At what percent does an article must be marked up such that after allowing a discount 20% the profit obtained is 20%?

Problem: In a video store, a DVD that sells for $15 is marked "10% off." What is the discount? What is the sale price of the DVD?

Analysis: Stores often sell goods for a discounted price. Typically, a store will discount an item by a percent of the original price. In this problem, an item that originally costs $15 is being discounted by 10%. So "10% off" refers to the rate of discount. To solve this problem, we need a procedure.

Procedure:

The rate is usually given as a percent.
To find the discount, multiply the rate by the original price.
To find the sale price, subtract the discount from original price.

Now that we have a procedure, we can solve the problem above.

Problem: In a video store, a DVD that sells for $15 is marked, "10% off". What is the discount? What is the sale price of the DVD?

Solution: The rate is 10%.

The discount is: 0.10 x $15.00 = $1.50

The sale price is calculated as follows:

$15.00	original price
- 1.50	- discount
$13.50	sale price

Answer: The discount is $1.50 and the sale price is $13.50.

Let's take a look at some more examples of calculating discount and sale price.

Example 1: In a department store, a $40 dress is marked, "Save 25%." What is the discount? What is the sale price of the dress?

Analysis: The phrase, "Save 25%," refers to the rate.

The original price of the dress is $40.

Solution: The rate is 25%.

The discount is: 0.25 x $40.00 = $10.00

The sale price is calculated as follows:

$40.00	original price
- 10.00	- discount
$30.00	sale price

Answer: The discount is $10.00 and the sale price is $30.00.

Example 2: In a grocery store, a $12 case of soda is labeled, "Get a 20% discount." What is the discount? What is the sale price of the case of soda?

Analysis: The phrase, "Get a 20% discount," refers to the rate.

Solution: The rate is 20%.

The discount is: 0.20 x $12.00 = $2.40

The sale price is calculated as follows:

$12.00	original price
- 2.40	- discount
$ 9.60	sale price

Answer: The discount is $2.40 and the sale price is $9.60.

Example 3: In a candy store, a $5.00 jar of candy is labeled, "50% off." What is the discount? What is the sale price of the jar of candy?

Analysis: The phrase, "50% off," refers to the rate.

Solution: The rate is 50%.

The discount is: 0.50 x $5.00 = $2.50

The sale price is calculated as follows:

$5.00	original price
- 2.50	- discount
$2.50	sale price

Answer: The discount is $2.50 and the sale price is $2.50.

In Example 3, note that the discount and the sale price are the same amount! Do you know what fraction is equal to 50%? Could you have done this problem using mental math? The phrase, "50% off," is the same as, "1/2 off". So using mental math, you would get that one-half of $5.00 is $2.50. Let's look at another example that uses a fraction.

Example 4: A pizzeria has a coupon that reads, "Get

off a $9.00 cheese pizza." What is the discount? What is the sale price of the cheese pizza?

Analysis: The phrase, "

off," refers to the rate. It is expressed as a fraction.

Solution: The rate is given as the fraction

The discount is:

x $9.00 = $3.00

The sale price is calculated as follows:

$9.00	original price
- 3.00	- discount
$6.00	sale price

Answer: The discount is $3.00 and the sale price is $6.00.

Once again, you could calculate the discount and sale price using mental math. Let's look at another way of calculating the sale price of an item. Below is a modified version of the problem from the top of this page.

Example 5: In a video store, a DVD that sells for $15 is marked, "10% off." What is the sale price of the DVD?

Solution: The rate is 10%. Thus, the customer is paying 90% for the DVD.

The sale price is: 0.90 x $15.00 = $13.50

Answer: The sale price is $13.50.

Note that we calculated the sale price in the above problem, but we did not calculate the discount.

Summary: Stores often sell goods for a discounted price. Typically, a store will discount an item by a percent of the original price. The rate of discount is usually given as a percent, but may also be given as a fraction. The phrases used for discounted items include, "

off," "Save 50%," and "Get a 20% discount."

Procedure:

To calculate the discount, multiply the rate by the original price.
To calculate the sale price, subtract the discount from original price.

