In order to increase sales or clear stocks, sometimes shopkeepers offer a certain per cent of rebate on the articles; this rebate is known as the discount. In Exercise 13.2 of Chapter 13, students shall study problems based on discounts. To access detailed solutions to problems, students can refer to RD Sharma Solutions, designed by our subject experts at BYJU’S. In order to help students understand the concepts clearly and solve the problems with competence and also to gain knowledge over the subject, students can use the best shortcut methods explained by the experts. The PDFs can be easily downloaded from the links provided below.
RD Sharma Solutions for Class 8 Maths Exercise 13.2 Chapter 13 Profit, Loss, Discount and Value Added Tax (VAT)
Access answers to Maths RD Sharma Solutions for Class 8 Exercise 13.2 Chapter 13 Profit, Loss, Discount and Value Added Tax (VAT)
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
11. A shopkeeper marks his goods in such a way that after allowing a discount of 25% on the marked price, he still makes a profit of 50%. Find the ratio of the C.P. to the M.P.
Solution:
Given,
Discount = 25%
Discount = (MP × Discount %)/100
= (MP×25)/100
= Rs 25MP/100
SP = MP – Discount
= (MP – 25MP/100)
= (100MP – 25MP)/100
= 75MP/100
We know that the given profit = 50%
Selling price = (100 + Gain %)/100 × CP
= (100 + 50)/100 × CP
= 150/100 × CP
= 150CP/100
By equating both SP we get,
75MP/100 = 150CP/100
75MP/150CP = 100/100
75MP/150CP = 1
(By cross multiplying)
CP/MP = 75/150
= 1/2
∴ The ratio CP to MP = 1:2
12. A cycle dealer offers a discount of 10% and still makes a profit of 26%. What is the actual cost to him of a cycle whose marked price is Rs. 840?
Solution:
Given,
Marked price (MP) on cycle = Rs 840
Discount = 10%
Discount = (MP × Discount %)/100
= (840×10)/100
= Rs 84
SP = MP – Discount
= 840 – 84
= Rs 756
Given, he makes a profit of 26% additionally
So, by using the formula,
CP = 100 / (100 + Gain %) × SP
= 100 / (100 + 26) × 756
= 100/126 × 756
= 600
∴ Actual cost of the cycle is Rs 600
13. A shopkeeper allows 23% commission in his advertised price and still makes a profit of 10%. If he gains Rs. 56 on one item, find his advertised price.
Solution:
Let us consider the advertised price be = Rs x
And the commission on the advertised price = 23% = Rs 23x/100
Selling price = advertised price – commission
= x – 23x/100
= (100x – 23x)/100
= Rs 77x/100 ……(equation 1)
Given gain = Rs 56
Profit percent = 10%
So, by using the formula,
Gain% = (gain/CP) × 100
10 = (56/CP) × 100
10/100 = 56/CP
CP = 560
Gain = SP – CP
SP = 560 + 56 = Rs 616
From the above equation 1 we get,
77x/100 = 616
x = (616 × 100)/77
= 800
∴ advertised price is Rs 800
14. A shopkeeper marked his goods at 40% above the cost price but allows a discount of 5% for cash payment to his customers. What actual profit does he make, if he receive Rs. 1064 after paying the discount?
Solution:
Given,
Shopkeeper marks his goods at 40% above the cost price.
Let the cost price be ‘x’
Marked price is 140x/100 (40 more than 100 if CP is 100)
Discount on marked price is 5%
Discount = (MP × Discount %)/100
= (140x/100×5)/100
= (7x/100)
SP = MP – Discount
= 140x/100 – 7x/100
= (140x-7x)/100
= Rs 133x/100
Given SP = Rs 1064
Equating both the SP we get,
1064 = 133x/100
133x = 1064×100
x = (1064×100)/133
= 800
Now, the cost price = Rs 800
SP = Rs 1064
Profit = SP – CP
= 1064 – 800
= 264
∴ The actual profit is Rs 264
15. By selling a pair of earrings at a discount of 25% on the marked price, a jeweller makes a profit of 16%. If the profit is Rs. 48, what is the cost price? What is the marked price and the price at which the pair was eventually bought?
Solution:
Given,
Earrings are bought at 25% discount
Profit percent of seller = 16%
Gain = Rs 48
So, by using the formula,
Gain% = (gain/CP) × 100
16 = (48/CP) × 100
16/100 = 48/CP
CP = (48×100)/16
= Rs 300
Now,
CP = Rs 300
Cost price of the earrings = Rs 300
Profit = Rs 48
Profit = SP – CP
SP = Profit + CP
= 48 + 300
= 348
Given, additional discount of 25%
By using the formula
MP = (100 × SP) / (100 – Discount %)
= (100 × 348) / (100 – 25)
= (100 × 348) / 75
= 34800/75
= Rs 464
∴ Marked Price is Rs 464, CP is 300 and Final selling price is 348
16. A publisher gives 32% discount on the printed price of a book to booksellers. What does a book seller pay for a book whose printed price is Rs. 275?
Solution:
Given,
Printed price (MP) = Rs 275
Discount = 32%
Discount = (MP × Discount %)/100
= (275×32)/100
= 88
SP = MP – Discount
= 275 – 88
= Rs 187
∴ The book seller pays Rs 187
17. After allowing a discount of 20% on the marked price of a lamp, a trader loses 10%. By what percentage is the marked price above the cost price?
