## Discount

#### Discount

1. The marked price of a piano was ₹ 15,000. At the time of sale, there were successive discounts of 20%, 10% and 10% respectively on it. The sale price was
1. ₹ 9,720
2. ₹ 9,750
3. ₹ 9,760
4. ₹ 9,780

1. Use the below formula to calculate the Equivalent single discount.

 Equivalent single discount = D1 + D2 − D1 × D2 % 100

 Single equivalent discount for 20% and 10% = 20 + 10 − 20 × 10 % = (30 - 2) = 28% 100

 Single equivalent discount for 28% and 10% = 28 + 10 − 28 × 10 % = ( 38 - 2.8 ) % = 35.2% 100

Alternate method to solve this question :
According to given question.
Here, M.P. = ₹ 15000 , S.P. = ?
D1 =20%, D2 = 10%, D3 = 10%
 S.P = M.P 100 − D1  100 − D2  100 − D3 100 100 100

 ⇒  S.P = 15000 100 − 20  100 − 10  100 − 10 100 100 100

##### Correct Option: A

Use the below formula to calculate the Equivalent single discount.

 Equivalent single discount = D1 + D2 − D1 × D2 % 100

 Single equivalent discount for 20% and 10% = 20 + 10 − 20 × 10 % = (30 - 2) = 28% 100

 Single equivalent discount for 28% and 10% = 28 + 10 − 28 × 10 % = ( 38 - 2.8 ) % = 35.2% 100

 ∴  S.P. of Piano = 15000 ×(100 −35.2) 100

∴  S.P. of Piano = ₹ 9,720
Alternate method to solve this question :
According to given question.
Here, M.P. = ₹ 15000 , S.P. = ?
D1 =20%, D2 = 10%, D3 = 10%
 S.P = M.P 100 − D1  100 − D2  100 − D3 100 100 100

 ⇒  S.P = 15000 100 − 20  100 − 10  100 − 10 100 100 100

 ⇒  S.P = 15000 × 80 × 90 × 90 100 100 100

⇒  S.P = 15 × 72 × 9 = ₹ 9720

1. A shopkeeper purchased a chair marked at ₹ 600 at two successive discounts of 15% and
20% respectively. He spent ₹ 28 on transportation and sold the chair for ₹ 545. His gain percent was
1. 25%
2. 30%
3. 35%
4. 20%

1.  C.P of chair = 600 − 600 × 15 × 80 100 100

##### Correct Option: A

 C.P of chair = 600 − 600 × 15 × 80 100 100

 C.P of chair = 510 × 80 = ₹ 408 100

Actual C.P. = 408 + 28 = ₹ 436
 Gain percent = 545 - 436 × 100 = 25 % 436

1. The cost price of an article is ₹ 100. A discount series of 5 %, 10 % successively reduces the price of a article by
1. ₹ 4.5
2. ₹ 14.5
3. ₹ 24.5
4. None of the above

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

 Equivalent single discount = D1 + D2 − D1 × D2 % 100

##### Correct Option: B

As we know the formula for two successive discount.

 Equivalent single discount = D1 + D2 − D1 × D2 % 100

 Single equivalent discount = 10 + 5 − 10 × 5 = 14.5% 100

i.e. ₹ 14.50

1. A dealer buys a table listed at ₹ 1,500 and gets successive discounts of 20 % and 10 %. He spends ₹ 20 on transportation and sells at a profit of 20 %. Find the Selling Price of the table (in rupees).
1. 1320
2. 1080
3. 1200
4. 1230

1.  Single equivalent discount = 20 + 10 − 20 × 10 = 28% 100

##### Correct Option: A

 Single equivalent discount = 20 + 10 − 20 × 10 = 28% 100

 ∴  C.P of table = 1500 × (100 - 28) 100

 ∴  C.P of table = 1500 × 72 100

∴  C.P of table = ₹ 1080
Actual C.P. = 1080 + 20 = ₹ 1100
 ∴  Required S.P. = 1100 × 120 = ₹ 1320 100

1. A purchased a dining table, marked at ₹ 3,000 at a successive discounts of 10% and 15% respectively. He gave ₹ 105 as transportation charge and sold it at ₹ 3,200. What is his gain percentage?
1.  22 1 % 3
2. 25%
3.  33 1 % 3
4.  37 17 % 24

1.  Cost Price for A = 3000 × 90 × 85 = ₹ 2295 100 100

##### Correct Option: C

 Cost Price for A = 3000 × 90 × 85 = ₹ 2295 100 100

Actual Cost Price for A = 2295 + 105 = ₹ 2400
 ∴  Gain % = 800 × 100 2400

 Gain % = 100 = 33 1 % 3 3