Discount
- The marked price of an article is ₹ 500. A shopkeeper gives a discount of 5% and still makes a profit of 25%. The cost price of the article is.
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Let Cost price of the article = ₹ p
∴ p × 125 = 500 × 95 100 100
2nd method to solve this question.
Here, R = 25%, D = 5%,
M.P. = ₹ 500, C.P. = ?M.P. = 100 + r C.P. 100 − D
Correct Option: B
Let Cost price of the article = ₹ p
∴ p × 125 = 500 × 95 100 100 ⇒ p = 500 × 95 = ₹ 380 125
2nd method to solve this question.
Here, R = 25%, D = 5%,
M.P. = ₹ 500, C.P. = ?M.P. = 100 + r C.P. 100 − D 500 = 100 + 25 C.P. 100 − 5 C.P.= 500 × 95 = ₹ 380 125
- Anand marks up the price of an article by 50 % and then allows a discount of 20 % and sells it to Balaji. Balaji sells it for ₹ 20 more than what he purchased for, this S.P is 30 % more than the original C.P of the article. Then Balaji’s profit % is
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Let us assume the cost price = ₹ p
For Anand,Marked price = ₹ 3 p 2 Selling price = 3p × 80 2 100
For Balaji,Cost price = ₹ 6p 5 Selling price = ₹ 
6p + 20 
5 ∴ 6p + 20 = p × 130 5 100
Correct Option: C
Let us assume the cost price = ₹ p
For Anand,Marked price = ₹ 3 p 2 Selling price = 3p × 80 2 100 = ₹ 6p 5
For Balaji,Cost price = ₹ 6p 5 Selling price = ₹ 6p + 20 5 ∴ 6p + 20 = p × 130 5 100 ⇒ 13p − 6p = 20 10 5 ⇒ 13p − 12p = 20 10 ⇒ p = 20 10
⇒ p = ₹ 200∴ Required gain percent = 20 ×100 6p 5 ⇒ Required gain percent = 20 × 5 × 100 6 × p ⇒ Required gain percent = 20 × 5 × 100 = 25 = 8.33% 6 × 200 3
∴ Required gain percent is 8.33% .
- A merchant purchases a wrist watch for ₹ 450 and fixes its list price in such a way that after allowing a discount of 10%, he earns a profit of 20%. Find the list price of the watch.
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Let marked price of the wrist watch be p.
∴ 90p = 450 × 120 100 100
⇒ 90p = 450 × 120∴ p = 450 × 120 = ₹ 600 90
2nd method to solve this question.
Here, r1 = 10%, profit = 20%,r = ?Gain % = r ×(100 − r1) − r1 100 20 = r × (100 − 10) − 10 100 20 = 9r − 10 10
Correct Option: C
Let marked price of the wrist watch be p
∴ 90p = 450 × 120 100 100
⇒ 90p = 450 × 120∴ p = 450 × 120 = ₹ 600 90
2nd method to solve this question.
Here, r1 = 10%, profit = 20%,r = ?Gain % = r ×(100 − r1) − r1 100 20 = r × (100 − 10) − 10 100 20 = 9r − 10 10 30 = 9r 10 r = 300 % 9 ∴ List price = 450 + 450 × 300 % 9 List price = 450 + 450 × 300 900
Required List price = 450 + 150 = ₹ 600
- A dealer marks his goods 20% above their cost price. He then allows some discount on marked price so that he makes a profit of 10%. The rate of discount is
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Let cost price of article = ₹ 100
∴ Marked price of article = 100 × 120 = ₹ 120 100
S.P. of article = ₹ 110
∴ Discount = 120 – 110 = ₹ 10
∴ Let us assume that the discount = p %, then solve the question.
2nd method to solve this question.
Here, r = 20%, Profit = 10%
Let, discount r1 = p%Profit % = r ×(100 − r1) − r1 100
Correct Option: D
Let cost price of article = ₹ 100
∴ Marked price of article = 100 × 120 = ₹ 120 100
S.P. of article = ₹ 110
∴ Discount = 120 – 110 = ₹ 10
∴ Let us assume that discount = p %, then12 × p = 10 100 ⇒ p= 10 × 100 = 25 = 8 1 % 120 3 3
2nd method to solve this question.
Here, r = 20%, Profit = 10%
Let, discount r1 = p%Profit % = r ×(100 − r1) − r1 100 10 = 20 × (100 − p) − r1 100
1000 = 2000 – 20p – 100p
–1000 = –120pp = 100 12 p = 25 = 8 1 % 3 3
- A shopkeeper marks the price of an item keeping 20% profit. If he offers a discount of
12 1 % on the marked price, his gain percent will be 2
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Let the cost price be ₹ 100.
∴ Marked price = ₹ 120SP = 87 1 % of 120 2 = 175 × 120 = ₹ 105 200
∴ Gain percent = 5%
Gain percent = 5%
2nd method to solve this question.
Here, r = 20%,r1 = 12 1 % 2
Correct Option: B
Let the cost price be ₹ 100.
∴ Marked price = ₹ 120SP = 87 1 % of 120 2 = 175 × 120 = ₹ 105 200
∴ Gain percent = 5%
Gain percent = 5%
2nd method to solve this question.
Here, r = 20%,r1 = 12 1 % 2 Profit % = r × (100 − r1) − r1 100 Profit % = 20 × 100 − 25 − 2 25 100 2 Profit % = 20 × 175 − 12.5 200
Required Profit % = 17.5 – 12.5 = 5%
