solving profit and loss related problem using shortcut method

Question

If price of an apple is redued by 40%, for 120 dollar, you can buy 4 more apples than you could buy at original price. How many apples could be bought for 120 dollar at original price?

is there any shortcut rule to solve this problem without much calculation?

Answer 1

What do you mean much calculation? Do you just want to avoid guess and check? Let $p$ be the original price of a pen. At the start you can buy $\frac {120}p$, at the end you can buy $\frac {120}{0.6p}$ and you are told the difference of these is $4$. Write an equation and solve for $p$.

Answer 2

We can write this as following: $$\begin{cases} x=\frac{120}{y}\\ x+4 = \frac{120}{.6 y} \end{cases}$$ Where $x$ is the number of pens you could have bought for $120\$$ at orriginal price, $y$ is the orriginal price.

We have then: $$\frac{120}{y}+4=\frac{200}{y}\\ y=20$$ And then: $$x=6$$

Answer 3

Let price of each pen x.

Then originally number of pens = $\frac{120}{x}$

Now price of pen 40% discounted so he has to pay 60%.

Now price of each pen 60% of x = 0.6 x

Number of pens = $\frac{120}{0.6 x}$

Difference of pens = 4

$\frac{120}{0.6 x} - \frac{120}{x} = 4$

Solve for x.