Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > Profit, Loss, Discount and Value Added Tax (VAT) - Exercise 13.2
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Page 1
EXERCISE 13.2 PAGES NO: 13.26
1. Find the S.P. if
(i) M.P. = Rs 1300 and Discount = 10%
(ii) M.P. = Rs 500 and Discount = 15%
Solution:
(i) Given,
M.P. = 1300
Discount = 10%
By using the formulas
SP = Marked price (MP) – Discount
Discount = (MP × Discount %)/100
Discount% = (Discount)/M.P. × 100
By using,
Discount = (MP × Discount %)/100
= (1300×10)/100
= Rs 130
SP = MP - Discount
= (1300 - 130) = Rs 1170
(ii) Given,
M.P. = 500
Discount = 15%
By using,
Discount = (MP × Discount %)/100
= (500×15)/100
= Rs 75
SP = MP - Discount
= (500 - 75) = Rs 425
2. Find the M.P. if
(i) S.P. = Rs 1222 and Discount = 6%
(ii) S.P. = Rs 495 and Discount = 1%
Solution:
(i) Given,
SP = Rs 1222
Discount = 6%
By using the formula
Page 2
EXERCISE 13.2 PAGES NO: 13.26
1. Find the S.P. if
(i) M.P. = Rs 1300 and Discount = 10%
(ii) M.P. = Rs 500 and Discount = 15%
Solution:
(i) Given,
M.P. = 1300
Discount = 10%
By using the formulas
SP = Marked price (MP) – Discount
Discount = (MP × Discount %)/100
Discount% = (Discount)/M.P. × 100
By using,
Discount = (MP × Discount %)/100
= (1300×10)/100
= Rs 130
SP = MP - Discount
= (1300 - 130) = Rs 1170
(ii) Given,
M.P. = 500
Discount = 15%
By using,
Discount = (MP × Discount %)/100
= (500×15)/100
= Rs 75
SP = MP - Discount
= (500 - 75) = Rs 425
2. Find the M.P. if
(i) S.P. = Rs 1222 and Discount = 6%
(ii) S.P. = Rs 495 and Discount = 1%
Solution:
(i) Given,
SP = Rs 1222
Discount = 6%
By using the formula
MP = (100 × SP) / (100 - Discount %)
= (100 × 1222) / (100 - 6)
= 122200/94
= Rs 1300
(ii) Given,
SP = Rs 495
Discount = 1%
By using the formula
MP = (100 × SP) / (100 - Discount %)
= (100 × 495) / (100 - 1)
= 49500/99
= Rs 500
3. Find the discount in percent when
(i) M.P. = Rs. 900 and S.P. = Rs. 873
(ii) M.P. = Rs. 500 and S.P. = Rs. 425
Solution:
(i) Given,
MP = Rs 900
SP = Rs 873
By using the formula
Discount% = (MP - SP)/MP × 100
= (900-873)/900 × 100
= 27/900 × 100
= 3%
(ii) Given,
MP = Rs 500
SP = Rs 425
By using the formula
Discount% = (MP - SP)/MP × 100
= (500-425)/500 × 100
= 75/500 × 100
= 15%
4. A shop selling sewing machines offers 3% discount on all cash purchases. What
cash amount does a customer pay for a sewing machine the price of which is marked
as Rs 650.
Page 3
EXERCISE 13.2 PAGES NO: 13.26
1. Find the S.P. if
(i) M.P. = Rs 1300 and Discount = 10%
(ii) M.P. = Rs 500 and Discount = 15%
Solution:
(i) Given,
M.P. = 1300
Discount = 10%
By using the formulas
SP = Marked price (MP) – Discount
Discount = (MP × Discount %)/100
Discount% = (Discount)/M.P. × 100
By using,
Discount = (MP × Discount %)/100
= (1300×10)/100
= Rs 130
SP = MP - Discount
= (1300 - 130) = Rs 1170
(ii) Given,
M.P. = 500
Discount = 15%
By using,
Discount = (MP × Discount %)/100
= (500×15)/100
= Rs 75
SP = MP - Discount
= (500 - 75) = Rs 425
2. Find the M.P. if
(i) S.P. = Rs 1222 and Discount = 6%
(ii) S.P. = Rs 495 and Discount = 1%
Solution:
(i) Given,
SP = Rs 1222
Discount = 6%
By using the formula
MP = (100 × SP) / (100 - Discount %)
= (100 × 1222) / (100 - 6)
= 122200/94
= Rs 1300
(ii) Given,
SP = Rs 495
Discount = 1%
By using the formula
MP = (100 × SP) / (100 - Discount %)
= (100 × 495) / (100 - 1)
= 49500/99
= Rs 500
3. Find the discount in percent when
(i) M.P. = Rs. 900 and S.P. = Rs. 873
(ii) M.P. = Rs. 500 and S.P. = Rs. 425
Solution:
(i) Given,
MP = Rs 900
SP = Rs 873
By using the formula
Discount% = (MP - SP)/MP × 100
= (900-873)/900 × 100
= 27/900 × 100
= 3%
(ii) Given,
MP = Rs 500
SP = Rs 425
By using the formula
Discount% = (MP - SP)/MP × 100
= (500-425)/500 × 100
= 75/500 × 100
= 15%
4. A shop selling sewing machines offers 3% discount on all cash purchases. What
cash amount does a customer pay for a sewing machine the price of which is marked
as Rs 650.
Solution:
Given,
MP = Rs 650
Discount = 3%
So, 3% of MP = 3/100 × 650
= Rs 19.5
MP = MP – discount
= 650 – 19.5
= Rs 630.5
? Customer has to pay Rs 630.50
5. The marked price of a ceiling fan is Rs 720. During off season, it is sold for Rs.
684. Determine the discount percent.
Solution:
Given,
MP = Rs 720
SP = Rs 684
By using the formula,
Discount = M.P. – S.P.
= 720 - 684 = Rs 36
Discount% = (Discount/MP) × 100
= 36/720 × 100
= 5%
? Discount% is 5%
6. On the eve of Gandhi Jayanti a saree is sold for Rs. 720 after allowing 20%
discount. What is its marked price?
Solution:
Given,
SP of the saree = Rs 720
Discount = 20%
By using the formula
MP = (100 × SP) / (100 - Discount %)
= (100 × 720) / (100 - 20)
= 72000/80
= Rs 900
? Marked Price = Rs 900
Page 4
EXERCISE 13.2 PAGES NO: 13.26
1. Find the S.P. if
(i) M.P. = Rs 1300 and Discount = 10%
(ii) M.P. = Rs 500 and Discount = 15%
Solution:
(i) Given,
M.P. = 1300
Discount = 10%
By using the formulas
SP = Marked price (MP) – Discount
Discount = (MP × Discount %)/100
Discount% = (Discount)/M.P. × 100
By using,
Discount = (MP × Discount %)/100
= (1300×10)/100
= Rs 130
SP = MP - Discount
= (1300 - 130) = Rs 1170
(ii) Given,
M.P. = 500
Discount = 15%
By using,
Discount = (MP × Discount %)/100
= (500×15)/100
= Rs 75
SP = MP - Discount
= (500 - 75) = Rs 425
2. Find the M.P. if
(i) S.P. = Rs 1222 and Discount = 6%
(ii) S.P. = Rs 495 and Discount = 1%
Solution:
(i) Given,
SP = Rs 1222
Discount = 6%
By using the formula
MP = (100 × SP) / (100 - Discount %)
= (100 × 1222) / (100 - 6)
= 122200/94
= Rs 1300
(ii) Given,
SP = Rs 495
Discount = 1%
By using the formula
MP = (100 × SP) / (100 - Discount %)
= (100 × 495) / (100 - 1)
= 49500/99
= Rs 500
3. Find the discount in percent when
(i) M.P. = Rs. 900 and S.P. = Rs. 873
(ii) M.P. = Rs. 500 and S.P. = Rs. 425
Solution:
(i) Given,
MP = Rs 900
SP = Rs 873
By using the formula
Discount% = (MP - SP)/MP × 100
= (900-873)/900 × 100
= 27/900 × 100
= 3%
(ii) Given,
MP = Rs 500
SP = Rs 425
By using the formula
Discount% = (MP - SP)/MP × 100
= (500-425)/500 × 100
= 75/500 × 100
= 15%
4. A shop selling sewing machines offers 3% discount on all cash purchases. What
cash amount does a customer pay for a sewing machine the price of which is marked
as Rs 650.
