## Discount

#### Discount

1. Two successive discounts of 20% and 20% is equivalent to a single discount of
1. 42%
2. 40%
3. 36%
4. 34%

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

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

##### Correct Option: C

Use the below formula to calculate the Equivalent single discount.

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

 Equivalent single discount = 20 + 20 − 20 × 20 % = 36% 100

1. Successive discounts of 10%, 20% and 30% is equivalent to a single discount of
1. 60%
2. 49.6%
3. 40.5%
4. 36%

1. Single equivalent discount for successive discounts of 10% and 20%.

 = 10 + 20 − 20 × 100 % = 28% 100

Single equivalent discount for 28% and 30%.
Similarly calculate by using the formula for Equivalent discount of two successive discount D1 and discount D2.

##### Correct Option: B

Using Rule 5,
Single equivalent discount for successive discounts of 10% and 20%.

 = 10 + 20 − 20 × 100 % = 28% 100

Single equivalent discount for 28% and 30%.
 = 28 + 30 − 28 × 30 % = 49.6% 100

1. The difference between a discount of 30% on ₹ 2,000 and two successive discounts of 25% and 5% on the same amount is
1. ₹ 30
2. ₹ 35
3. ₹ 25
4. ₹ 40

1.  Discount = 30 × 2000 = ₹ 600 100

Single equivalent discount for discounts of 25% and 5%.
 = 25 + 5 − 25 × 5 % 100

##### Correct Option: C

 Discount = 30 × 2000 = ₹ 600 100

Single equivalent discount for discounts of 25% and 5%.
 = 25 + 5 − 25 × 5 % 100

= (30 – 1.25)% = 28.75%
 ∴  Discount = 28.75 × 2000 = ₹ 575 100

∴  Difference = ₹ (600 − 575) = ₹ 25

1. The marked price of a T.V. is ₹ 16,000. After two successive discounts it is sold for ₹ 11,400. If the first discount is 5%, then the rate of second discount is
1. 15%
2. 20%
3. 30%
4. 25%

1. After a discount of 5%

 SP = 95 × 16000 = ₹ 15200 100

Let the second discount be x%
&there;  D2 % of 15200 = (15200 – 11400)
 ⇒ x × 15200 = 3800 100

Alternate method to solve this question :
Here, M.P. = 16000,
S.P. = 11400, D1 = 5%, D2 = ?
 S.P. = M.P. 100 − D1 100 − D2 100 100

##### Correct Option: D

After a discount of 5%

 SP = 95 × 16000 = ₹ 15200 100

Let the second discount be x%
&there;  D2 % of 15200 = (15200 – 11400)
 ⇒ x × 15200 = 3800 100

 ⇒  x = 3800 × 100 = 25 15200

∴  Second discount = 25%
Alternate method to solve this question :
Here, M.P. = 16000,
S.P. = 11400, D1 = 5%, D2 = ?
 S.P. = M.P. 100 − D1 100 − D2 100 100

 11400 = 16000 100 − 5 100 − D2 100 100

 11400 = 100 − D2 16 × 95

75 = 100 − D2
D2 = 25%

1. The difference between a discount of 40% on ₹ 500 and two successive discounts of 30% and 10% on the same amount is
1. ₹ 15
2. ₹ 0
3. ₹ 20
4. ₹ 10

1. As we know the formula for Equivalent discount.
Single equivalent discount of two consecutive discount of 30% and 10%

 = 30 + 10 – 30 × 10 = 37% 100

∴  Required difference = 40% of 500 – 37% of 500

##### Correct Option: A

As we know the formula for Equivalent discount.
Single equivalent discount of two consecutive discount of 30% and 10%

 = 30 + 10 – 30 × 10 = 37% 100

∴  Required difference = 40% of 500 – 37% of 500
= 3% of 500
 = 500 × 3 = ₹ 15 100