If A : B = 2 : 3 and B : C = 4 : 5, what is A : B : C?
8 : 12 : 15. Make the common term B equal in both ratios. B is 3 in the first and 4 in the second, so scale the first by 4 and the second by 3: A : B = 8 : 12 and B : C = 12 : 15.
Explain it simply
Two ratios can be joined only through the person they share. Here B appears in both, but as 3 parts in one and 4 parts in the other. That is like measuring one friend's height in two different units. Convert both so B has the same number of parts (the LCM of 3 and 4, which is 12), then read off all three.
Example
Question: A : B = 2 : 3 and B : C = 4 : 5. Find A : B : C.
- B appears as 3 and 4. LCM = 12.
- Multiply the first ratio by 4: A : B = 8 : 12.
- Multiply the second ratio by 3: B : C = 12 : 15.
- So A : B : C = 8 : 12 : 15.
Follow-up: if the three share ₹7,000 in this ratio, the parts total 35, one part = ₹200, so A = ₹1,600, B = ₹2,400, C = ₹3,000.
Shortcut for A : C directly: A/C = (A/B) x (B/C) = (2/3) x (4/5) = 8/15.
const part = 7000 / (8 + 12 + 15);
console.log([8, 12, 15].map(x => x * part)); // Output: [1600,2400,3000]What to say in the interview
"I equalise the common term. B is 3 and 4, so I scale both to make it 12, giving 8 to 12 to 15. Then any total splits by dividing by 35 parts."
Common mistakes
- Writing 2 : 3 : 5 by just gluing the ratios together.
- Scaling only one ratio.