If \(a:b::\frac{12}{5}:\frac{3}{10}\) and \(b:c::\frac{7}{9}:\frac{12}{7}\) then \(a:c\) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{98}{27}\)
A ratio \(a:b\) can be written as the fraction \(\frac{a}{b}\). Each given ratio is simplified first, and then the two are multiplied so that \(b\) cancels: \(\frac{a}{c}=\frac{a}{b}\times\frac{b}{c}\).
\(\displaystyle \frac{a}{b}=\frac{12}{5}\div\frac{3}{10}=\frac{12}{5}\times\frac{10}{3}=8\)
\(\displaystyle \frac{b}{c}=\frac{7}{9}\div\frac{12}{7}=\frac{7}{9}\times\frac{7}{12}=\frac{49}{108}\)
\(\displaystyle \frac{a}{c}=8\times\frac{49}{108}=\frac{392}{108}=\frac{98}{27}\)