## Discount

#### Discount

1. The single discount equivalent to the discount series of 20%,10% and 5% is :
1. 11.66%
2. 31.6%
3. 35.66%
4. 32%

1. Single equivalent discount for 20% and 10%

 = 20 + 10 − 20 × 10 % = 28% 100

Single equivalent discount for 28% and 5%
 = 28 + 5 − 28 × 5 % = 31.6% 100

##### Correct Option: B

Single equivalent discount for 20% and 10%

 = 20 + 10 − 20 × 10 % = 28% 100

Single equivalent discount for 28% and 5%
 = 28 + 5 − 28 × 5 % = 31.6% 100

Alternate method to solve this question :
Here, D1 = 20%, D2 = 10%,D3 = 5%
Single equivalent discount
 = 100 − 100 − D1 100 − D2 100 − D3 × 100 100 100 100

 = 100 − 100 − 20 100 − 10 100 − 5 × 100 100 100 100

 = 100 − 80 × 90 × 95 × 100 100 100 100

= 100 – 68.40 = 31.60%

1. The single discount which is equivalent to successive discounts of 20%, 15% and 10% is
1. 32·7%
2. 34·2%
3. 36·9%
4. 38·8%

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 15 %
 = 20 + 15 − 20 × 15 % = 32% 100

Single equivalent discount for 32% and 10%
 = 32 + 10 − 32 × 10 % = 38.8% 100

##### Correct Option: D

Use the below formula to calculate the Equivalent single discount.

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

Single equivalent discount for 20% and 15%
 = 20 + 15 − 20 × 15 % = 32% 100

Single equivalent discount for 32% and 10%
 = 32 + 10 − 32 × 10 % = 38.8% 100

Alternate method to solve this question :
Here, D1 = 20%, D2 = 15%,D3 = 10%
Single equivalent discount
 = 100 − 100 − D1 100 − D2 100 − D3 × 100 100 100 100

 = 100 − 100 − 20 100 − 15 100 − 10 × 100 100 100 100

 Equivalent single discount = 100 − 80 × 85 × 90 × 100 100 100 100

Hence Equivalent single discount = 100 – 61.20 = 38.80%

1. A single discount equivalent to discount series 20%, 20% and 10% is
1. 50%
2. 48.4%
3. 42.4%
4. 40.4%

1. Single equivalent discount for 20% and 20%

 = 20 + 20 − 20 × 20 % = 36% 100

Single equivalent discount for 36% and 10%
 = 36 + 10 − 36 × 10 % = 42.4% 100

##### Correct Option: C

Single equivalent discount for 20% and 20%

 = 20 + 20 − 20 × 20 % = 36% 100

Single equivalent discount for 36% and 10%
 = 36 + 10 − 36 × 10 % = 42.4% 100

Alternate method to solve this question :
 = 100 − 100 − D1 100 − D2 100 − D3 × 100 100 100 100

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

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

= 100 – 57.60 = 42.40

1. The difference between a discount of 35 % and two successive discounts of 20 % on a certain bill was ₹ 22. The amount of the bill was
1. ₹ 200
2. ₹ 220
3. ₹ 1,100
4. ₹ 2,200

1. Single equivalent discount of two successive discounts of 20 % each

 = 20 + 20 − 20 × 20 % 100

##### Correct Option: D

Single equivalent discount of two successive discounts of 20% each

 = 20 + 20 − 20 × 20 % 100

= 36%
If the amount of the bill be A, then
∴  (36 – 35)% of A = 22
 ⇒ A = 22 100

⇒ A = ₹ 2200

1. The single discount equivalent to two successive discounts of 20% and 5% is
1. 24%
2. 25%
3. 22%
4. 23%

1.  Equivalent single discount = x + y − xy % 100

##### Correct Option: A

 Equivalent single discount = x + y − xy % 100

 Equivalent single discount = 20 + 5 − 20 × 5 % 100

Equivalent single discount = (25 – 1)% = 24%