## Discount

#### Discount

1. The list price of a book is Rs. 100. A dealer sells three such books for Rs. 274.50 after allowing discount at a certain rate. Find the rate of discount.
1. 8.16%
2. 8.5%
3. 8.34%
4. 8.33%

1. Total marked price of three books = Rs. 300
Their S.P. = Rs. 244.50
Discount = Rs. (300 – 274.50) = Rs. 25.50
If the rate of discount be x%, then

 300 × x = 25.50 100

⇒  300x = 25.50 × 100
 ⇒  x = 25.50 × 100 = 8.5% 300

Second Method :
M.P. = Rs. 300 (for three books)
S.P. = Rs. 274.50
 = M.P. − S.P. ×100% M.P.

 = 300 − 274.50 ×100% 300

 25.5 × 100 = 8.5% 300

##### Correct Option: B

Total marked price of three books = Rs. 300
Their S.P. = Rs. 244.50
Discount = Rs. (300 – 274.50) = Rs. 25.50
If the rate of discount be x%, then

 300 × x = 25.50 100

⇒  300x = 25.50 × 100
 ⇒  x = 25.50 × 100 = 8.5% 300

Second Method :
M.P. = Rs. 300 (for three books)
S.P. = Rs. 274.50
 = M.P. − S.P. ×100% M.P.

 = 300 − 274.50 ×100% 300

 25.5 × 100 = 8.5% 300

1. A builder purchases 25 windows at 25% off the total price of ₹ 1,20,000. If the builder receives an additional discount of ₹ 7500 for the purchase, then the cost of each window is
1. ₹ 3300
2. ₹ 3100
3. ₹ 3400
4. ₹ 3200

1.  C.P. of 25 windows = 120000 × 75 = Rs. 90,000 100

C.P. for builder
= Rs. (90000 – 7500)
= Rs. 82500
 ∴ Cost of each window = 82500 = Rs. 3300 25

##### Correct Option: A

 C.P. of 25 windows = 120000 × 75 = Rs. 90,000 100

C.P. for builder
= Rs. (90000 – 7500)
= Rs. 82500
 ∴ Cost of each window = 82500 = Rs. 3300 25

1. The price of an antique is reduced by 20% and then this price is again reduced by 10%. The total reduction of the price is
1. 25 %
2. 30 %
3. 23 %
4. 28 %

1.  Percentage decrease = x + y + xy % 100

 = − 20 − 10 + 20 × 10 % = −28% 100

Second Method :
Here, D1 = 20%
D2 = 10%
 Net reduction= D1 + D2 − D1D2 % 100

 = 20 + 10 − 20 × 10 % 100

= (30 – 2)% = 28%

##### Correct Option: D

 Percentage decrease = x + y + xy % 100

 = − 20 − 10 + 20 × 10 % = −28% 100

Second Method :
Here, D1 = 20%
D2 = 10%
 Net reduction= D1 + D2 − D1D2 % 100

 = 20 + 10 − 20 × 10 % 100

= (30 – 2)% = 28%

1. Mr. x and Mr. y each bought the same motorcycle using a 10% off coupon. Mr. x’s cashier took 10% off the price and then added 8.5% sales tax whereas Mr. y’s cashier first added the sales tax and then took 10% off the total price. The amount Mr. x paid is
1. less by ₹ 550 as the amount Mr. y paid
2. same as the amount Mr. y paid
3. greater by ₹ 85 as the amount Mr. y paid
4. greater by ₹ 850 as the amount Mr. y paid

1. Price of motor cycle = Rs. α
(let)
For Mr. x

 C.P. of motor cycle = Rs. 90α × 108.5 100 100

For Mr y
 C.P. of motor cycle = Rs. 108.5α × 90 100 100

##### Correct Option: B

Price of motor cycle = Rs. α
(let)
For Mr. x

 C.P. of motor cycle = Rs. 90α × 108.5 100 100

For Mr y
 C.P. of motor cycle = Rs. 108.5α × 90 100 100

1. After allowing a discount of 10% on marked price a trader makes a profit of 15%. The ratio of the marked price to the cost price is
1. 23 : 9
2. 23 : 10
3. 23 : 18
4. 23 : 19

1. Marked price = Rs. x and cost price = Rs. y (let)
According to question,

 x × 90 = y × 115 100 100

 ⇒ x = 115 = 23 = 23 : 18 y 90 18

##### Correct Option: C

Marked price = Rs. x and cost price = Rs. y (let)
According to question,

 x × 90 = y × 115 100 100

 ⇒ x = 115 = 23 = 23 : 18 y 90 18