Solution:
Given,
Let the cost price of the lamp be = Rs x
Then, SP = (100 – loss%)/100 × CP
= (100 – 10)/100 × x
= 90x/100
Now,
SP = Rs 90x/100 and Discount = 20%
By using the formula,
MP = (100×SP) / (100 – Discount%)
= (100×90x/100) / (100 – 20)
= 90x/80
= 9x/8
Required difference = MP – CP
= Rs (9x/8 – x)
= (9x-8x)/8
= Rs x/8
Discount% = (x/8)/x × 100
= 100/8
= 12.5%
∴ The trader must mark his goods 12.5% above the cost price.
18. The list price of a table fan is Rs. 480 and it is available to a retailer at 25% discount. For how much should a retailer sell it to gain 15%?
Solution:
Given,
List price of table fan (MP) is = Rs 480
Retailer buys it at discount of = 25%
Cost price for the retailer is (75/100) × 480
So, CP = (75/100) × 480
= Rs 360
Now, the retailer sells the fan to get 15%
Gain% = (gain)/CP × 100
15% = (SP-CP)/CP × 100
SP = 115/100 CP
= 115/100 × 360
= 414
∴ The retailer should sell the fan at Rs 414 to get a gain of 15%
19. Rohit buys items at 25% discount on the marked price. He sells it for Rs. 660, making a profit of 10%. What is the marked price of the item?
Solution:
20. A cycle merchant allows 20% discount on the marked price of the cycles and still makes a profit of 20%. If he gains Rs. 360 over the sale of one cycle, find the marked price of the cycle.
Solution:
Given,
Profit% = 20%
Gain over 1 cycle = Rs 360
Gain% = (gain/CP) × 100
20 = 360/CP × 100
20/100 = 360/CP
CP = Rs 1800
By using the formula,
SP = (100 + gain%)/100 × CP
= (100 + 20)/100 × 1800
= 120/100 × 1800
= Rs 2160
Given, Discount = 20%
MP = (100 × SP) / (100 – Discount %)
= (100 × 2160) / (100 – 20)
= 216000/80
= Rs 2700
∴ The marked price of the cycle is Rs 2700
21. Jyoti and Meena run a ready-made garment shop. They mark the garments at such a price that even after allowing a discount of 12.5%, they make a profit of 10%. Find the marked price of a suit which costs them Rs. 1470.
Solution:
Given,
CP of suit = Rs 1470
Gain = 10%
By using the formula,
SP = (100 + gain%)/100 × CP
= (100 + 10)/100 × 1470
= 110/100 × 1470
= Rs 1617
Given, Discount = 12.5%
So, MP = (100 × SP) / (100 – Discount %)
= (100 × 1617) / (100 – 12.5)
= 161700/87.5
= Rs 1848
∴ The marked price of the suit is Rs 1848
22. What price should Aslam mark on a pair of shoes which costs him Rs. 1200 so as to gain 12% after allowing a discount of 16%?
Solution:
Given,
CP of pair of shoes = Rs 1200
Gain = 12%
By using the formula,
SP = (100 + gain %)/100 × CP
= (100 + 12)/100 × 1200
= 112/100 × 1200
= Rs 1344
Given, Discount = 16%
MP = (100 × SP) / (100 – Discount %)
= (100 × 1344) / (100 – 16)
= 134400/84
= Rs 1600
∴ Aslam should mark pair of the shoes at Rs 1600
23. Jasmine allows 4% discount on the marked price of her goods and still earns a profit of 20%. What is the cost price of a shirt for her marked at Rs. 850?
Solution:
Given,
Gain = 20%
MP of the shirt = Rs 850
Discount = 4%
Discount allowed on the marked price of goods = 4/100 × 850
= Rs 34
So, SP of the shirt = (850 – 34) = Rs 816
By using the formula,
CP = 100/(100 + gain%) × SP
= 100/(100 + 20) × 816
= 100/120 × 816
= Rs 680
∴ Cost price of a shirt is Rs 680
24. A shopkeeper offers 10% off-season discount to the customers and still makes a profit of 26%. What is the cost price for the shopkeeper on a pair of shoes marked at Rs. 1120?
Solution:
Given,
MP of pair of shoes = Rs 1120
Profit = 26%
Discount = 10%
Discount allowed = 10/100 × 1120
= Rs 112
So, SP of the shoes = (1120 – 112) = Rs 1008
By using the formula,
CP = 100/(100 + gain%) × SP
= 100/(100 + 26) × 1008
= 100/126 × 1008
= Rs 800
∴ Cost price of a pair shoes is Rs 800
25. A lady shopkeeper allows her customers 10% discount on the marked price of the goods and still gets a profit of 25%. What is the cost price of a fan for her marked at Rs. 1250?
Solution:
Given,
MP of the fan = Rs 1250
Profit = 25%
Discount = 10%
Discount allowed = 10/100 × 1250
= Rs 125
So, SP of the shoes = (1250 – 125) = Rs 1125
By using the formula,
CP = 100/(100 + gain%) × SP
= 100/(100 + 25) × 1125
= 100/125 × 1125
= Rs 900
∴ Cost price of the fan is Rs 900
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