Welcome to this, our second Medium level Eleven Plus maths quiz on ratios. As you will know if you have played the first, ratios are ways to express or show proportions of amounts. They are quite similar to fractions but slightly different.
The best way to explain is with an example:
Let’s say that the ratio of vegetarians to meateaters is 2:5. That means that for every 2 vegetarians there are 5 meateaters.
You can also represent this with fractions: In the above example ^{2}⁄_{7} are vegetarians and ^{5}⁄_{7} are meateaters. That’s because 2 + 5 = 7.
Okay then, now we’ve refreshed our memories, it’s time to get on with the quiz. Good luck!














3 + 4 = 7 ∴ the fractional parts are ^{3}⁄_{7} × 70 = 30 portrait pictures and ^{4}⁄_{7} × 70 = 40 landscape pictures. CHECK 30:40 = 3:4 (dividing by 10). Your answer MUST preserve (keep) the same ratio

5:6 = 1:1.2 (dividing by 5). This means that there is 1 cow for every 1.2 sheep ∴ there are 1.2 as many sheep as there are cows = 1.2 × 20 = 24. CHECK 20:24 = 1:1.2 (dividing by 20). Your answer MUST preserve (keep) the same ratio. ALWAYS try to REDUCE your ratios so as to get a '1' in one of the terms of the ratio. Incidentally, 20 + 24 = 44 animals in all!


7 + 5 = 12 so ^{7}⁄_{12} of the sandwiches are cheese and ^{5}⁄_{12} are ham. 36 ÷ 12 = 3 so each unit in the ratio represents 3 sandwiches. 3 x 7 = 21 and 3 x 5 = 15. There are 21 cheese sandwiches and 15 ham sandwiches

7 + 9 = 16. You DON'T have to know what the total number of items is in order to find the fractional amounts of each type of item


9:24 = 3:8 (dividing by 3)

1:1 represents an equal number of wins and defeats. 9:10 and 14:24 both represent fewer wins than defeats. Only 21:17 represents more games won than lost


If ^{4}⁄_{7} of the children in a class are girls, then ^{3}⁄_{7} of the children must be boys

10:12 is the same as 5:6 (multiply by 2), 25:30 is the same as 5:6 (multiply by 5), 45:54 is the same as 5:6 (multiply by 9). 60:78 is NOT the same as 5:6 – the 5 has been multiplied by 12 but the 6 has been multiplied by 13


1.75:2 = 7:8 (multiplying by 4)

9 is greater than 2 and it represents the number of swimmers. There are clearly more swimmers than nonswimmers
