## Discount

#### Discount

1. If on a marked price, the difference of selling prices with a discount of 30 % and two successive discounts of 20 % and 10 % is ₹ 72, then the marked price (in ₹) is
1. ₹ 3600
2. ₹ 3000
3. ₹ 2500
4. ₹ 2400

1. Let the marked price = ₹ N
The discount equivalent to successive discounts 20 % and 10 % = { r1 + r2 - (r1 r2)/100 } %
Where, r1 = 20 and r2 = 10
Then, 30 - 2 = 28 %
According to the question,
{(100 - 28)N}/100 - {(100 - 30)N}/100 = 72

##### Correct Option: A

Let the marked price = ₹ N
The discount equivalent to successive discounts 20 % and 10 % = { r1 + r2 - (r1 r2)/100 } %
Where, r1 = 20 and r2 = 10
Then, 30 - 2 = 28 %
According to the question,
{(100 - 28)N}/100 - {(100 - 30)N}/100 = 72
⇒ (72N - 70N)/100 = 72
∴ N = (72 x 100)/2 = ₹ 3600

1. A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is
1. 45 : 56
2. 8 : 11
3. 47 : 56
4. 3 : 4

1. Let the CP of book = ₹ P
Then, SP of book = {(100 + 12) x P}/100 = 112P/100
Now, the printed price = ₹ Q
Then, after discount,
the SP = (100 - 10)Q/100 = 90Q/100
Since, both SP are same.
Then, 112P/100 = 90Q/100

##### Correct Option: A

Let the CP of book = ₹ P
Then, SP of book = {(100 + 12) x P}/100 = 112P/100
Now, the printed price = ₹ Q
Then, after discount,
the SP = (100 - 10)Q/100 = 90Q/100
Since, both SP are same.
Then, 112P/100 = 90Q/100
⇒ P/Q = 45/56
⇒ 45 : 56

1. A manufacturer marked an article at ₹ 50 and sold it allowing 20% discount. If his profit was 25%, then the cost price of the article was
1. ₹ 40
2. ₹ 35
3. ₹ 32
4. ₹ 30

1. ∵ Marked price of an article = ₹ 50
∴ SP of an article = 50 x (100 - 20)/100
= (50 x 80)/100
= ₹ 40

Hence, cost price of an article = (40 x 100)/(100 + 25)

##### Correct Option: C

∵ Marked price of an article = ₹ 50
∴ SP of an article = 50 x (100 - 20)/100
= (50 x 80)/100
= ₹ 40

Hence, cost price of an article = (40 x 100)/(100 + 25)
= (40 x 100)/125
= ₹ 32

1. A seller marks his goods 30% above their cost price but allows 15% discount for cash payment. His percentage of profit when sold in cash, is ?
1. 10.5%
2. 15%
3. 9%
4. 8.5%

1. Let CP of the goods = ₹ N
∴ Marked price of the goods = N x {(100 + 30)/100} = ₹ 13N/10

Now, SP of the goods = (13N/10) x (100 - 15/100)
= (13N/10) x (85/100) = ₹ 221N/200

⇒ Profit = {(221 x N)/200} - N = ₹ 21N/200

##### Correct Option: A

Let CP of the goods = ₹ N
∴ Marked price of the goods = N x {(100 + 30)/100} = ₹ 13N/10

Now, SP of the goods = (13N/10) x (100 - 15/100)
= (13N/10) x (85/100) = ₹ 221N/200

⇒ Profit = {(221 x N)/200} - N = ₹ 21N/200

Hence, profit per cent = [{21N/200} /N] x 100 % = 2100/200 = 10.5 %

1. By selling an article at 3/4th of the marked price, there is a gain of 25%. The ratio of the marked price and the cost price is
1. 5 : 3
2. 3 : 5
3. 3 : 4
4. 4 : 3

1. Let MP of an article = ₹ R
∴ SP of an article = ₹ 3R/4
and CP of an article
= (3R/4) x {100/(100 + 25)}

##### Correct Option: A

Let MP of an article = ₹ R
∴ SP of an article = ₹ 3R/4
and CP of an article
= (3R/4) x {100/(100 + 25)}
= 3R/4 x (100/125)
= ₹ 3R/5
Required ratio = R : 3R/5 = 5 : 3