## Discount

#### Discount

1. When a discount of 20% is given on a sweater, the profit is 28%. If the discount is 14%, then the profit is
1. 42 percent
2. 46.4 percent
3. 33.2 percent
4. 37.6 percent

1. Let the C.P. of sweater be Rs. 100 and its marked price be Rs. x.
According to the question,

 x × 80 = 128 100

 ⇒  x × 4 = 128 5

##### Correct Option: D

Let the C.P. of sweater be Rs. 100 and its marked price be Rs. x.
According to the question,

 x × 80 = 128 100

 ⇒  x × 4 = 128 5

 ⇒  x = 128 × 5 = Rs. 160 4

When discount = 14%, then
S.P. of sweater
= 160 × (100 – 1(4)%
 = 160 × 86 = Rs. 137.6 100

∵  C.P. = Rs. 100
∴  Profit per cent = 37.6%

1. Two shopkeepers announce the same price of Rs. 700 for a sewing machine. The first offers successive discounts of 30% and 6% while the second offers successive discounts of 20% and 16%. The difference in their selling price is :
1. Rs. 9.8
2. Rs. 16.8
3. Rs. 22.4
4. Rs. 36.4

1. For the first shopkeeper,
Single equivalent discount for two successive discounts of 30% and 6%

 = 30 + 6 − 30 × 6 % 100

= ( 36 –1.8 ) % = 34.2 %
∴  S.P. of sewing machine = ( 100 – 34.2 ) % of Rs. 700

For the second shopkeeper,
Single equivalent discount
 = 20 + 16 − 20 × 16 % 100

= ( 36 – 3.2 )% = 32.8 %
∴  S.P. of sewing machine = 700 × ( 100 – 32.8 ) %

##### Correct Option: A

For the first shopkeeper,
Single equivalent discount for two successive discounts of 30% and 6%

 = 30 + 6 − 30 × 6 % 100

= ( 36 –1.8 ) % = 34.2 %
∴  S.P. of sewing machine = ( 100 – 34.2 ) % of Rs. 700
 = Rs. 700 × 65.8 = Rs. 460.6 100

For the second shopkeeper,
Single equivalent discount
 = 20 + 16 − 20 × 16 % 100

= ( 36 – 3.2 )% = 32.8 %
∴  S.P. of sewing machine = 700 × ( 100 – 32.8 ) %
 = Rs. 700 × 67.8 = Rs. 470.4 100

Required difference = Rs. (470.4 – 460.6) = Rs. 9.8
Alternate method to find the difference
Difference between single equivalent discounts = ( 34.2 – 32.8 ) % = 1.4 %
 ∴  Difference of S.P. = Rs. 700 × 1.4 = Rs. 9.8 100

1. A merchant changed his trade discount from 25% to 15%. This would increase selling price by
1.  3 1 % 3
2.  6 1 % 6
3.  13 1 % 3
4.  16 1 % 3

1. Let us assume the price of article be Rs. M.

 ∴  S.P. at 25% discount = Rs. 75M = Rs. 3M 100 4

 S.P. at 15% discount = Rs. 85M = Rs. 17M 100 20

 Increased Price = Rs. 17M − 3M 20 4

 Increased Price = Rs. 17M − 15M = Rs. M 20 10

##### Correct Option: C

Let us assume the price of article be Rs. M.

 ∴  S.P. at 25% discount = Rs. 75M = Rs. 3M 100 4

 S.P. at 15% discount = Rs. 85M = Rs. 17M 100 20

 Increased Price = Rs. 17M − 3M 20 4

 Increased Price = Rs. 17M − 15M = Rs. M 20 10

 ∴  Percentage increase = M × 100 10 3M 4

 ∴  Percentage increase = M × 4 × 100 10 3M

 ∴  Percentage increase = 40 = 13 1 % 3 3

1. The list price of an article is Rs. 900. It is available at two successive discounts of 20% and 10%. The selling price of the article is :
1. Rs. 640
2. Rs. 648
3. Rs. 540
4. Rs. 548

1. Single equivalent discount for 20% and 10%

 = 20 + 10 − 20 × 10 % = 28% 100

##### Correct Option: B

Single equivalent discount for 20% and 10%

 = 20 + 10 − 20 × 10 % = 28% 100

Marked price of article = Rs. 900
S.P. of article = (100 – 28)% of 900
 S.P. of article = 900 × 72 = Rs. 648 100

1. A single discount equivalent to the series of discounts 20%, 10% and 5% is equal to :
1. 32%
2. 30%
3. 30.7%
4. 31.6%

1. Single equivalent discount for x% and y%.

 = x + y − xy % 100

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

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

 = 33 − 140 % 100

2nd Method to solve this question :
According to given question.
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

##### Correct Option: D

Single equivalent discount for x% and y%.

 = x + y − xy % 100

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

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

 = 33 − 140 % 100

= (33 – 1.4)% = 31.6%
2nd Method to solve this question :
According to given question.
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

= 31.6%