Solution:
Given,
MP = Rs 650
Discount = 3%
So, 3% of MP = 3/100 × 650
= Rs 19.5
MP = MP – discount
= 650 – 19.5
= Rs 630.5
? Customer has to pay Rs 630.50
5. The marked price of a ceiling fan is Rs 720. During off season, it is sold for Rs.
684. Determine the discount percent.
Solution:
Given,
MP = Rs 720
SP = Rs 684
By using the formula,
Discount = M.P. – S.P.
= 720 - 684 = Rs 36
Discount% = (Discount/MP) × 100
= 36/720 × 100
= 5%
? Discount% is 5%
6. On the eve of Gandhi Jayanti a saree is sold for Rs. 720 after allowing 20%
discount. What is its marked price?
Solution:
Given,
SP of the saree = Rs 720
Discount = 20%
By using the formula
MP = (100 × SP) / (100 - Discount %)
= (100 × 720) / (100 - 20)
= 72000/80
= Rs 900
? Marked Price = Rs 900
7. After allowing a discount of 7½ % on the marked price, an article is sold for Rs.
555. Find its marked price.
Solution:
Given,
SP of the article = Rs 555
Discount = 7½ % = 15/2%
By using the formula
MP = (100 × SP) / (100 - Discount %)
= (100 × 555) / (100 – (15/2))
= (100 × 555) / ((200 – 15)/2)
= (100 × 555) / (92.5)
= 55500/92.5
= Rs 600
? Marked Price = Rs 600
8. A shopkeeper allows his customers 10% off on the marked price of goods and still
gets a profit of 25%. What is the actual cost to him of an article marked Rs. 250?
Solution:
Given, 10% off on marked price
M.P. = 250
Discount = 10%
By using,
Discount = (MP × Discount %)/100
= (250×10)/100
= Rs 25
SP = MP - Discount
= (250 - 25) = Rs 225
And 25% profit he gets additionally,
So, by using the formula,
CP = 100 / (100 + Gain %) × SP
= 100 / (100 + 25) × 225
= 100/125 × 225
= 180
? Actual cost of the article is Rs 180
9. A shopkeeper allows 20% off on the marked price of goods and still gets a profit
of 25%. What is the actual cost to him of an article marked Rs. 500?
Solution:
Page 5
EXERCISE 13.2 PAGES NO: 13.26
1. Find the S.P. if
(i) M.P. = Rs 1300 and Discount = 10%
(ii) M.P. = Rs 500 and Discount = 15%
Solution:
(i) Given,
M.P. = 1300
Discount = 10%
By using the formulas
SP = Marked price (MP) – Discount
Discount = (MP × Discount %)/100
Discount% = (Discount)/M.P. × 100
By using,
Discount = (MP × Discount %)/100
= (1300×10)/100
= Rs 130
SP = MP - Discount
= (1300 - 130) = Rs 1170
(ii) Given,
M.P. = 500
Discount = 15%
By using,
Discount = (MP × Discount %)/100
= (500×15)/100
= Rs 75
SP = MP - Discount
= (500 - 75) = Rs 425
2. Find the M.P. if
(i) S.P. = Rs 1222 and Discount = 6%
(ii) S.P. = Rs 495 and Discount = 1%
Solution:
(i) Given,
SP = Rs 1222
Discount = 6%
By using the formula
MP = (100 × SP) / (100 - Discount %)
= (100 × 1222) / (100 - 6)
= 122200/94
= Rs 1300
(ii) Given,
SP = Rs 495
Discount = 1%
By using the formula
MP = (100 × SP) / (100 - Discount %)
= (100 × 495) / (100 - 1)
= 49500/99
= Rs 500
3. Find the discount in percent when
(i) M.P. = Rs. 900 and S.P. = Rs. 873
(ii) M.P. = Rs. 500 and S.P. = Rs. 425
Solution:
(i) Given,
MP = Rs 900
SP = Rs 873
By using the formula
Discount% = (MP - SP)/MP × 100
= (900-873)/900 × 100
= 27/900 × 100
= 3%
(ii) Given,
MP = Rs 500
SP = Rs 425
By using the formula
Discount% = (MP - SP)/MP × 100
= (500-425)/500 × 100
= 75/500 × 100
= 15%
4. A shop selling sewing machines offers 3% discount on all cash purchases. What
cash amount does a customer pay for a sewing machine the price of which is marked
as Rs 650.
