Question

If \(A:B = 3:4\), \(B:C = 5:7\) and \(C:D = 8:9\), then find \(A:D\).

• A. \(3:7\)
• B. \(7:3\)
• C. \(21:10\)
• D. \(10:21\)

Hint:

In chained ratio problems:

• Equalize the common terms first.
• Use LCM to match common quantities.
• Simplify the final ratio at the end.

Answer 1

The Correct Option is C

Concept: To combine multiple ratios, we first make the common terms equal and then multiply corresponding ratios systematically.

Step 1: Write the first ratio. \[ A:B = 3:4 \]

Step 2: Write the second ratio. \[ B:C = 5:7 \] The common term here is \(B\). LCM of \(4\) and \(5\) is: \[ 20 \] Multiply the first ratio by \(5\): \[ A:B = 15:20 \] Multiply the second ratio by \(4\): \[ B:C = 20:28 \] Therefore, \[ A:B:C = 15:20:28 \]

Step 3: Use the third ratio. \[ C:D = 8:9 \] Now match the value of \(C\). Current \(C = 28\). LCM of \(28\) and \(8\): \[ 56 \] Multiply: \[ A:B:C = 30:40:56 \] and \[ C:D = 56:63 \] Thus, \[ A:B:C:D = 30:40:56:63 \]

Step 4: Find \(A:D\). \[ A:D = 30:63 \] Divide by \(3\): \[ A:D = 10:21 \] Hence, \[ \boxed{10:21} \]