PRACTICE PROBLEMS ON COST PRICE AND SELLING PRICE

Problem 1 :

A washing machine has a selling price of $420, but a 15% discount is given. Find the actual price paid for the washing machine.

Solution :

Selling price = $420

Discount = 15%

Let x be the original price and it is 100%

After giving 15% discount, the new price will be (100 - 15)%

85% of x = 420

0.85x = 420

x = 420/0.85

x = 494.1

Approximately $494.

So, the actual price of the washing machine is $494.

Problem 2 :

30% of a farmer’s crop was barley and the rest was wheat. If he planted 750 hectares with barley, what area was planted with wheat?

Solution :

Let x be the quantity of crop.

30% of x = 750

0.30x = 750

x = 750/0.30

x = 2500 hectares

So, the required area is 2500 hectares.

Problem 3 :

At the grocery store, Gigi buys apples, a magazine, and a gallon of milk. The apples are priced per pound. In her state, there is no sales tax on food. If the total cost of her items is given by the function

C(p) = 1.89p + 1.07(3.99) + 4.49

then the term

1.07(3.99)

most likely represents

a)  the cost of one gallon of milk.

b) the per-pound cost of the apples.

c) the cost of the magazine, includinq tax.

d) the cost of the magazine, not including tax.

Solution :

C(p) = 1.89p + 1.07(3.99) + 4.49

The product Gigi is purchasing, apples, a magazine, and a gallon of milk.

Here 1.07 (3.99) will represents cost of magazine including tax, because it is mentioned that for food product there is no tax. So, option c is correct.

Problem 4 :

When a homeowner hires a contractor to renovate a bathroom, the homeowner is charged for both labor and materials. By law, the contractor can charge sales tax on the materials, but not on the labor. If the contractor quotes the homeowner $3,000 for materials and $40 per hour for labor, and sales tax in the homeowner's state is 5.5%, which equation represents the total cost for the bathroom renovation if it takes the contractor h hours to complete the job?

a) c = (40h + 3,000)(1.055)     b) c = 1.055(40 + 3,000)h

c) c = 40h(l.055) + 3,000        d) c = 40h + 1.055(3,000)

Solution :

Material cost = 3000

Labor charge = $40 per hour

Sales tax = 5.5%

Including sales tax = 100% + 5.5%

= 1.055

Labor charge for h hours of work = 40h

So, required cost is 40h + 1.055(3000)

Problem 5 :

The sale price of a laptop is $505.44 after 35% discount and 8% additional tax. What was the original price of the laptop before discount and tax?

Solution :

Sales price of laptop = $505.44

Discount of 35% and 8% of additional tax.

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

(100 - 35)% ==> 65%

In this 65%, we have to include 8% additional tax.

0.65(1 + 0.08)x = 505.44

0.65(1.08x) = 505.44

x = 505.44/(0.65)(1.08)

x = 777.6/1.08

= 720

So, the original price of the $720.

Problem 6 :

A family sees the kitchen they want priced at $7200 but it is offered at a discount of 40% in a sale. What is the sale price?

Solution :

The original price = $7200

Discount = 40%

(100 - 40)% ==> 60%

Sale price after the discount = 60% of 7200

= 0.60(7200)

= 4320

So, the sales price is $4320.

Problem 7 :

A car cost $11500 new but lost 35% of its value in the first three years. What is it worth after three years? This loss in value is called depreciation

Solution :

Cost of car = $11500

Loss of 35%.

Worth of car after three years = (100 - 35)% of 11500

= 65% of 11500

= 0.65(11500)

= 7475

Problem 8 :

A mobile phone was sold for $1040 at a gain of 4%. What will be the gain or loss % if it is sold for $960?

Solution :

Selling price of mobile phone with 4% gain = 1040

Let x be the cost price of 100%.

104% of x = 1040

1.04x = 1040

x = 1040/1.04

x = 1000

Cost price = 1000, if selling price is 960, then it is loss.

Loss percentage

= (Cost price - selling price)/cost price x 100%

= [(1000 - 960) / 1000] x 100%

= (40/1000) x 100%

= 4%

So, the required loss is 4%.

Problem 9 :

The marked price of a shirt is $940 and the shopkeeper allows a discount of 15% on it .Find the discount and the selling price of the shirt.

Solution :

Market price = $940

Discount = 15%

Selling price = (100 - 15)%

85% of cost price 

Then 85% of cost price = 0.85(940)

= 799

So, the selling price of the shirt after discount is $799.

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