## Discount

#### Discount

1. A scooter is sold at three successive discounts of 10%, 5% and 2%. If the marked price of the scooter is Rs. 18,000, find its net selling price.
1. Rs. 15028.20
2. Rs. 15082.00
3. Rs. 15082.20
4. Rs. 15080.00

1. According to given question.
Here, D1 = 10%, D2 = 5%, D3 = 2%
Net Selling Price of Sccoter

 = Marked Price x 100 − D1 100 − D2 100 − D3 100 100 100

##### Correct Option: C

According to given question.
Here, D1 = 10%, D2 = 5%, D3 = 2%
Net Selling Price of Sccoter

 = Marked Price x 100 − D1 100 − D2 100 − D3 100 100 100

Net selling price of scooter.
 = Rs. 18000 × 90 × 95 × 98 100 100 100

= Rs. 15082.2

1. The difference between successive discounts of 40% followed by 30% and 45% followed by 20% on the marked price of an article is Rs. 12. The marked price of the article is :
1. ₹ 800
2. ₹ 400
3. ₹ 200
4. ₹ 600

1. Single equivalent discount for 40% and 30%

 = 40 + 30 − 40 × 30 % 100

= (70 – 12)% = 58%
Single equivalent discount for 45% and 20%
 = 45 + 20 − 45 × 20 % 100

= (65 – 9)% = 56%
Let the marked price be Rs. M.
According to the question,
M × (58 – 56)% = 12

##### Correct Option: D

Single equivalent discount for 40% and 30%

 = 40 + 30 − 40 × 30 % 100

= (70 – 12)% = 58%
Single equivalent discount for 45% and 20%
 = 45 + 20 − 45 × 20 % 100

= (65 – 9)% = 56%
Let the marked price be Rs. M.
According to the question,
M × (58 – 56)% = 12
 ⇒ M × 2 = 12 100

 ⇒  M = 1200 = Rs. 600 2

1. A double bed is marked at ₹ 7,500. The shopkeeper allows successive discounts of 8%, 5% and 2% on it. What is the net selling price ?
1. ₹ 6, 500
2. ₹ 6,000
3. ₹ 6,423.90
4. ₹ 6,500.50

1. As we know the formula for two successive discount.

 Single equivalent discount = D1 + D2 − D1 × D2 % 100

 Single equivalent discount for 8% and 5% = 8 + 5 − 8 × 5 % 100

Single equivalent discount for 8% and 5% = (13 – 0.4) = 12.6 %
Similarly calculate other discount and Solve the question for Net Selling price of product.
Alternate method to solve this question :
According to given question.
M.P. = ₹ 7500, S.P. = ?, D1 = 8%, D2 = 5%, D3 = 2%
 S.P = M.P. 100 − D1 100 − D2 100 − D3 100 100 100

 S.P = 7500 100 − 8 100 − 5 100 − 2 100 100 100

##### Correct Option: C

As we know the formula for two successive discount.

 Single equivalent discount = D1 + D2 − D1 × D2 % 100

 Single equivalent discount for 8% and 5% = 8 + 5 − 8 × 5 % 100

 Single equivalent discount for 8% and 5% = 8 + 5 − 8 × 5 % 100

Single equivalent discount for 8% and 5% = (13 – 0.4) = 12.6 %
 Single equivalent disconut for 12.6% and 2% = 12.6 + 2 − 12.6 × 2 % 100

Single equivalent disconut for 12.6% and 2% = 14.6 – 0.252 = 14.348 %
∴  Net S.P = (100 – 14.348) % of 7500
 ∴  Net S.P = 7500 × 85.652 = ₹ 6423.90 100

Alternate method to solve this question :
According to given question.
M.P. = ₹ 7500, S.P = ?, D1 = 8%, D2 = 5%, D3 = 2%
 S.P = M.P. 100 − D1 100 − D2 100 − D3 100 100 100

 S.P = 7500 100 − 8 100 − 5 100 − 2 100 100 100

 S.P = 7500 × 92 × 95 × 98 100 100 100

S.P = ₹ 6423.90

1. A plate was sold for 6,300 after giving two successive discounts of
 12 1 %   and 10%. Find the marked price. 2
1. ₹ 7,300
2. ₹ 7,700
3. ₹ 8,000
4. ₹ 7,250

1. Single equivalent discount for two successive discounts

 = x + y − xy % 100

 = 25 + 10 − 25 × 10 % 2 100

= ( 12.5 + 10 – 1.25 )%
= 21.25 %
If the marked price of the plate be ₹ M and solve this question further.

Alternate method to solve this question :
According to given question.
Here, S.P. = 6300, M.P. = ?
D1 = 25/2 %, D2 = 10%
 S.P. = M.P. 100 − D1 100 − D2 100 100

 6300 = M.P. 100 − 25/2 100 − 10 100 100

 ⇒  6300 = M.P. 175 90 200 100

##### Correct Option: C

Single equivalent discount for two successive discounts

 = x + y − xy % 100

 = 25 + 10 − 25 × 10 % 2 100

= ( 12.5 + 10 – 1.25 )%
= 21.25 %
If the marked price of the plate be ₹ M, then
= (100 – 21.25 ) % of M = 6300
 ⇒  M × 78.75 = 6300 100

 ⇒  M = 6300 × 100 = ₹ 8000 78.75

Alternate method to solve this question :
According to given question.
Here, S.P. = 6300, M.P. = ?
D1 = 25/2 %, D2 = 10%
 S.P. = M.P. 100 − D1 100 − D2 100 100

 6300 = M.P. 100 − 25/2 100 − 10 100 100

 ⇒  6300 = M.P. 175 90 200 100

 ⇒  M.P. = 6300 × 200 ×100 175 × 90

⇒  M.P. = ₹ 8000

1. Two successive discounts of 10% and 5%, in this order, are given on a bill of ₹ 110. Find the net amount of money payable to clear the bill. (answer to the nearest rupee)
1. ₹ 94
2. ₹ 95
3. ₹ 96
4. ₹ 97

1. Use the below formula to calculate the Single equivalent discount.

 Single equivalent discount = D1 + D2 − D1× D2 % 100

 Single equivalent discount = 10 + 5 − 10 × 5 % 100

##### Correct Option: A

Use the below formula to calculate the Single equivalent discount.

 Single equivalent discount = D1 + D2 − D1× D2 % 100

 Single equivalent discount = 10 + 5 − 10 × 5 % 100

Single equivalent discount = 14.5 %
∴  Amount to be paid = (100 – 14.5)% of 110
 ⇒  Amount to be paid = 110 ×85.5 = ₹ 94.05 100

⇒  Amount to be paid ≈ ₹ 94