Share 40 sweets in the ratio 3 : 5. Find each share.
(2)
8
Share 90 pounds in the ratio 2 : 7. Find each share.
(2)
9
A box of pens has blue pens and black pens in the ratio 5 : 3. There are 24 pens in total. How many black pens are there?
(2)
10
At an animal shelter, the ratio of cats to dogs is 3 : 4. There are 35 animals in total. How many dogs are there?
(2)
11
A ribbon of length 96 cm is cut in the ratio 5 : 3. Find the length of the longer piece.
(2)
12
The three angles of a triangle are in the ratio 2 : 3 : 4. Find the smallest angle.
(2)
13
Two numbers are in the ratio 7 : 9. Their sum is 96. Find the smaller number.
(2)
14
A mixture requires flour and sugar in the ratio 8 : 3. The total mixture uses 220 g. Find the mass of sugar.
(2)
15
Sam and Leo share a sum of money in the ratio 4 : 7. The difference between their shares is 45 pounds. Work out the total sum of money shared.
(3)
16
A fruit basket contains apples and oranges in the ratio 5 : 8. There are 27 more oranges than apples. How many pieces of fruit are there in total?
(3)
17
A charity raises money from two collections in the ratio 3 : 5. The total raised was 960 pounds. Work out how much more the second collection raised than the first.
(3)
18
The ratio of red counters to blue counters in a bag is 6 : 11. There are 40 more blue counters than red counters. Work out the total number of counters in the bag.
(3)
19
On a school trip, adults and students are in the ratio 2 : 9. The number of students exceeds the number of adults by 63. Work out the total number of people on the trip.
(3)
20
Stretch question. Two jars contain marbles in the ratio 5 : 6 (Jar A to Jar B). Jar B contains 21 more marbles than Jar A. Then 3 marbles are moved from Jar B to Jar A. Work out the new ratio of marbles in Jar A to Jar B, giving your answer in its simplest form.
(3)
Mark scheme · KS3.M-R4D Ratio Problems with Totals and Differences: Fluency and Exam Drill
Question 1
B1 3 : 5 cao
Answer: 3 : 5
Question 2
B1 2 : 3 cao
Answer: 2 : 3
Question 3
B1 3 : 2 cao
Answer: 3 : 2
Question 4
B1 2 : 5 cao
Answer: 2 : 5
Question 5
B1 3 : 2 cao
Answer: 3 : 2
Question 6
B1 5 : 9 cao
Answer: 5 : 9
Question 7
M1 one part = 40 / (3+5) = 5
A1 15 and 25 cao
Answer: 15 and 25
Question 8
M1 one part = 90 / (2+7) = 10
A1 20 pounds and 70 pounds cao
Answer: 20 pounds and 70 pounds
Question 9
M1 one part = 24 / (5+3) = 3
A1 9 cao
Answer: 9
Question 10
M1 one part = 35 / (3+4) = 5
A1 20 cao
Answer: 20
Question 11
M1 one part = 96 / (5+3) = 12
A1 60 cm cao
Answer: 60 cm
Question 12
M1 one part = 180 / (2+3+4) = 20
A1 40 degrees cao
Answer: 40 degrees
Question 13
M1 one part = 96 / (7+9) = 6
A1 42 cao
Answer: 42
Question 14
M1 one part = 220 / (8+3) = 20
A1 60 g cao
Answer: 60 g
Question 15
M1 difference in parts = 7 - 4 = 3, so one part = 45 / 3 = 15
M1 compute total parts = 4 + 7 = 11 and multiply by 15
A1 165 pounds cao
Answer: 165 pounds
Question 16
M1 difference in parts = 8 - 5 = 3, so one part = 27 / 3 = 9
M1 compute total parts = 5 + 8 = 13 and multiply by 9
A1 117 cao
Answer: 117
Question 17
M1 one part = 960 / (3+5) = 120
M1 find each collection: 3x120=360, 5x120=600
A1 240 pounds cao
Answer: 240 pounds
Question 18
M1 difference in parts = 11 - 6 = 5, so one part = 40 / 5 = 8
M1 compute total parts = 6 + 11 = 17 and multiply by 8
A1 136 cao
Answer: 136
Question 19
M1 difference in parts = 9 - 2 = 7, so one part = 63 / 7 = 9
M1 compute total parts = 2 + 9 = 11 and multiply by 9
A1 99 cao
Answer: 99
Question 20
M1 difference in parts = 6 - 5 = 1, so one part = 21 / 1 = 21
M1 find amounts before transfer (A=105, B=126) and adjust: A=108, B=123