WORD PROBLEMS ON SUCCESSIVE DISCOUNTS

Problem 1 :

The marked price of a shirt is $1000. A shopkeeper offers 10% discount on this shirt and then again offers 20% discount on the new price. How much will you have to pay, finally?

Solution :

Cost price of the shirt = $1000

Cost price = 100%

After the first discount = 90% of 1000

= 0.90(1000)

= 900

After the second discount :

80% of 900 = 0.80(900)

= 720

So, finally he has to pay $720.

Problem 2 :

The marked price of a shirt is $1000. A shopkeeper offers 10% discount on this shirt and then again offers 20% discount on the new price, and then and then again offers 30% discount on the new price . How much will you have to pay, finally?

Solution :

Marked price of the shirt = $1000

Price of the shirt after 1^st discount :

90% of the price = 0.90(1000)

= $900

Price of the shirt after 2^nd discount :

80% of the price = 0.80(900)

= $720

Price of the shirt after 3^rd discount :

70% of the price = 0.70(720)

= $504

Problem 3 :

Jorge bought a watch on sale for 25% off the original price and another 75% off the discounted price. If the watch originally costs $64, what was the final sale price that Jorge paid for the watch?

Solution :

Original cost of the watch = $64

After the 1st discount :

Discount = 25%

75% of the original price = 0.75(64)

= 48

After the 2nd discount :

Discount = 75%

= 25% of the 48

= 0.25(48)

= 12

Problem 4 :

Antonia is buying a space heater that regularly costs $90. It is on sale for 40% off with an additional 25% off the discounted price. What is the final sale price of the heater?

Solution :

Regular cost of heater = $90

Price of heater after the 1st discount :

Discount = 40%

60% of the price = 0.60(90)

= 54

Price of heater after the 2nd discount :

Discount = 25%

75% of 54 = 0.75(54)

= 40.5

Problem 5 :

The price of a new pair of shoes is $40. If there is a 20% discount on all shoes, how much is deducted from the original price?

Solution :

Price of shoes = $40

Discount = 20%

20% of the price of shoe = 0.20(40)

= 8

The deduction amount = 8

The new price = 40 - 8

= $32

Problem 6 :

A jacket originally costs $70. Wilasha bought it yesterday at 30% off. How much was her discount?

Solution :

Original price of the jacket = $70

30% of the original price = 0.30(70)

= $21

The deduction amount = $21.

Problem 7 :

You buy a bicycle helmet for $22.26, which includes 6% sales tax. The helmet is discounted 30% off the selling price. What is the original price?

Solution :

Let x be the selling price of the bicycle.

selling price will be 100%.

106% of selling price of helmet = $22.26

1.06 x selling price of helmet = 22.26

Selling price of helmet = 22.26/1.06

= 21

70% of the original price = 21

0.70 x original price = 21

original price = 21/0.70

= 30

So, the original price is $30.

Problem 8 :

After getting two successive discounts, a shirt with list price of $150 is available at $105. If the second discount is 12.5%, find the first discount.

Solution :

List price of the shirt = $150

After the second discount, it costs = $105

Let x% be the first discount.

(100 - 12.5)% of the (100 - x) % of 150 = 105

87.5% of (100 - x)% of 150 = 105

0.875[(100 - x)/100] ⋅ 150 = 105

(0.875 ⋅ 150) (100 - x) / 100 = 105

100 - x = 105(100) / (0.875 ⋅ 150)

100 - x = 10500/131.25

100 - x = 80

x = 100 - 80

x = 20%

So, the first discount is 20%.

Problem 9 :

A pair of articles was bought for $37.40 at a discount of 15%. What must be the marked price of each of the article ?

Solution :

Let x be the marked price and it is 100%.

Discount of 15%.

(100-15)% of original price = 37.40

85% of original price = 37.40

Original price = 37.40/85%

= 37.40/0.85

= 44

So, the marked price of each article is $44.

Problem 10 :

A shopkeeper gives 12% additional discount on the discounted price, after giving an initial discount of 20% on the lablled price of a radio. If the final sale price of the radio is $704, then what is its lablled price ?

Solution :

Let x be the marked price and it is 100%.

80% of x = amount to be paid after the first dscount.

(100 - 12)% of 80% of x = 704

88% of 80% of x = 704

0.88(0.80x) = 704

x = 704/0.88(0.80)

x = 1000

So, the lablled price of the radio is $1000.