# How many percent does a company have to increase its profit compared to another year in order for the profit to be the same as an earlier year?

1. A company's profit was lower in 1997 than in 1996. By how many percent did the company have to increase its profit in 1998, compared to 1997, in order for the profit to be the same as in 1996?

(1) The company's profit was 1/8 lower in 1997 than in 1996.

(2) The company's profit was SEK 125,000 lower in 1997 than in 1996.

Sufficient information for the solution is obtained:

A in (1) but not in (2)

B in (2) but not in (1)

C in (1) together with (2)

D in (1) and (2) separately

E not by both statements

Don't understand how to solve this problem. We know from (1) that the company's profit was 7x/8 in 1997, and that it was 8x/8 in 1996. But how do we find what profit is needed to end up at the same profit again in 1998? On (2), we do not know how big the profit was in 1996, so the information is insufficient here. Do you agree?

Someone told me that we've to write it like this:

Profit in 1996: X

Profit in 1997: 7X/8

Profit in 1998: 7/8X·t = X

t = 8/7

Why do we write it like that? Which formula says to multiply it like that?

A company's profit was lower in 1997 than in 1996. (1) The company's profit was 1/8 lower in 1997 than in 1996. (2) The company's profit was SEK 125,000 lower in 1997 than in 1996.

The trick to solve these types of problem is to read the statement and form an equation based on the situation. The first statement tells us that in 1997, the company's prophet is lower than in 1996. So we can write the following: Prophet in 1996 minus certain amount is prophet in 1997 Now, we are also given that the amount of money earned in 1997 is $$\frac{1}{8}$$ lower than 1996. Also, alongside of that information, the problem also tell us that the gap between 1997's prophet and 1996 was $$125000$$. Based on this info let us write another equation. $$\frac{7x}{8} = x-125000$$ Explaination: The variable $$x$$ represents 1996's prophet. Since 1997's prophet is $$\frac{1}{8}$$ lower than 1996. Therefore, $$\frac{7}{8}$$ of the 1996's prophet is equivalent to prophet in 1997. You might wonder why do we subtract $$125000$$ from $$x$$. This is because as we have defined previously, $$x$$ is 1996's prophet. So if we subtract 125000 from 1996's prophet (x), we get 1997's prophet. Hopefully that is clear to you. Now to solve this, multiply every side by 8 to get rid of the fraction. $$7x=8x-1000000$$ Subtract $$8x$$ from both side to cancel out the $$x$$ variable on the right side. $$-x=-1000000$$ $$x=1000000$$ Now we have figured out 1996's prophet, we can proceed to figure out the prophet for 1997. Remember the equation that we first set up? If you do, simply plug in the value and solve. If not, here it is again:

Prophet in 1996 minus certain amount is prophet in 1997

We do not know what 1997's prophet is, so replace it with $$y$$

However, we do know what the value for "certain amount" is, so replace $$125000$$ for "certain amount"

$$1000000-125000=y$$ $$y=875000$$ We have determined two important information that will help us to solve the problem. Let us read the question and form an equation based on it.

By how many percent did the company have to increase its profit in 1998, compared to 1997, in order for the profit to be the same as in 1996?

So let $$z$$ represent the percentage. We know that $$1000000$$ is the prophet in 1996 and $$875000$$ is the prophet for 1997. It is asking "How much percent increase from 1997 must the company make to break even from 1996" To make this easier for you, we will write out the equation in plain English.

Prophet in 1997 (the same thing as 1998) + percent increase is prophet in 1996 Now, plug in the value and solve. $$875000+\frac{z}{100}(875000)=1000000$$ $$875000+8750z=1000000$$ $$8750z=125000$$ $$z=14$$ So it needs to increase 14% (I rounded this).