Combine two ratios with a common term (a:b and b:c)

This type of question, asked 2 times: 26 Oct 2023 Tier II, 20 Jan 2025 Tier II. All 2 questions below, oldest first.

Try each one first, then open its answer.

Question 1
26 Oct 2023 Tier II
21 $If P : Q = 3 : 4 and Q : R = 4 : 7, then find the value of (P + Q) : (Q + R) : (R + P).$
Tap an option to check your answer.
Question 2
20 Jan 2025 Tier II
20 $If a : b = 2 : 3, b : c = 5 : 7, then find the ratio c : a.$
Tap an option to check your answer.