Exercises

Directions: Solve each problem below by entering a dollar amount with cents. For each exercise below, click once in the ANSWER BOX, type in your answer and then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

1.	In a boutique, a $14 scarf is marked, "20% off." What is the sale price of the scarf?

2.	In an electronics store, a $75 iPod is labeled, "Save 15%." What is the sale price of the iPod?

3.	What is the discount for the iPod in Exercise 2?

4.	A $30 shirt is marked, "Get off." What is the sale price of the shirt?

5.	In a bicycle store, a $500 bicycle is marked, "Get a 30% discount." What is the sale price of the bicycle?

APPLICATION SUMS

PROFIT, LOSS AND DISCOUNT SET-II

Question No : 1

Mohan bought a watch with 25% discount on the selling price. If the watch cost him Rs.1,545, What is the original selling price of the watch?

(1) Rs.2,050

(2) Rs.2,000

(3) Rs.2,040

(4) Can’t say

(5) None of these

Answer with Explanation

Question No : 2

The owner of an electronics shop charges his customer 22% more than the cost price. If a customer paid Rs.10,980 for a DVD player, then what was the cost price of the DVD player?

(1) Rs.8000

(2) Rs.8800

(3) Rs.9500

(4) Rs.9200

(5) None of these

Answer with Explanation

Question No : 3

Vinita bought a watch with 24% discount on the selling price. If the watch cost her Rs.779, what is the original selling price of the watch?

(1) Rs.1000

(2) Rs.950

(3) Rs.1040

(4) Can’t say

(5) None of these

Answer with Explanation

Question No : 4

Mohan purchased an article and sold it for Rs.2817.50 and earned 15 percent profit on the cost price. What was the cost price of the article?

(1) Rs.2,500

(2) Rs.2,450

(3) Rs.2,540

(4) Rs,3,315

(5) None of these

Answer with Explanation

Question No : 5

The profit earned after selling an article for Rs.1,754 is the same as loss incurred after selling the article for Rs.1,492. What is the cost price of the article?

(1) Rs.1,623

(2) Rs.1,523

(3) Rs.1,689

(4) Rs.1,589

(5) None of these

Answer with Explanation

Question No : 6

Prathik sold a music system to Karthik at 20% gain and Karthik sold it to Swasthik at 40% gain. If Swasthik paid Rs.10,500 for the music system, what amount did Prathik pay for the same?

(1) Rs.8,240

(2) Rs.7,500

(3) Rs.6,250

(4) Can’t say

(5) None of these

Answer with Explanation

Question No : 7

In a sale, a perfume is available at a discount of 15% on the selling price. If the perfume’s discounted selling price is Rs.3675.40, what was the original selling price of the perfume?

(1) Rs.4,324

(2) Rs.4,386

(3) Rs.4,400

(4) Rs.4,294

(5) None of these

Answer with Explanation

Question No : 8

What profit/loss percent did Ravi earn if he purchased an item of Rs.5,600 and sold it at three-fourth of its cost price?

(1) Loss of 20 percent

(2) Gain of 25 percent

(3) Neither gain nor loss

(4) Loss of 25 percent

(5) None of these

Answer with Explanation

Question No : 9

Shri Ramlal purchased a TV set for Rs.12,500 and spent Rs.300 on transportation and Rs.800 on installation. At what price should he sell it so as to earn an overall profit of 15%?

(1) Rs.14,560

(2) Rs.14,375

(3) Rs.15,460

(4) Rs.15,375

(5) None of these

Answer with Explanation

Question No : 10

A manufacturer marked an article at Rs.50 and sold it allowing 20% discount. If his profit was 25% then the cost price of the article was

(1) Rs.40

(2) Rs.35

(3) Rs.32

(4) Rs.30

(5) None of these

Answer with Explanation

Question No : 11

If on a marked price, the difference of selling prices with a discount of 30% and two successive discounts of 20% and 10% is Rs.72, then the marked price (in rupees) is

(1) 3,600

(2) 3,000

(3) 2,500

(4) 2,400

(5) None of these

Answer with Explanation

Question No : 12

Successive discounts of 10%, 20% and 30% is equivalent to a single discount of

(1) 60%

(2) 49.6%

(3) 40.5%

(4) 36%

(5) None of these

Answer with Explanation

Question No : 13

While selling a watch, a shopkeeper gives a discount of 5%. If he gives a discount of 6%, he earns Rs.15 less as profit. What is the marked price of the watch?

