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
🌟 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.
