if £10 becomes £25, has it been increased or decreased, and in what ratio?

Question

I'm currently working on simple ratios for GCSE and I am comfortable calculating shares via ratios and increasing/decreasing a value by a ratio. However, I dont understand how to calculate the ratio when it comes to questions as per the title. Could anyone please shed some light and explain it to me?

Spit balling

I think its obvious its an increase, and it has increased by £15. So 25 / 5 = 5 parts, originaly it was 2 parts to = 10 it increased by 3 parts to make 25. So is that 5:2?

Answer 1

You're basically on target. Just divide the result by the starting value to see the ratio (you'll probably want to simplify it as much as possible). If the result is bigger than the starting value (ie. the ratio is bigger than 1) it's an increase. If it's smaller, it's a decrease, because it went down in amount. In this case: $$\frac{25}{10} = \frac52$$ which is greater than 1, as expected.

Answer 2

The easiest way to wrap your head around it is to set up an equation.

What times 10 is equal to 25?

$$10x = 25$$ which means $$x = 25/10$$ which means $$x = 5/2$$ where x is your ratio.