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Question

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This question has multiple correct options.

(a) 21: 16

(b) 16: 21

(c) 48: 63

(d) 63: 48

Answer
Verified

We are given two ratios.

The two ratios are A: B = 6: 7 and B: C = 8: 9,

We can write the ratios in form of a fraction.

Both of the ratios are given by $\dfrac{A}{B}=\dfrac{6}{7}$ and $\dfrac{B}{C}=\dfrac{8}{9}$ .

But need to find the ratio of A: C.

Therefore, our aim is to eliminate B.

We can cross multiply both the fractions and we can get two-equation.

Solving the first equation we get,

$\begin{align}

& \dfrac{A}{B}=\dfrac{6}{7} \\

& 7A=6B........................(i) \\

\end{align}$

Solving the second equation we get,

$\begin{align}

& \dfrac{B}{C}=\dfrac{8}{9} \\

& 9B=8C.................(ii) \\

\end{align}$

Let’s solve equation (i) to get the value of B in terms of A, we get,

$\begin{align}

& 7A=6B \\

& B=\dfrac{7A}{6}..................(iii) \\

\end{align}$

Substituting the value of the equation (iii) in equation (ii) we get,

$9\left( \dfrac{7A}{6} \right)=8C$

Solving this equation, we get,

$\begin{align}

& 3\left( \dfrac{7A}{2} \right)=8C \\

& 21A=16C \\

\end{align}$

As we are asked in the form of a ratio, we get,

$\dfrac{A}{C}=\dfrac{16}{21}$

Therefore, A : C = 16 : 21.

As we are given that there are multiple answers are correct, we need to try other options as well,

Let’s multiply both the sides by 3, we get,

$\dfrac{A}{C}=\dfrac{16\times 3}{21\times 3}=\dfrac{48}{63}$ .

Writing in the ratio form we get, A: C = 48: 63.