For ratio problems where there are three groups of items with two ratios given – it is usually the case that you’ll need to express them into a common ratio.
Here’s an example: "A fruit seller had some oranges, pears and mangoes. After selling some of them, there were 6 pears for every 5 oranges left and 7 oranges for every 3 mangoes left. He sold 168 oranges. The number of pears sold was the same as the number of mangoes sold. He had a total of 456 pears and mangoes left. How many oranges had he at first?"
1. Express the three groups in a common ratio. P:O -> 6:5. O:M -> 7:3. so P:O:M -> 42:35:15
2. 456 P and M left. so 42u+15u = 456 so u = 8.
3. oranges left = 35u = 35*8 = 280.
4. oranges at first = 280 + 168 = 448.