Q1. Write the following ratio in its simplest form:



Q2. Write the following ratio in its simplest form:

Q3. Write the following ratio in its simplest form:

Q4. Write the following ratio in its simplest form:


Q5. Write the following ratio in its simplest form: 


"2 Bank Robbers go out and hold up a security van, they managed to get away with £250,000. Bank Robber A was the "mastermind" and so he decided that he would take £150,000 of the haul, leaving Bank Robber B with the remaining £100,000. What is the ratio of the split of the stolen money between Bank Robbers A and B?"



Notice that in this answer, it could be left as 1.5:1 or the fractional part could be removed by simply doubling up. Either way we are saying that Bank Robber A would receive £3 for every £2 that Bank Robber B received.


Q6. On a map, 2 cities are shown as being a 12 cm apart on paper, in reality the cities are 96 km apart. Find the ratio of the map in distance to the true distance.



The first thing that we need to do is to convert both values to the same units, we need to convert kilometres into centimetres. We know that there are 100 cm in a metre, and that there are 1000 m in a kilometre. Therefore there would be 100,000 cm in 1 km. As we have 96 km this becomes 96×100,000= 9,600,000cm



Q7. The 2 Bank Robbers in Question 5 are located not far from the scene and arrested. At the court appearance they are convicted of Robbery. Bank Robber A admits to being the mastermind and is sentenced to 14 years imprisonment. Bank Robber B receives a sentence of 5 1/2 years. What is the ratio of the sentences, in months, of the 2 Bank Robbers?


Q8. John has a bag of 42 sweets, he decides to share them with two of his friends Jane and Richard. The intention is that the sweets will be split in a ratio of 3:2:2 so that (as the provider) John gets more than his friends. If John ends up with 18 sweets, how many will Jane and Richard get ?


The ratio is 3:2:2 which adds up to 7. There are 6 x 7 in 42 which means that John gets 3/7 of 42, or 18, so the other friends will both get 2/7 of 42 each, which is 12.


Q9. There is a drawer full of socks, in the ratio of 5:2:7 red, blue and yellow. What fraction of the total number of socks are red ones?


5+2+7 = 14, and 5 is the proportion of red, therefore there will be 5/14 as a fraction of red socks.


Q10. A scale model aircraft kit states that "when completed, this model will be in the scale of 5:70 compared to the actual aircraft". The model measures 80cm length when built, how long is the real aircraft in metres?


The 5:70 ratio can be simplified to 1:14, this means that for every "1" in the model (80cm) the real aircraft will be 14 times larger. This equates to 14 x 80cm = 1120cm or 11.2m


Q11. A local authority plans to build a new leisure centre. The "family friendly" swimming pool in the design model measures 25cm long, by 14cm wide and 1.2cm deep. The ratio of the model to the real pool is intended to be 1:120. 


  • (a) Calculate the volume of the model pool, in cubic centimetres.


The volume of the model is 25 cm x 14 cm x 1.2 cm = 420cm3


  • (b) Calculate the dimensions of the real pool, in metres.


Using the ratio of 1:120 we "upscale" all dimensions, so the:


Length = 120 x 25 = 3000cm = 30m

Width = 120 x 14 = 1680cm = 16.8m

Depth = 120 x 1.2 = 144cm = 1.44m


  • (c) Calculate the volume of the real pool, in cubic metres.


Volume = Length x Width x Depth = 30 x 16.8 x 1.44 = 725.76m3


Q12. In a library section, there are 225 History Books, 125 Geography Books and 25 MFL (Modern Foreign Languages) Books. Write down, in it's simplest form, the ratio of History:Geography:MFL books.


225:125:25 - divide by the smallest number leaves you with 9:5:1 ratio, this is as simple as it can be made.


Q13. On a School Trip, the guidelines say that there should be at least 1 adult for every 6 children for supervision and safety. If 56 children are going on the trip, what is the minimum number of adults recommended?


6 divides into 56 a non-integral number of times, 9 with a remainder of 2. Of course you can't have 2/6 (1/3) of an adult so you would 'round up' to 10 adults in this case.



Back To >> Questions <<

Back To >> Ratio and Proportion <<