## Discount

#### Discount

1. An item is offered for sale at Rs. 250, less by successive discounts of 20 % and 15 %, The sale price of the item is :
1. 82% of Rs. 250
2. 77% of Rs. 250
3. 68% of Rs. 250
4. 65% of Rs. 250

1. Single equivalent discount

 = x + y − xy % 100

 = 20 + 15 − 20 × 15 = 32% 100

##### Correct Option: C

Single equivalent discount

 = x + y − xy % 100

 = 20 + 15 − 20 × 15 = 32% 100

∴  Required S.P. = (100 – 32)% of 250
∴  Required S.P. = 68% of 250

1. If the successive discounts be 20 %, 10 % and 5 %, then the single equivalent rate of discount is :
1. 31.6%
2. 31.5%
3. 31%
4. 31.4%

1. As we know that ,

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

Single equivalent discount for 20% and 10%
 = 20 + 10 − 20 × 10 % 100

= (30 – 2)% = 28%
Calculate the Single equivalent discount for 28% and 5% further.

##### Correct Option: A

As we know that ,

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

Single equivalent discount for 20% and 10%
 = 20 + 10 − 20 × 10 % 100

= (30 – 2)% = 28%
Single equivalent discount for 28% and 5%
 = 28 + 5 − 28 × 5 % 100

 = 33 − 140 = 31.6% 100

1. The successive discount of 15 %, 20 % and 25 % on an article is equivalent to the single discount of
1. 60%
2. 47%
3. 49%
4. 40%

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

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

Single equivalent discount for 15% and 20%
 = 15 + 20 − 15 × 20 % 100

= (35 – 3)% = 32%
Single equivalent discount for 32% and 25%.
Calculate the equation to find the equivalent discount.

##### Correct Option: C

Use the below formula to calculate the Equivalent single discount.

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

Single equivalent discount for 15% and 20%
 = 15 + 20 − 15 × 20 % 100

= (35 – 3)% = 32%
Single equivalent discount for 32% and 25%
 = 32 + 25 − 32 × 25 % 100

= (57 – 8)% = 49%

1. Successive discounts of 20% and 10% are equivalent to a single discount of :
1. 15%
2. 28%
3. 25%
4. 30%

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

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

##### Correct Option: B

Use the below formula to calculate the Single equivalent discount.

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

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

1. Find a simple discount equivalent to a discount series of 10%, 20% and 25%.
1. 55%
2. 45%
3. 52%
4. 46%

1. First method to solve this question :
According to given question.
Here, D1 = 10%, D2 = 20%, D3 = 25%
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

2nd Method to solve this question :
According to given question.
Single equivalent discount for discounts of 10% and 20%
 = 20 + 10 − 20 × 10 % 100

= (30 – 2)% = 28%
Single equivalent discounts for discounts of 28% and 25%
Calculate further to solve this question.

##### Correct Option: D

First method to solve this question :
According to given question.
Here, D1 = 10%, D2 = 20%, D3 = 25%
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%
2nd Method to solve this question :
According to given question.
Single equivalent discount for discounts of 10% and 20%
 = 20 + 10 − 20 × 10 % 100

= (30 – 2)% = 28%
Single equivalent discounts for discounts of 28% and 25%
 = 28 + 25 − 28 × 25 % 100

= (53 –7)% = 46%