# Percentages question

John brought a flat at $\\540,000$ and he sold it to Tanny at a loss. Tanny then sold it at a profit to Kimberly at $\\535,000$ .

If the loss percentage on the cost of John is equal to the percentage profit of Tanny on his cost , find the price that Tanny paid for the flat

I'm stuck by just reading the question... Can I get a hint on how to solve this ?

• Tanny had paid 500,000 for the flat, would you know how to calculate the percentage loss on John's cost when John sold the flat and the percentage gain on Tanny's cost when Tanny sold the flat? – David K May 7 '16 at 13:13
• @DavidK How did you find out that Tanny paid 500,000 for the flat ? – user337744 May 7 '16 at 13:16
• I don't think he paid 500,000. I'm trying to find out if you need help understanding what we mean by percentage profit or loss, or whether you're having trouble only because one price is unknown. (There was supposed to be an "if" at the beginning of my previous comment, not sure what happened to it; oops.) – David K May 7 '16 at 13:48
• @DavidK Oh yea, I have a problem finding the unknown amount , I understand how to find percentage profit / loss. – user337744 May 7 '16 at 13:57

Since you don't know how much Tanny paid, assign a name to that quantity. The letter $x$ is a good choice. Then $x$ is the unknown value you want to find out.

Take the way you would have calculated John's loss and Tanny's profit if you had known the price Tanny paid, but use the symbol $x$ instead of a known price. Write out the calculations of how much John lost (as a percentage of his cost, which was $540,000$) and how much Tanny gained (as a percentage of his cost, which was $x$). You will not be able to get a simple numerical percentage out of these because of the unknown value $x$, but you will have two expressions involving some known numbers, the unknown $x$, and some operations, each representing a percentage.

The "is equal to" part of the problem tells you these two percentages are equal. So you can put them on each side of an $=$ sign. Now you have an equation, and the only unknown quantity in the equation is $x$. You have to solve for $x$.

Hint: If the first step goes OK, on one side you'll have a fraction that is kind of ugly because it has $x$ in both the numerator and the denominator. You may want to recall rules such as cross-multiplying so you don't have an $x$ in a denominator.

Second hint: you'll probably end up wanting to solve a quadratic equation in order to finish.

It will be harder to follow these hints than if I had written out all the formulas explicitly. What I'm trying to do here is to explain a little of what would go through my head when looking at a problem like this, and how I would get past the "what does this question even mean?" phase and get something I could actually use some math to solve.

$$540000(1-\frac{x}{100})(1+\frac{x}{100})=535000$$ on solving, $x = 9.62\%$ Cost paid by tanny = $488038$

Reference for formulas used: www.prep4paper.com

Selling Price = Cost Price * $(1-\dfrac{\text{Loss}}{100})$

where $\text{Loss}$ is in percentage.

Selling price for John = Cost price for tanny = $540000*(1-\dfrac{x}{100})$

where $x$ is the loss percentage for John.

Selling price for tanny = Cost price for tanny * $(1+\dfrac{x}{100})$ $= 540000*(1-\dfrac{x}{100})*(1+\dfrac{x}{100}) = 535000$

On solving this equation $x = 9.62\%$ Cost price for tanny = $540000*(1-\dfrac{9.62}{100}) = 488038$