(1) Rs.1,250

(2) Rs.1,400

(3) Rs.1,500

(4) Rs.750

(5) None of these

Answer with Explanation

Question No : 14

Marked price of an article is Rs.275. Shopkeeper allows a discount of 5% and he gets a profit of 4.5%. The actual cost (in Rs.) of the article is

(1) 250

(2) 225

(3) 215

(4) 210

(5) None of these

Answer with Explanation

Question No : 15

The cost price of an article is 64% of the marked price. The gain percentage after allowing a discount of 12% on the marked price is

(1) 37.5%

(2) 48%

(3) 50.5%

(4) 52%

(5) None of these

Answer with Explanation

Question No : 16

The printed price of a book is Rs.320. A retailer pays Rs.244.80 for it. He gets successive discounts of 10% and an another rate. He second rate is:

(1) 15%

(2) 16%

(3) 14%

(4) 12%

(5) None of these

Answer with Explanation

Question No : 17

A sells an article to B at a gain of 10%, B sells it to C at a gain of 5%. If C pays Rs.462 for it, what did it cost to A?

(1) Rs.500

(2) Rs.450

(3) Rs.600

(4) Rs.400

(5) None of these

Answer with Explanation

Question No : 18

A merchant purchases a wrist watch for Rs.450 and fixes its list price in such a way that after allowing a discount of 10%, he earns a profit of 20%. Then the list price of the watch is

(1) Rs.600

(2) Rs.650

(3) Rs.700

(4) Rs.550

(5) None of these

Answer with Explanation

Question No : 19

A merchant allows a discount of 10% on marked price for the cash payment. To make a profit of 17%, he must mark his goods higher than their cost price by

(1) 30%

(2) 33%

(3) 40%

(4) 27%

(5) None of these

Answer with Explanation

Question No : 20

By selling a fan for Rs.600, a man loses 10%. To make a gain of 20%, the selling price of the fan should be

(1) Rs.800

(2) Rs.900

(3) Rs.1000

(4) Rs.700

(5) None of these

Answer with Explanation

Question No : 21

An article was sold at 16% gain. Had it been sold for Rs.200 more, the gain would have been 20%. Then the cost price of the article is:

(1) Rs.5000

(2) Rs.4800

(3) Rs.4500

(4) Rs.5200

(5) None of these

Answer with Explanation

Question No : 22

A got 30% concession on the label price of an article sold for Rs.8,750 with 25% profit on the price he bought. The label price was

(1) Rs.10,000

(2) Rs.13,000

(3) Rs.16,000

(4) Rs.12,000

(5) None of these

Answer with Explanation

Question No : 23

Which of the following successive discounts is better to a customer?

A. 20%, 15%, 10%

B. 25%, 12%, 8%

(1) A is better

(2) B is better

(3) A or B (both are same)

(4) None of these

(5) Can’t say

Answer with Explanation

Question No : 24

On selling an article for Rs.170, a shopkeeper loses 15%. In order to gain 20%, he must sell that article at rupees:

(1) 210

(2) 215.50

(3) 212.50

(4) 240

(5) None of these

Answer with Explanation

Question No : 25

A retailer purchased radio sets at the rate of Rs.400 each from a wholesaler. He raised the price by 30% and then allowed a discount of 8% on each set. His profit will be

(1) 19%

(2) 78.4%

(3) 22%

(4) 19.6%

(5) None of these

Answer with Explanation

Question No : 26

A shopkeeper earns a profit of 12% on selling a book at 10% discount on printed price. The ratio of the cost price to printed price of the book is

(1) 45 : 56

(2) 50 : 61

(3) 90 : 97

(4) 99 : 125

(5) None of these

Answer with Explanation

Question No : 27

A trade men sold an article at a loss of 20%. If the selling price had been increased by Rs.100. There would have been a gain of 5%. The cost price of the article (in Rs.) was

(1) 100

(2) 200

(3) 400

(4) 500

(5) None of these

Answer with Explanation

Question No : 28

By selling an article for Rs.450, I lose 20%. For what amount, should sell it to gain 20%?

(1) 490

(2) Rs.470

(3) Rs.562.50

(4) Rs.675

(5) None of these

Answer with Explanation

Question No : 29

A house was sold for Rs.y by giving a discount of x%, then the list price was:

Answer with Explanation

Question No : 30

A man purchased an article for Rs.1500 and sold it at 25% above the cost price. If he has to pay Rs.75 as tax on it his net profit percentage will be:

(1) 25%

(2) 30%

(3) 15%

(4) 20%

(5) None of these

Answer with Explanation

Question No : 31

10% discount and then 20% discount in succession is equivalent to total discount of

(1) 15%

(2) 30%

(3) 24%

(4) 28%

(5) None of these

Answer with Explanation

Question No : 32

The marked price of a watch was Rs.720. A man bought the same for Rs.550.80 after getting two successive discounts, the first being 10%. The second discount rate is

(1) 12%

(2) 14%

(3) 15%

(4) 18%

(5) None of these

Answer with Explanation

Question No : 33

Allowing 20% and 15% successive discounts, the selling price of an article becomes Rs.3,060; then the marked price will be

(1) Rs.4,400

(2) Rs.5,000

(3) Rs.4,500

(4) Rs.4,000

(5) None of these

Answer with Explanation

Question No : 34

The difference between successive discounts of 40% followed by 30% and 45% followed by 20% on the marked price of an article is Rs.12. The marked price of the article is:

(1) Rs.400

(2) Rs.200

(3) Rs.800

(4) Rs.600

(5) None of these

Answer with Explanation

Question No : 35

Find a simple discount equivalent to a discount series of 10%, 20% and 25%

(1) 45%

(2) 55%

(3) 52%

(4) 46%

(5) None of these

Answer with Explanation

Question No : 36

Cost price of 100 books is equal to the selling price of 60 books. The loss percentage will be:

Answer with Explanation

Question No : 37

The profit earned after selling an article for Rs.1,516 is the same as loss incurred after selling the article for Rs.1,112. What is the cost price of the article?

(1) Rs.1,314

(2) Rs.1,343

(3) Rs.1,414

(4) Rs.1,434

(5) None of these

Answer with Explanation

Question No : 38

Meenal purchased a car for Rs.2,50,000 and sold it for Rs.3,48,000. What is the percent profit she made on the car?

(1) 40%

(2) 39.2%

(3) 38.4%

(4) 38%

(5) None of these

Answer with Explanation

Question No : 39

Rajni purchased a mobile phone and a refrigerator for Rs.12,000 and Rs.10,000 respectively. She sold the refrigerator at a loss of 12 percent and mobile phone at a profit of 8 percent. What is her overall loss/profit?

(1) Loss of Rs.280

(2) Profit of Rs.2,160

(3) Loss of Rs.240

(4) Profit of Rs.2,060

(5) None of these

Answer with Explanation

Question No : 40

A man sold a wristwatch for Rs.2,400 at a loss of twenty five percent. At what rate should he have sold the wristwatch to earn a profit of twenty five percent?

(1) Rs.3,600

(2) Rs.4,000

(3) Rs.3,500

(4) Rs.3,800

(5) None of these

Answer with Explanation

Question No : 41

Prasad sold his work tools for Rs.1,850 and earned a profit of 25 percent. At what price did Prasad buy the work tools?

(1) Rs.1,360

(2) Rs.1,300

(3) Rs.1,240

(4) Rs.1,480

(5) None of these

Answer with Explanation

Question No : 42

Rehaan purchased a bike for Rs.54,000. He sold it at a loss of 8 percent. With that money he again purchased another bike and sold it at a profit of 10 percent. What is his overall loss/profit?

