## Discount

#### Discount

1. List price of an article at a show room is ₹ 2,000 and it is being sold at successive discounts of 20 % and 10 %. Its net selling price will be :
1. ₹ 1900
2. ₹1700
3. ₹ 1440
4. ₹ 1400

1. Equivalent discount for successive discounts of 20 % and 10 %

 = 20 + 10 − 20 × 10 % 100

Alternate method to solve this question:
Here, M.P. = ₹ 2000,
D1 = 20%, D2 = 10%
 S.P. = M.P.  100 − D1  100 − D2  100 100

##### Correct Option: C

Equivalent discount for successive discounts of 20% and 10%

 = 20 + 10 − 20 × 10 % 100

= 28%
∴  Net selling price = 72 % of 2000
 = ₹ 72 × 2000 = ₹ 1440 100

Alternate method to solve this question:
Here, M.P. = ₹ 2000,
D1 = 20%, D2 = 10%
 S.P. = M.P.  100 − D1  100 − D2  100 100

 = 2000 × 100 − 20  100 − 10  100 100

 = 2000 × 80 × 90 = ₹ 1440 10000

1. A single discount equivalent to the successive discounts of 10 %, 20 % and 25 % is
1. 55%
2. 45%
3. 46%
4. 60%

1. First Method
Single of discount for successive discounts 10 % and 20 %

 = 20 + 10 − 20 × 10 % = 28 % 100

∴  Equivalent discount for discounts 28% and 25%
 = 28 + 25 − 28 × 25 % 100

2nd Method :
Single equivalent discount
 = 100 −  100 − D1  100 − D2  100 − D3 × 100 100 100 100

 = 100 −  100 − 10  100 − 20  100 − 25 × 100 100 100 100

##### Correct Option: C

First Method to solve this question.
Single of discount for successive discounts 10 % and 20 %

 = 20 + 10 − 20 × 10 % = 28 % 100

∴  Equivalent discount for discounts 28% and 25%
 = 28 + 25 − 28 × 25 % 100

= 53 – 7 = 46%
Second method :
Single equivalent discount
 = 100 −  100 − D1  100 − D2  100 − D3 × 100 100 100 100

 = 100 −  100 − 10  100 − 20  100 − 25 × 100 100 100 100

 = 100 − 90 × 80 × 75 × 100 100 100 100

= 100 – 54 = 46%

1. An item is marked for ₹ 240 for sale. If two successive discounts of 10 % and 5 % are allowed on the sale price, the selling price of the article will be
1. ₹ 205.20
2. ₹ 204
3. ₹ 34.80
4. ₹ 36

1. A single discount equal to the two successive discounts

 = 10 + 5 − 10 × 5 % = 14.5 % 100

2nd Method :
Here, M.P. = Rs. 240,
D1 = 10%, D2 = 5%
 S.P. = M.P. 100 − D1  100 − D2 100 100

 = 240 100 − 10  100 − 5 100 100

##### Correct Option: A

A single discount equal to the two successive discounts

 = 10 + 5 − 10 × 5 % = 14.5 % 100

∴  Selling price of the article
= 85.5% of ₹ 240
 = ₹ 85.5 × 240 = ₹ 205.20 100

IInd Method :
Here, M.P. = Rs. 240,
D1 = 10%, D2 = 5%
 S.P. = M.P. 100 − D1  100 − D2 100 100

 = 240 100 − 10  100 − 5 100 100

 = 240 × 90 × 95 = Rs. 205.20 100 100

1. The marked price of an article is ₹ 500. It is sold at successive discounts of 20 % and 10 %. The selling price of the article (in rupees) is :
1. 350
2. 375
3. 360
4. 400

1.  Equivalent discount of successive discounts of 20 % and 10 % = 20 + 10 − 20 × 10 % = 28 % 100

∴  Selling Price = (100 – 28) % of ₹ 500

IInd Method to Solve this question.
M.P. = Rs. 500
D1 = 20%
D2 = 10%
 S.P. = M.P. 100 − D1  100 − D2 100 100

##### Correct Option: C

Equivalent discount of successive discounts of 20% and 10%

 = 20 + 10 − 20 × 10 % = 28 % 100

∴  Selling Price = (100 – 28) % of ₹ 500 = 72 % of 500
 = ₹ 500 × 72 = ₹ 360 100

IInd Method to Solve this question.
M.P. = Rs. 500
D1 = 20%
D2 = 10%
 S.P. = M.P. 100 − D1  100 − D2 100 100

 = 500 100 − 20  100 − 10 100 100

 = 500 × 80 × 90 = Rs. 360 100 100

1. The marked price of a watch is ₹ 1000. A retailer buys it at ₹ 810 after getting two successive discounts of 10% and another rate which is illegible. What is the second discount rate?
1. 15%
2. 10%
3. 8%
4. 6.5%

1. Price after 10% first discount

 = 1000 × 100 − 10 100

 = 1000 × 90 = ₹ 900 100

##### Correct Option: B

Price after 10% first discount

 = 1000 × 100 − 10 100

 = 1000 × 90 = ₹ 900 100

Given that :
Price after second discount = ₹ 810
∴  Second discount = 900 – 810 = 90
 ∴  Percentage of second discount = 90 × 100 = 10 % 100