## Discount

#### Discount

1. A chair listed at ₹ 350 is available at successive discounts of 25% and 10%. The selling price of the chair is
1. ₹ 236.25
2. ₹ 230.25
3. ₹ 240.25
4. ₹ 242.25

1.  Single equivalent discount = 25 + 10 − 25 × 10 = 32.5% 100

Alternate method to solve this question :
Here, M.P. = 350, D1 = 25 %, D2 = 10 %
 S.P. = M.P. 100 − D1  100 − D2 100 100

##### Correct Option: A

 Single equivalent discount = 25 + 10 − 25 × 10 = 32.5% 100

 ∴  S.P. of chair = 350 (100 − 32.5) 100

 ∴  S.P. of chair = 350 × 67.5 = ₹ 236.25 100

Alternate method to solve this question :
Here, M.P. = 350, D1 = 25 %, D2 = 10 %
 S.P. = M.P. 100 − D1  100 − D2 100 100

 S.P = 350 × 100 − 25  100 − 10 100 100

 S. P = 350 × 75 × 90 = ₹ 236.25 100 100

1. The price of a certain television set is discounted by 10% and the reduced price is then discounted by 10%. This series of successive discounts is equivalent to a single discount of
1. 20%
2. 19%
3. 18%
4. 11%

1. As we know that ,

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

##### Correct Option: B

As we know that ,

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

 Single equivalent discount = 10 + 10 − 10 × 10 % = 19% 100

1. The marked price of a watch is ₹ 1,600. The shopkeeper gives successive discounts of 10 % and D % to the customer. If the customer pays ₹ 1,224 for the watch, the value of D is
1. 5%
2. 10%
3. 15%
4. 20%

1.  S.P after first discount = 1600 × 90 = ₹ 1440 100

∴  Second discount = 1440 – 1224 = ₹ 216

##### Correct Option: C

 S.P after first discount = 1600 × 90 = ₹ 1440 100

∴  Second discount = 1440 – 1224 = ₹ 216
 ∴ 1440 × D = 216 100

 ∴  D = 216 × 100 = 15% 1440

1. A shopkeeper purchased a chair marked at ₹ 800, at two successive discounts of 10% and 15% respectively. He spent ₹ 28 on transportation and sold the chair for 800. His gain percent is :
1. 40%
2. 30%
3. 25%
4. 14%

1. Single equivalent discount

 = 15 + 10 − 15 × 10 = 23.5% 100

 ∴  Cost price = 800 × 76.5 100

##### Correct Option: C

Single equivalent discount

 = 15 + 10 − 15 × 10 = 23.5% 100

 ∴  Cost price = 800 × 76.5 100

= ₹ 612
Actual C.P = ₹ (612 + 28) = ₹ 640
 ∴ Gain % = 800 − 640 × 100 100

 ∴ Gain % = 160 − 100 = 25 % 640

1. The single discount equal to three consecutive discounts of 10%, 12% and 5% is
1. 26.27%
2. 24.76%
3. 9%
4. 11%

1. Single equivalent discount for 10% and 12%.

 = 12 + 10 − 20 × 10 % = 20.8% 100

Single equivalent discount for 20.8% and 5%.
Similarly calculate the same.

Alternate method to solve this question :
Here, D1 = 10%, D2 = 12%,D3 = 5%
Single equivalent discount
 = 100 −  100 − D1  100 − D2  100 − D3 × 100 100 100 100

 = 100 −  100 − 10  100 − 12  100 − 5 × 100 100 100 100

##### Correct Option: B

Single equivalent discount for 10% and 12%.

 = 12 + 10 − 20 × 10 % = 20.8% 100

Single equivalent discount for 20.8% and 5%.
 = 20.8 + 5 − 20.8 × 5 % = 24.76% 100

Alternate method to solve this question :
Here, D1 = 10%, D2 = 12%,D3 = 5%
Single equivalent discount
 = 100 −  100 − D1  100 − D2  100 − D3 × 100 100 100 100

 = 100 −  100 − 10  100 − 12  100 − 5 × 100 100 100 100

 = 100 − 90 × 88 × 95 × 100 100 100 100

= 100 – 75.24 = 24.76%