Share £60 in the ratio \( 2:3 \).
Parts: \( 2+3=5 \). One part \( = 60 \div 5 = 12 \). Shares: \( £24 \) and \( £36 \).
Ratio & Proportion
8 exam-style questions on sharing in a ratio, unitary method, best buys and proportional quantities.
3 Easy 3 Medium 2 Hard
A recipe for 4 people uses \( 300 \) g of flour. How much flour is needed for 6 people?
Per person: \( 300 \div 4 = 75 \) g. For 6: \( 75 \times 6 = 450 \) g.
Simplify the ratio \( 24:36 \).
Divide by \( 12 \): \( 2:3 \).
The ratio of boys to girls in a class is \( 3:5 \). There are \( 12 \) boys. How many girls are there?
Boys: \( 3 \) parts \( = 12 \), so \( 1 \) part \( = 4 \). Girls: \( 5 \times 4 = 20 \).
Shop A sells 6 pens for £4.50. Shop B sells 8 pens for £5.60. Which is better value?
A: \( 4.50 \div 6 = £0.75 \) per pen. B: \( 5.60 \div 8 = £0.70 \) per pen. Shop B is better value.
\( y \) is directly proportional to \( x \). When \( x = 5 \), \( y = 20 \). Find \( y \) when \( x = 8 \).
\( y = kx \). \( 20 = 5k \) ⇒ \( k = 4 \). When \( x=8 \), \( y = 32 \).
A map has scale \( 1:25000 \). Two towns are \( 8 \) cm apart on the map. What is the actual distance in kilometres?
Actual: \( 8 \times 25000 = 200\,000 \) cm \( = 2000 \) m \( = 2 \) km.
\( y \) is inversely proportional to \( x \). When \( x = 4 \), \( y = 6 \). Find \( y \) when \( x = 3 \).
\( y = \dfrac{k}{x} \). \( 6 = \dfrac{k}{4} \) ⇒ \( k = 24 \). When \( x=3 \), \( y = 8 \).