Class 8 Mathematics
Exercise 8.2 — Comparing Quantities: Discount
📘 Points to Remember
1. Discount is always calculated on the Marked Price (M.P.).
2. Selling Price:
S.P. = M.P. − Discount
S.P. = M.P. − Discount
3. Discount Percentage:
Discount % = \[ \frac{\text{Discount}}{\text{M.P.}}\times100 \]
Discount % = \[ \frac{\text{Discount}}{\text{M.P.}}\times100 \]
4. Selling Price when discount is given:
\[ S.P. = M.P.\times \frac{100-\text{Discount%}}{100} \]
\[ S.P. = M.P.\times \frac{100-\text{Discount%}}{100} \]
5. Marked Price:
\[ M.P. = \frac{100\times S.P.} {100-\text{Discount%}} \]
\[ M.P. = \frac{100\times S.P.} {100-\text{Discount%}} \]
6. Successive Discounts:
When two or more discounts are given one after another, they are called successive discounts or discounts in series.
When two or more discounts are given one after another, they are called successive discounts or discounts in series.
Question 1
Find the selling price if:
(a) M.P. = ₹1300 and Discount = 10%
Discount = 10% of ₹1300
\[
=\frac{10}{100}\times1300
\]
\[
=₹130
\]
Selling Price = Marked Price − Discount
\[
=₹1300-₹130
\]
\[
=₹1170
\]
✅ Answer: S.P. = ₹1170
(b) M.P. = ₹4650 and Discount = 18%
Discount = 18% of ₹4650
\[
=\frac{18}{100}\times4650
\]
\[
=₹837
\]
Selling Price = ₹4650 − ₹837
\[
=₹3813
\]
✅ Answer: S.P. = ₹3813
Question 2
Find the marked price if:
(a) S.P. = ₹1222 and Discount = 6%
After a 6% discount, the selling price is:
\[
100%-6%=94%
\]
Therefore,
\[
94%\text{ of M.P.}=₹1222
\]
\[
M.P.
=
\frac{1222\times100}{94}
\]
\[
=₹1300
\]
✅ Answer: M.P. = ₹1300
(b) S.P. = ₹540 and Discount = 10%
After a 10% discount, the selling price is 90% of the marked price.
\[
90%\text{ of M.P.}=₹540
\]
\[
M.P.
=
\frac{540\times100}{90}
\]
\[
=₹600
\]
✅ Answer: M.P. = ₹600
Question 3
Find discount in per cent, when:
(a) M.P. = ₹900 and S.P. = ₹873
Discount = M.P. − S.P.
\[
=₹900-₹873
\]
\[
=₹27
\]
Discount percentage:
\[
\text{Discount%}
=
\frac{27}{900}\times100
\]
\[
=3%
\]
✅ Answer: Discount = 3%
(b) M.P. = ₹1000 and S.P. = ₹850
Discount = ₹1000 − ₹850
\[
=₹150
\]
Therefore,
\[
\text{Discount%}
=
\frac{150}{1000}\times100
\]
\[
=15%
\]
✅ Answer: Discount = 15%
Question 4
A shopkeeper offers 2.5% discount on cash purchases.
What cash amount would Anju should pay for a cycle the marked price of which is ₹1300?
Discount = 2.5% of ₹1300
\[
=\frac{2.5}{100}\times1300
\]
\[
=₹32.50
\]
Therefore, cash amount to be paid:
\[
S.P.=₹1300-₹32.50
\]
\[
=₹1267.50
\]
✅ Answer: Anju should pay ₹1267.50.
Question 5
The marked price of a ceiling fan is ₹720. During off-season, it is sold for ₹684.
Determine the discount per cent.
Discount = M.P. − S.P.
\[
=₹720-₹684
\]
\[
=₹36
\]
Discount percentage:
\[
\text{Discount%}
=
\frac{36}{720}\times100
\]
\[
=5%
\]
✅ Answer: Discount = 5%
Question 6
Find the rate of discount being given on a shirt whose selling price is ₹546
after deducting a discount of ₹104 on its marked price.