Solution:
Given,
MP = Rs 650
Discount = 3%
So, 3% of MP = 3/100 × 650
= Rs 19.5
MP = MP – discount
= 650 – 19.5
= Rs 630.5
? Customer has to pay Rs 630.50
5. The marked price of a ceiling fan is Rs 720. During off season, it is sold for Rs.
684. Determine the discount percent.
Solution:
Given,
MP = Rs 720
SP = Rs 684
By using the formula,
Discount = M.P. – S.P.
= 720 - 684 = Rs 36
Discount% = (Discount/MP) × 100
= 36/720 × 100
= 5%
? Discount% is 5%
6. On the eve of Gandhi Jayanti a saree is sold for Rs. 720 after allowing 20%
discount. What is its marked price?
Solution:
Given,
SP of the saree = Rs 720
Discount = 20%
By using the formula
MP = (100 × SP) / (100 - Discount %)
= (100 × 720) / (100 - 20)
= 72000/80
= Rs 900
? Marked Price = Rs 900
7. After allowing a discount of 7½ % on the marked price, an article is sold for Rs.
555. Find its marked price.
Solution:
Given,
SP of the article = Rs 555
Discount = 7½ % = 15/2%
By using the formula
MP = (100 × SP) / (100 - Discount %)
= (100 × 555) / (100 – (15/2))
= (100 × 555) / ((200 – 15)/2)
= (100 × 555) / (92.5)
= 55500/92.5
= Rs 600
? Marked Price = Rs 600
8. A shopkeeper allows his customers 10% off on the marked price of goods and still
gets a profit of 25%. What is the actual cost to him of an article marked Rs. 250?
Solution:
Given, 10% off on marked price
M.P. = 250
Discount = 10%
By using,
Discount = (MP × Discount %)/100
= (250×10)/100
= Rs 25
SP = MP - Discount
= (250 - 25) = Rs 225
And 25% profit he gets additionally,
So, by using the formula,
CP = 100 / (100 + Gain %) × SP
= 100 / (100 + 25) × 225
= 100/125 × 225
= 180
? Actual cost of the article is Rs 180
9. A shopkeeper allows 20% off on the marked price of goods and still gets a profit
of 25%. What is the actual cost to him of an article marked Rs. 500?
Solution:
Given, 20% off on marked price
MP = 500
Discount = 20%
Discount = (MP × Discount %)/100
= (500×20)/100
= Rs 100
SP = MP - Discount
= (500 - 100) = Rs 400
And 25% profit he gets additionally,
So, by using the formula,
CP = 100 / (100 + Gain %) × SP
= 100 / (100 + 25) × 400
= 100/125 × 400
= 320
? Actual cost of the article is Rs 320
10. A tradesman marks his goods at such a price that after allowing a discount of
15%, he makes a profit of 20%. What is the marked price of an article whose cost
price is Rs. 170?
Solution:
Given,
CP of the article = Rs 170
Profit = 20%
So, by using the formula,
Selling price = (100 + Gain %)/100 × CP
= (100 + 20)/100 × 170
= 120/100 × 170
= 204
SP = Rs 204
Discount = 15%
By using the formula
MP = (100 × SP) / (100 - Discount %)
= (100 × 204) / (100 – 15)
= (100 × 204) / 85
= 20400/85
= Rs 240
? Marked Price = Rs 240
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