Ever wondered how candidates achieve the highest score in the UKCAT quantitative reasoning section?

One answer may be that they are potential geniuses but the more plausible explanation is that they know some special methods and tricks for certain operations (in the mathematical and not medical sense, of course!).

**So let’s see what they do and how when it comes to ratios!**

- A carpenter makes and sells 5 items of furniture in his workshop.
- The table above shows the percentage breakdown of the items' retail price.
- He sells everything he makes.
- He makes 15 wardrobes during the year.
- Wardrobes account for 10% of his total profit.

**Question: the carpenter makes 504 stools during the year which provide 42% of his total profit. What is the ratio in price of a wardrobe to that of a stool?**

First of all we notice that the question is asking us about a ratio rather than an actual price. This means that we don't need to know a specific value of anything, we just need to know the *relative* cost of one thing in terms of another. In this case it is the price of a wardrobe relative to that of a stool.

As with all these questions, we need to sort the chaff from the wheat and decide which information is relevant to this particular question. Only wardrobes and stools are mentioned so only the left and right columns in the chart are required. Moreover, it is only the profit element (the top section) that is needed.

**How would the best UKCAT candidates solve this?**

It helps the thought process if we have a price for a wardrobe because it's more intuitive. We can use X as the price which will cancel out at some point in the calculation but algebra puts some people off. My advice is to make up a price that is convenient; if it's going to cancel out it really doesn't matter what you choose.

So, let's say a wardrobe cost £100. From the supplementary information we know that he makes 15 wardrobes which makes 15*£100=£1500. From the chart we can see that he makes 20% profit on a wardrobe so his profit from wardrobe sales would be £1500*20%=£300. Then, once more from the supplementary data we see that this profit accounts for 10% of all his profit which is £300/10%=£3000.

Now, in the question we are told that stool sales account for 42% of the total profit which is £3000*42%=£1260 which is the amount of profit generated from stool sales. From the chart we see that stools also have a profit margin of 20% and so the amount of sales required to generate £1260 profit is £1260/20%=£6300. We now know that 504 stools cost £6300 so the cost of 1 stool is £6300/504=£12.50.

**And the answer is...**

Now we can finally answer the question: 'What is the ratio in price of a wardrobe to that of a stool?'

A wardrobe costs £100 to a stool at £12.50 a ratio of 8:1.

Magic? Not so much, just some smart thinking that saves you time and adds invaluable points to your UKCAT score.

**Interested in practicing more? Check our UKCAT quantitative reasoning practice tests!**

## Joe 13 Sep 2018

## Joe 13 Sep 2018

15 wardrobes=10% and 504 stools=42%, so he makes the same profit with stools as he would have made selling 15x4.2 wardrobes (4.2 because 10% x 4.2= 42 %)(ie finding and equivalent number of wardrobes that would make the same profit as the stools did), giving 63 wardrobes that make the same profit as 504 stools. Hence 63/504=8