We know:
\[
S.P.=M.P.-\text{Discount}
\]
Therefore,
\[
M.P.=S.P.+\text{Discount}
\]
\[
=₹546+₹104
\]
\[
=₹650
\]
Now find the discount percentage:
\[
\text{Discount%}
=
\frac{104}{650}\times100
\]
\[
=16%
\]
✅ Answer: Rate of discount = 16%
Question 7
The marked price of an article is ₹500. The shopkeeper gives a discount of 5%
and still makes a profit of 25%. What is the cost price of the article?
First, find the selling price.
Discount = 5% of ₹500
\[
=\frac{5}{100}\times500
=₹25
\]
Therefore,
\[
S.P.=₹500-₹25
\]
\[
=₹475
\]
The shopkeeper makes a profit of 25%.
Therefore, S.P. = 125% of C.P.
\[
C.P.
=
\frac{475\times100}{125}
\]
\[
=₹380
\]
✅ Answer: Cost Price = ₹380
Question 8
A dealer marks his goods at 35% above the cost price and allows a discount of
20% on the marked price. Find his gain or loss per cent.
Let the cost price be ₹100.
Marked price is 35% above the cost price:
\[
M.P.=₹100+35%=₹135
\]
Discount = 20% of ₹135
\[
=\frac{20}{100}\times135
=₹27
\]
Therefore, selling price:
\[
S.P.=₹135-₹27
\]
\[
=₹108
\]
Cost price = ₹100 and selling price = ₹108.
\[
\text{Gain}=₹108-₹100
=₹8
\]
\[
\text{Gain%}
=
\frac{8}{100}\times100
=8%
\]
✅ Answer: Gain = 8%
Question 9
A trader allows a discount of 15% on the written price. How much above the
cost price must he mark his good to make a profit of 19%?
Let the cost price be ₹100.
To make a profit of 19%, the required selling price is:
\[
S.P.=₹100+19%
\]
\[
=₹119
\]
A discount of 15% is allowed on the marked price.
Therefore, the selling price is 85% of the marked price.
\[
85%\text{ of M.P.}=₹119
\]
\[
M.P.
=
\frac{119\times100}{85}
\]
\[
=₹140
\]
Therefore, the marked price is ₹140 when the cost price is ₹100.
\[
\text{Increase over C.P.}
=
₹140-₹100
=₹40
\]
\[
\text{Percentage increase}
=
\frac{40}{100}\times100
=40%
\]
✅ Answer: He must mark the goods 40% above the cost price.
Question 10
A shopkeeper allows 23% commission on his advertised price and still makes a
profit of 10%. If he gains ₹56 on one item, find his advertised price.
Let the cost price be ₹x.
Gain = ₹56 and gain = 10%.
\[
10%\text{ of C.P.}=₹56
\]
\[
C.P.
=
\frac{56\times100}{10}
\]
\[
=₹560
\]
Therefore, the selling price is:
\[
S.P.=₹560+₹56
\]
\[
=₹616
\]
The shopkeeper allows 23% commission on the advertised price.
Therefore, he receives 77% of the advertised price.
\[
100%-23%=77%
\]
\[
77%\text{ of Advertised Price}=₹616
\]
\[
\text{Advertised Price}
=
\frac{616\times100}{77}
\]
\[
=₹800
\]
✅ Answer: Advertised Price = ₹800
📋 Quick Answer Check
| Question | Answer |
|---|---|
| 1(a) | ₹1170 |
| 1(b) | ₹3813 |
| 2(a) | ₹1300 |
| 2(b) | ₹600 |
| 3(a) | 3% |
| 3(b) | 15% |
| 4 | ₹1267.50 |
| 5 | 5% |
| 6 | 16% |
| 7 | ₹380 |
| 8 | Gain = 8% |
| 9 | 40% above C.P. |
| 10 | ₹800 |
🌟 Remember:
Discount is always calculated on the Marked Price.
So, whenever you see a discount question, remember:
M.P. → Discount → S.P.
Also remember that profit or loss is calculated on the Cost Price, not on the Marked Price.
Discount is always calculated on the Marked Price.
So, whenever you see a discount question, remember:
M.P. → Discount → S.P.
Also remember that profit or loss is calculated on the Cost Price, not on the Marked Price.
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