Cost price (CP)
Profit = 40,950 - 45,000
Profit = -Rs. 4,050 (Loss)
10. Rahaman marks the price of a suitcase as Rs. 6,000. If 15% discount is allowed on the suitcase, he got Rs. 500 profit, then,Solution:
Here, the marked price (MP) of the suitcase = Rs. 6,000
Discount (D) = 15%
Profit = Rs. 500
(a) What is the discount amount?Discount amount = 15% of Rs. 6,000
Discount amount = (15/100) x 6,000 = Rs. 900
(b) What is the selling price of the suitcase?Selling price (SP) = MP - Discount amount
SP = 6,000 - 900
SP = Rs. 5,100
(c) What was the cost price of the suitcase for Rahaman?Cost price (CP) = Selling price (SP) - Profit
CP = 5,100 - 500
CP = Rs. 4,600
(d) What was his profit percent from the suitcase?Profit percent = (Profit / Cost price) x 100
Profit percent = (500 / 4,600) x 100
Profit percent = 10.87%
No comments:
Post a Comment
Note: Only a member of this blog may post a comment.