Consider the following statements:
I. If \(a:b=2:3\) and \(b:c=4:5\), then \(a:c=8:15\).
II. If \(a:b=2:3\) and \(b:c=4:5\), then \(a:b:c=2:3:5\).
Which of the above statements is/are correct?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Only I
To join \(a:b\) and \(b:c\), first make the two values of \(b\) equal (use their LCM).
I. If \(a:b=2:3\) and \(b:c=4:5\), then \(a:c=8:15\). — Correct. With \(b\) made 12 in both ratios, \(a=8\) and \(c=15\).
LCM of 3 and 4 is 12
\(a:b=8:12\) and \(b:c=12:15\)
So \(a:b:c=8:12:15\) and \(a:c=8:15\)
II. If \(a:b=2:3\) and \(b:c=4:5\), then \(a:b:c=2:3:5\). — Incorrect. The 3 in the first ratio and the 4 in the second both stand for \(b\), so the ratios cannot be joined as they are; the correct result is \(a:b:c=8:12:15\).