If a: b=2:3, b:c=5: 7, then find the ratio c: a.
21:10
Given:
- a : b = 2 : 3
- b : c = 5 : 7
Step 1: Expressing in Terms of a Common b
- Let a = 2k and b = 3k
- Let b = 5m and c = 7m
Since b must be the same in both cases, we equate:
3k = 5m
Step 2: Expressing in Terms of a and c
Solving for k and m:
k = 5m / 3
a = 2k = 2 × (5m / 3) = 10m / 3
c = 7m
Thus, the ratio c : a is:
c : a = 7m : (10m / 3)
Multiplying both terms by 3:
(7m × 3) : (10m) = 21m : 10m
Final Answer: 21 : 10
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