﻿ e-LJam Mathematics - Module 2 Unit 3 Section 1 : Buying and Paying

The objectives of this section are to

• understand the difference between cash price and hire purchase
• be able to calculate percentage increase and decrease in price
• be able to calculate GCT in context.

You are familiar with buying items in shops and markets but often, when buying expensive goods, different methods of payment are available.

You might be offered a hire purchase agreement: you would pay a deposit and then pay the remainder of the cost of the item in a specified number of (often monthly) instalments. In a sale, the cash price might be reduced.

You need to remember that most goods are subject to a government sales tax, often referred to as VAT (value added tax). In Jamaica this government tax is GCT (general consumption tax) which is currently charged at 16%.

1

The monthly water bill for domestic users is calculated from information shown in the table below.

 Fixed charge J\$350 Charge per gallon 20 cents

Calculate the TOTAL amount of the bill for a month when a consumer used 3850 gallons.

Show

 Total amount of bill = J\$350 + 3850 × J\$0.20 = J\$350 + J\$770 = J\$1120

2

A printer is advertised for sale at J\$84 000. A discount of 12% is given if it is bought for cash. It can also be bought on hire purchase by paying a deposit of J\$29 400 followed by 24 monthly payments of J\$2300 each. Calculate

(a)

the cash price,

Show

 Cash price = J\$84 000 − 12% of J\$84 000 = J\$⎧⎨⎩ 84000 − × 84 000⎫⎬⎭ = J\$73920

Note: it is quicker to calculate the cash price as

 88% of J\$84 000 = J\$ ⎛⎝ × 84 000⎞⎠ = J\$73 920

(b)

the hire purchase price,

Show

 Hire purchase price = J\$29 400 + 24 × J\$2300 = J\$(29 400 + 55 200) = J\$84 600

(c)

the amount saved by buying the printer for cash rather than on hire purchase.

Show

 Amount saved = J\$84 600 − J\$73 920 = J\$10 680

3

In selling an article, a shopkeeper made a profit of 20% on his cost price of J\$8000. What was the selling price?

Show
 20% of J\$8000 = J\$⎛⎝ × 8000⎞⎠ = J\$1600

This is the shopkeeper's profit, so the selling price is

J\$8000 + J\$1600 = J\$9600

Note: It is quicker to calculate

 120% of cost price = J\$ × 8000 = J\$9600
4 (a)

Calculate the TOTAL amount a customer pays for the television set.

Show
 Total amount paid = \$1600 + 15% of \$1600 = \$⎛⎝1600 + × 1600⎞⎠ = \$(1600 + 240) = \$1840
(b)

The sale price of \$1600 is 20% LESS THAN the original price. Calculate the ORIGINAL price of the television set.

Show

If the original price is \$p, then

 80% of p = 1600 that is, × p = 1600 p = 1600 × = 2000

So the original price was \$2000.

 Check: 20% of \$2000 = × \$2000 = \$400 So sale price = \$2000 − \$400 = \$1600, as expected.

In 2011 a store charged 17% GCT on all sales. What was the total cost of a shirt marked at J\$1200?

J\$

In a sale, all prices are reduced by 30%. Calculate the sale price of each of the following items.

(a)
a coat that cost J\$5000, J\$
(b)
a T-shirt that cost J\$1200, J\$
(c)
a football shirt that cost J\$2200. J\$

A 12% service charge is added to the cost of food ordered in a restaurant. If the food costs J\$2700, what is the total cost, including the service charge?

J\$

The cash price of a computer in the USA is \$696. The hire purchase price is 10% deposit and 15 monthly payments of \$45. How much more is the hire purchase price than the cash price?

\$

The cost of some building materials is J\$6480 plus 16% GCT.

(a)

How much GCT is charged?

J\$
(b)

What is the total cost of the building materials?

J\$

A clothing manufacturer determines the selling price of items by adding 32% to the production costs. Calculate the selling price of a dress that cost J\$2500 to produce.

J\$

What is the percentage decrease in the price of a television set which is reduced from \$248 to \$200? Give your answer to the nearest 1%.

%

An electronic game is sold for J\$1998 and the seller makes an 11% profit on the amount he paid for the game. How much did the seller pay for the game?

J\$

Consumption tax and customs duty are calculated as follows:

 Consumption tax 20% of value Customs duty 50% of value

What is the total tax paid on an article which is valued at \$150.00 ?

\$

The water authority charges J\$350 per month for the meter rent, J\$750 for the first 100 litres and J\$30 for each additional 10 litres. What is the total bill for 250 litres used in one month?

J\$

A computer has a sale price of J\$18 000. This is a saving of 25% on the original price. What was the original price?

J\$

In a sale the prices of each of the items listed below is to be reduced by 35%.

 Coat \$28 Jeans \$42 Trainers \$36 Shirt \$14

Calculate the sale price of each item.

Coat     \$

Jeans     \$

Trainers     \$

Shirt     \$

A jacket was priced at \$180. Its price was increased by 8%. Later, this increased price was reduced by 20% in a sale.

Calculate the sale price of the jacket.

\$