(1) Loss of Rs.657

(2) Profit of Rs.567

(3) Loss of Rs.648

(4) Profit of Rs.648

(5) None of these

Answer with Explanation

Question No : 43

Meera purchased an item for Rs.62,000 and sold it at a loss of 25 percent. With that amount she purchased another item and sold it at a gain of 30 percent. What was her overall gain/loss?

(1) Loss of Rs.1560

(2) Profit of Rs.1560

(3) Loss of Rs.1550

(4) Profit of Rs.1550

(5) None of these

Answer with Explanation

Question No : 44

Kamya purchased an item of Rs.46,000 and sold it at a loss of 12 percent. With that amount she purchased another item and sold it at a gain of 12 percent. What was her overall gain/loss?

(1) Loss of Rs.662.40

(2) Profit of Rs.662.40

(3) Loss of Rs.642.80

(4) Profit of Rs.642.80

(5) None of these

Answer with Explanation

Question No : 45

The value of machine depreciates at the rate of 12 percent per-annum. It was purchased three years ago. Its present value is Rs.29644.032, what was the purchase price of the machine?

(1) Rs.48700

(2) Rs.43500

(3) Rs.38900

(4) Rs.39000

(5) None of these

Answer with Explanation

Question No : 46

On selling an article for Rs.756, a loss of 68% is incurred. To gain 30%, the selling price of the article will be

(1) Rs.3171.25

(2) Rs.3071.25

(3) Rs.3107.25

(4) Rs.3200

(5) None of these

Answer with Explanation

Question No : 47

An article was purchased for Rs.78,350. Its price was marked up by 30%. It was sold at a discount of 20% on the marked up price. What was the profit percent on the cost price?

(1) 4%

(2) 7%

(3) 5%

(4) 3%

(5) 6%

Answer with Explanation

Question No : 48

A discount of 15% is given on the marked price of an article. The shopkeeper charges sales tax of 6% on the discounted price. If the selling price be Rs.1081.20. What is the marked price of the article?

(1) Rs.1185.20

(2) Rs.1250.20

(3) Rs.302

(4) Rs.1200

(5) None of these

Answer with Explanation

Question No : 49

A shopkeeper purchased an artefact and marked its price up by 20%. He sold the artefact to a customer after allowing a certain discount and made a profit of 10%. Find the discount percent given by the shopkeeper.

Answer with Explanation

Question No : 50

Deepa bought a calculator with 30% discount on the listed price. Had she not got the discount, she would have paid Rs.82.50 extra. At what price did she buy the calculator?

(1) Rs.192.50

(2) Rs.2745

(3) Rs.117.85

(4) Can’t say

(5) None of these

Answer with Explanation

Question No : 51

While selling a watch, a shopkeeper gives a discount of 15%. If he gives a discount of 20%, he earns Rs.51 less as profit. What is the original price of the watch?

(1) Rs.920

(2) Rs.985

(3) Rs.1125

(4) Rs.1020

(5) None of these

Answer with Explanation

Question No : 52

A book is listed at Rs.150, with a discount of 20 per cent. What additional discount must be offered to bring the net price to Rs.108?

Answer with Explanation

Question No : 53

A man purchases two fans for Rs.2,160. By selling one fan at a profit of 15% and the other at a loss of 9% he neither gains nor loss in the whole transaction. Find the cost price of each fan in Rs.

(1) 710, 1450

(2) 1530, 630

(3) 810, 1350

(4) 1340, 820

(5) None of these

Answer with Explanation

Question No : 54

Answer with Explanation

Question No : 55

Nikita bought 30 kg of wheat at the rate of Rs.9.50 per kg of wheat and the same amount of wheat at the rate of Rs.8.50 per kg and mixed them. She sold the mixture at the rate of Rs.8.90 per kg. Her total profit or loss in the transaction was:

(1) Rs.2 loss

(2) Rs.2 profit

(3) Rs.6 loss

(4) Rs.6 profit

(5) None of these

Answer with Explanation

Ans (3): Rs.6 loss

CP = 30 ´ 9.50 + 30 ´ 8.5 = 30 [9.5 + 8.5] = 30 ´ 10 = Rs.540

SP = 60 ´ 8.90 =Rs.534

Loss = CP – SP = 540 – 534 = Rs.6

Question No : 56

Ramesh bought 10 cycles for Rs.500 each. He spent Rs.2,000 on the repair of all cycles. He sold five of them for Rs.750 each and the remaining for Rs.550 each. Then the total gain or loss % is

Answer with Explanation

Question No : 57

A vendor purchased 40 dozens bananas for Rs.250. Out of these 30 bananas were rotten and could not be sold. At what rate per dozen should he sell the remaining bananas to make a profit of 20%?

(1) Rs.12

(2) Rs.10

(3) Rs.8

(4) Rs.6

(5) None of these

Answer with Explanation

Question No : 58

A merchant purchases a wrist watch for Rs.1200 and fixed its list price in such a way that after allowing a discount of 10%, he earns a profit of 20%. The list price of the watch is

(1) Rs.1800

(2) Rs.1200

(3) Rs.1600

(4) Rs.1400

(5) None of these

Answer with Explanation

Question No : 59

A shopkeeper purchased 50 dozens cups for Rs.3000. Out of these 60 cups were broken and could not be sold. At what rate per dozen should he sell the remaining cup to make a profit of 20%?

(1) Rs.60

(2) Rs.75

(3) Rs.80

(4) Rs.90

(5) None of these

Answer with Explanation

Question No : 60

If a commission at the rate of 10% is given to a bookseller on the marked price of a book by the publisher, the publisher gains 20%. If the commission is increased to 15%, then the gain percent would be.

Answer with Explanation

Question No : 61

A trader purchased a gift box for Rs.150. What should be the marked price on the gift box so that after allowing a discount of 10%, he makes a profit of 10%?

(1) Rs.180

(2) Rs.183.3

(3) Rs.186.6

(4) Rs.190

(5) None of these

Answer with Explanation

Question No : 62

A vegetable seller sells his vegetables at 20% profit. At the same time he uses false weights, which is 10% less than the actual weight. What will be his total gain percentage?

Answer with Explanation

Question No : 63

A fan in a shop is offered at a discount of 10%. It is sold during clearance sale at 6% discount over the already discount price of Rs.846. The original marked price of the fan is

(1) Rs.900

(2) Rs.946

(3) Rs.850

(4) Rs.1000

(5) None of these

Answer with Explanation

Question No : 64

During month-long annual sale, a shopkeeper sells his goods at a discount of 50%. But in the last week, he offers an additional discount of 40%. If the original price of a shirt is Rs.x then the price, (in rupees) during the last week of the sale will be

(1) 90% of x

(2) 70% of x

(3) 30% of x

(4) 10% of x

(5) None of these

Answer with Explanation

Question No : 65

A shop offers 10% discount on every purchase of an article. It also offers an additional discount of 12%, if the payment is made in cash. If the original price of an item is Rs.250, how much a customer will pay. If he wants to pay the price is cash?

(1) Rs.180

(2) Rs.192

(3) Rs.198

(4) Rs.195

(5) None of these

Answer with Explanation

Question No : 66

Jesmine allows 4% discount on the marked price of her goods and still earns a profit of 20%. What is the cost price of a shirt if its marked price is Rs.850?

(1) Rs.650

(2) Rs.720

(3) Rs.700

(4) Rs.680

(5) None of these

Answer with Explanation

Question No : 67

A shopkeeper allows a discount of 10% on the marked price of an item but charges a sales tax of 8% on the discounted price. If the customer pays Rs.3,402 as the price including the sales tax, then the marked price is

(1) Rs.3,400

(2) Rs.3,500

(3) Rs.3,600

(4) Rs.3,800

(5) None of these

Answer with Explanation

Question No : 68

Ramesh marks his goods 30% above cost price. If he sells the item for Rs.910 after allowing of 15% discount find his cost price.

(1) Rs.823.5

(2) Rs.758

(3) Rs.814.2

(4) Rs.856.5