Question

9. An article was sold at a profit of 12%. Had it been sold for Nu 80 more, there would be a profit of

20%. Find
1) the cost price of the article
2)the selling price of the article​

Answer 1

The cost price of the article was Nu 1,000

The original selling price was Nu 1,120

The second selling price was Nu 1,200

Explanation:

System of Equations

Let's call:

x = Original selling price of the article

y = Cost of the article

The first condition implies that the difference between the selling price and the cost price (the profit) is 12%. Recall the profit % is always calculated with respect to the cost, that is, the profit at the first condition is:

0.12y = Original profit

Setting up the equation, we have:

`x-y=0.12y`

The second condition states the selling price is 80 Nu more than before, that is:

x+80= Second selling price of the article

y = Cost of the article (it doesn't change)

The profit of this condition is 20%, thus:

0.2y = Second profit

This produces a second equation:

`x+80-y=0.2y`

Let's put both equations together to form a system of equations:

`x-y=0.12y`

`x+80-y=0.2y`

Operating on both equations:

`x=1.12y`

`x=1.2y-80`

Equating both equations, we have an equation with only y's:

`1.12y=1.2y-80`

Subtracting 1.2y on each side:

`1.12y-1.2y=-80`

Operating:

`-0.08y=-80`

Solving:

`\displaystyle y=(-80)/(-0.08)=1,000`

a)

The cost price of the article was Nu 1,000

b) The selling price of the article will be calculated in both cases:

Original selling price: x=1.12y= 1.12*1000=1,120

The original selling price was Nu 1,120

The second selling price was x+80=1,200

The second selling price was Nu 1,200