The ages of Tunde and Ola are in the ratio 1:2. If the ratio of Ola's age to Musa's age is 4:5, what is the ratio of Tunde's age to Musa's age?

Analyze the question: We have two ratios that share Ola. Tunde : Ola = 1 : 2 and Ola : Musa = 4 : 5. We want Tunde : Musa.

Concept: To combine ratios, make the common term (Ola) the same number in both ratios.

Solution:

• Tunde : Ola = 1 : 2
• Ola : Musa = 4 : 5

Ola is 2 in the first ratio and 4 in the second. The LCM of 2 and 4 is 4, so multiply the first ratio by 2:

• Tunde : Ola = 2 : 4

Now Ola is 4 in both, so we can combine them:

• Tunde : Ola : Musa = 2 : 4 : 5

So Tunde : Musa = 2 : 5.

Check with numbers: Let Tunde = 2 years, so Ola = 4 years (ratio 1:2 ✓.). If Ola : Musa = 4 : 5, then Musa = 5 years. Tunde : Musa = 2 : 5 ✓.

Exam tip: When two ratios share a common person or item, always rewrite them so the shared term has the same value. Then chain the ratios together. Do not just multiply across without matching that term.