Question:
If A : B = 2 : 3, A : C = 6 : 7, C : D = 14 : 15, then find A : B : C : D.
If A : B = 2 : 3, A : C = 6 : 7, C : D = 14 : 15, then find A : B : C : D.
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Make common variable equal in both ratios
Updated On: Apr 21, 2026
- 6 : 9 : 7 : 15
- 2 : 18 : 14 : 30
- 12 : 18 : 14 : 15
- 8 : 12 : 14 : 15
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The Correct Option is C
Solution and Explanation
Step 1: Write the given ratios.
A : B = 2 : 3
A : C = 6 : 7
C : D = 14 : 15 Step 2: Make the value of A common in first two ratios.
A : B = 2 : 3. Multiply by 3: \(2 \times 3 = 6\), \(3 \times 3 = 9\).
So A : B = 6 : 9.
A : C is already 6 : 7.
Thus, A : B : C = 6 : 9 : 7. Step 3: Incorporate C : D = 14 : 15.
Current C value in A : B : C is 7. Target C in C : D is 14.
Multiply A : B : C = 6 : 9 : 7 by 2:
\(6 \times 2 = 12\), \(9 \times 2 = 18\), \(7 \times 2 = 14\).
So A : B : C = 12 : 18 : 14. Step 4: Combine with C : D = 14 : 15.
Since C is now 14 in both ratios,
A : B : C : D = 12 : 18 : 14 : 15. Step 5: Verify the ratio.
A : B = 12 : 18 = 2 : 3 ✓
A : C = 12 : 14 = 6 : 7 ✓
C : D = 14 : 15 ✓
A : B = 2 : 3
A : C = 6 : 7
C : D = 14 : 15 Step 2: Make the value of A common in first two ratios.
A : B = 2 : 3. Multiply by 3: \(2 \times 3 = 6\), \(3 \times 3 = 9\).
So A : B = 6 : 9.
A : C is already 6 : 7.
Thus, A : B : C = 6 : 9 : 7. Step 3: Incorporate C : D = 14 : 15.
Current C value in A : B : C is 7. Target C in C : D is 14.
Multiply A : B : C = 6 : 9 : 7 by 2:
\(6 \times 2 = 12\), \(9 \times 2 = 18\), \(7 \times 2 = 14\).
So A : B : C = 12 : 18 : 14. Step 4: Combine with C : D = 14 : 15.
Since C is now 14 in both ratios,
A : B : C : D = 12 : 18 : 14 : 15. Step 5: Verify the ratio.
A : B = 12 : 18 = 2 : 3 ✓
A : C = 12 : 14 = 6 : 7 ✓
C : D = 14 : 15 ✓
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