All 8 problems from "Difference & Ratio" with complete step-by-step worked solutions: recognising the type, the idea, the working steps and the conclusion. Use this page to review with your child after the animated lesson, or let them check their own working against it.
Two numbers are in the ratio 3:1. Their difference is 10. What is the larger number?
Key idea: The difference is worth (a − b) parts — divide it to find one part.
Ratio 3:1 with a difference of 10 — a difference–ratio problem.
The difference of 10 covers 3 − 1 = 2 parts.
One part = 10 ÷ 2 = 5.
Larger = 3 × 5 = 15.
So: So the larger number is 15.
A:B = 4:1 and A − B = 12. What is B?
Key idea: The difference is worth (a − b) parts — divide it to find one part.
A:B = 4:1 and A − B = 12, with B asked for.
The difference covers 4 − 1 = 3 parts; B is just 1 part.
One part = 12 ÷ 3 = 4.
B = 1 × 4 = 4.
So: So B is 4.
Two quantities are in the ratio 5:2 with a difference of 18. What is the smaller quantity?
Key idea: The difference is worth (a − b) parts — divide it to find one part.
Ratio 5:2 with a difference of 18.
The difference covers 5 − 2 = 3 parts.
One part = 18 ÷ 3 = 6.
Smaller = 2 × 6 = 12.
So: So the smaller quantity is 12.
A:B = 7:3 and A − B = 20. A = ___ and B = ___.
Key idea: The difference is worth (a − b) parts — divide it to find one part.
A:B = 7:3 and A − B = 20, with both values to fill in.
The difference covers 7 − 3 = 4 parts.
One part = 20 ÷ 4 = 5.
A = 7 × 5 = 35 and B = 3 × 5 = 15.
So: So A = 35 and B = 15.
The ratio of marbles Tom has to marbles Jerry has is 5:2. Tom has 21 more marbles than Jerry. How many marbles does Tom have?
Key idea: Turn “21 more” into parts: the gap is worth (5 − 2) parts.
Tom to Jerry is 5:2 and Tom has 21 more marbles.
The 21 extra marbles cover 3 parts.
One part = 21 ÷ 3 = 7.
Tom = 5 × 7 = 35.
So: So Tom has 35 marbles.
Heights of two plants are in ratio 8:3. The taller plant is 30 cm taller. How tall is the shorter plant?
Key idea: The difference is worth (a − b) parts — divide it to find one part.
Plant heights in the ratio 8:3, the taller one 30 cm taller.
The 30 cm gap covers 8 − 3 = 5 parts.
One part = 30 ÷ 5 = 6 cm.
Shorter = 3 × 6 = 18 cm.
So: So the shorter plant is 18 cm.
Father is 4 times as old as his son. The difference in their ages is 36 years. How old is the son?
Key idea: “4 times as old” is the ratio 4:1 — then it is difference–ratio.
Father is 4 times as old as his son and their ages differ by 36 years.
The 36-year gap covers 4 − 1 = 3 parts; the son is 1 part.
One part = 36 ÷ 3 = 12.
Son = 1 × 12 = 12 years old.
So: So the son is 12.
A and B are in the ratio 9:4 with a difference of 35. What is their total?
Key idea: For the total, multiply one part by (a + b) — not by a or b alone.
Ratio 9:4 with a difference of 35 — but the TOTAL is asked for.
One part from the difference, then add both sides' parts.
One part = 35 ÷ (9 − 4) = 7.
Total = (9 + 4) × 7 = 91.
So: So their total is 91.
Two quantities are in the ratio 5:2, and their difference is 30. What is the value of each quantity?
Pick an answer to unlock the next step.
Shortcuts: Space (play), Arrow keys (step), R (reset), F (fullscreen)
Bar A has 5 parts and Bar B has 2 parts. How many more parts does A have than B?
Pick an answer to unlock the next step.
We have two numbers with a ratio of 5:2 and a difference of 30. Bar A has 5 units and Bar B has 2 units.
Keep your eye on the part of A that sticks out beyond B — that is where the answer hides.
Change the numbers and watch the diagram redraw itself:
