## Discount

#### Discount

1. A retailer offers the following discount schemes for buyers on an article .
i. Two successive discounts of 10 % .
ii. A discount of 12 % followed by a discount of 8 %.
iii. Successive discount of 15 % and 5 % .
iv. A discount of 20 % .
The selling price will be minimum under the scheme
1. i
2. ii
3. iii
4. iv

1. i. Equivalent single discount to 10 % and 10 % = 10 + 10 - (10 x 10)/100 % = 19 %
ii. Equivalent single discount to 12 % and 8 % = 12 + 8 - (12 x 8)/100 = 20 - 0.96 = 19.04 %
iii. Equivalent single discount to 15 % and 5 % = 15 + 5 - (15 x 5)/100 = 20 - 0.75 = 19.25 %
iv. Equivalent single discount to 20 % = 20 %

##### Correct Option: D

i. Equivalent single discount to 10 % and 10 % = 10 + 10 - (10 x 10)/100 % = 19 %
ii. Equivalent single discount to 12 % and 8 % = 12 + 8 - (12 x 8)/100 = 20 - 0.96 = 19.04 %
iii. Equivalent single discount to 15 % and 5 % = 15 + 5 - (15 x 5)/100 = 20 - 0.75 = 19.25 %
iv. Equivalent single discount to 20 % = 20 % So, the selling price will be minimum under the scheme iv as in this scheme, the discount is maximum .

1. The market price of a clock is ₹ 3200 . It is to be sold at ₹ 2448 at two successive discounts . If the first discount is 10 %, then the second discount is
1. 5 %
2. 10 %
3. 15 %
4. 20 %

1. Let rate of second discount = r %
MP = ₹ 3200 , SP = ₹ 2448 ,
r1 = 10 % and r2 = r %
∴ y = MP x (100 - r1/100) (100 - r2/100)

##### Correct Option: C

Let rate of second discount = r %
MP = ₹ 3200 , SP = ₹ 2448 ,
r1 = 10 % and r2 = r %
∴ y = MP x (100 - r1/100) (100 - r2/100)
⇒ 2448 = [3200 x (100 - 10) x (100 - r)] / (100 x 100)
⇒ (2448 x 100 x 100) / (3200 x 90) = 100 - r
∴ r = 100 - 85 = 15 %

1. A shopkeeper sells not books at the rate of ₹ 457 each and earns a commission of 4% He also sells pencil boxes at the rate of ₹ 80 each and earns a commission of 20%. How much amount of commission will he he earn in two weeks, if he sells 10 notebooks and 6 pencil boxes a boy ?
1. ₹ 1956
2. ₹ 1586
3. ₹1496
4. ₹ 1596
5. None of the above

1. ∴ S.P of the notebook = ₹457
∴ Commission on one notebook = ₹ (4 x 457)/100
and commission on 10 notebooks = 10 x (4 x 457)/100 = ₹ 18280
Now,S.P of the pencil box = ₹ 80
∴ Commission on 1 pencil box = ₹ (80 x 20)/100
Commission on 6 pencil boxes = (80 x 20 x 6)/100 = ₹ 96

Hence ,total commission of 1 day = (182.80 + 96 ) = ₹ 278.80

##### Correct Option: E

∴ S.P of the notebook = ₹457
∴ Commission on one notebook = ₹ (4 x 457)/100
and commission on 10 notebooks = 10 x (4 x 457)/100 = ₹ 18280
Now,S.P of the pencil box = ₹ 80
∴ Commission on 1 pencil box = ₹ (80 x 20)/100
Commission on 6 pencil boxes = (80 x 20 x 6)/100 = ₹ 96

Hence ,total commission of 1 day = (182.80 + 96 ) = ₹ 278.80
Thus, total commission of 2 weeks = 278.80 x 14 = ₹ 3903.20

1. If the price of an item is increased by 30 % and then allows two successive discounts of 10 % and 10 % . In last the price of an item is?
1. Increased by 10%
2. Increased by 5.3%
3. decreased by 3%
4. decreased by 5.3%

1. Let the cost price of item = ₹ N
∴ Marked price of item = N x (100 + 30)/100 = ₹ 13N/10

Selling price of the item after two successive discount = (13N/10) x[ (100 - 10)/100 x (100 - 10)/100]
= (13N/10) x (90/100) x (90/100) = ₹ 1053N/1000

##### Correct Option: B

Let the cost price of item = ₹ N
∴ Marked price of item = N x (100 + 30)/100 = ₹ 13N/10

Selling price of the item after two successive discount = (13N/10) x[ (100 - 10)/100 x (100 - 10)/100]
= (13N/10) x (90/100) x (90/100) = ₹ 1053N/1000

Increment in the price of item = [{(1053N/1000) - N} / N] x 100 %
= 53/10 %
= 5.3 %

1. The difference between a discount of 30% on ₹ 2000 and two successive discounts of 25% and 5% on the same amount is
1. ₹ 30
2. ₹ 35
3. ₹ 25
4. ₹ 40

1. Single equivalent discount per cent to 25% and 5%
= r1 + r2 - (r1 . r2)/100 %

##### Correct Option: C

Single equivalent discount per cent to 25% and 5%
= r1 + r2 - (r1 . r2)/100 %
= 25 + 5 - (25 x 5)/100
= 30 - 1.25
= 28.78 %

∴ Required difference = [(30 - 28.75) x 2000]/100
= 1.25 x 2000/100 = ₹ 25