FIND THE ORIGINAL PRICE AFTER A PERCENTAGE INCREASE OR DECREASE

Find the original amount given that:

Problem 1 :

After an increase of 25% the price was $250

Solution :

Let the original amount be x.

Percent increase = 25%

Increase in price = 25% of x

= 0.25 × x

= 0.25x

Final amount = original amount + increase

= x + 0.25x

= 1.25x

Price after increase = $250 = 1.25x

Solving for x,

x = 250/1.25

x = $200

So, original amount is $200.

Problem 2 :

After an increase of 35% the price was $243

Solution :

Let the original amount be x.

Percent increase = 35%

Increase in price = 35% of x

= 0.35 × x

= 0.35x

Final amount = original amount + increase

= x + 0.35x

= 1.35x

Final amount = $243 = 1.35x

Solving for x,

x = 243/1.35

x = $180

So, original amount is $180.

Problem 3 :

After a decrease of 10% the price was ₤81

Solution :

Let the original amount be x.

Percent decrease = 10%

Decrease in price = 10% of x

= 0.10 × x

= 0.1x

Final amount = original amount - decrease

= x - 0.1x

= 0.9x

Final amount = ₤81 = 0.9x

Solving for x,

x = 81/0.9

x = ₤90

So, original amount is ₤90.

Problem 4 :

After a decrease of 17% the price was €37.35

Solution :

Let the original amount be x.

Percent decrease = 17%

Decrease in price = 17% of x

= 0.17 × x

= 0.17x

Final amount = original amount - decrease

= x - 0.17x

= 0.83x

Final amount = €37.35 = 0.83x

Solving for x,

x = 37.35/0.83

x = €45

So, original amount is €45.

Problem 5 :

 After a decrease of 37.5% the price was 115 pesos

Solution :

Let the original amount be x.

Percent decrease = 37.5%

Decrease in price = 37.5% of x

= 0.375 × x

= 0.375x

Final amount = original amount - decrease

= x - 0.375x

= 0.625x

Final amount = 115 = 0.625x

Solving for x,

x = 115/0.625

x = 184

So, original amount is 184.

Problem 6 :

After a decrease of 22 1/2 % the price was $9300

Solution :

Let the original amount be x.

Percent decrease = 22 1/2 % = 22.5

Decrease in price = 22.5% of x

= 0.225 × x

= 0.225x

Final amount = original amount - decrease

= x - 0.225x

= 0.775x

Final amount = $9300 = 0.775x

Solving for x,

x = 9300/0.775

x = $12000

So, original amount is $12000.

Problem 7 :

‘Blacks Furniture Mart’ sells a lounge suite for $3280.50, making a profit of 35% on the cost price. How much did the business pay for the lounge suite?

Solution :

Let the original amount be x.

The selling price = $3280.50

Profit = 35%

The amount of profit = 35% of the cost price

= 0.35 × x

= 0.35x

Selling price = cost price + profit

3280.50 = x + 0.35x

3280.50 = 1.35x

x = 3280.50/1.35

x = $2430

Therefore, the cost price of the lounge suite is $2430.

Problem 8 :

A retailer sells a microwave oven for $640. This is a 25% profit on the cost price. How much did the retailer pay for the microwave oven?

Solution :

Let the original amount be x.

The selling price = $640

Profit = 25%

The amount of profit = 25% of the cost price

= 0.25 × x

= 0.25x

Selling price = cost price + profit

640 = x + 0.25x

640 = 1.25x

x = 640/1.25

x = $512

Therefore, the cost price of the micro oven is $512.

Problem 9 :

An electrical firm sells a washing machine for $383.50, making a 30% profit on the wholesale or cost price. Find the wholesale price of the machine.

Solution :

Let the original amount be x.

The selling price of washing machine = $383.50

Profit = 30%

Cost price = selling price - profit

Cost price = 383.50 - 0.3x

383.50 = 1.3x

x = 383.50/1.3

x = $295

Therefore, the cost price of the washing machine is $295. 

Problem 10 :

Jason sells a bicycle for $247 at a loss of 35%. What did Jason pay for the bicycle originally?

Solution :

Let the original amount be x.

The selling price of bicycle = $247

Loss = 35 % = 0.35

Loss amount = 0.35% of x

= 0.35 × x

= 0.35x

Original amount = original amount - loss amount

= x - 0.35x

= 0.65x

Original amount = $247 = 0.65x

x = 247/0.65

x = $380

So, original amount of bicycle is $380