Find the missing number in the box:
$\frac{□}{4 5} = \frac{1 6}{4 0} = \frac{2 4}{□}$

Question

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Answer 1

$Part 1: Find the missing number in the first two ratios$
Consider first two ratios
Let the missing number be x
$\frac{x}{4 5} = \frac{1 6}{4 0}$
By cross multiplying, we get
$16 \times 45 = x \times 40 x = \frac{1 6 \times 4 5}{4 0} = 18 ∴ \frac{1 8}{4 5} = \frac{1 6}{4 0}$

$Part 2: Find the missing number in the last two ratios$
Consider last two ratios
Let the missing number be y
$\frac{1 6}{4 0} = \frac{2 4}{y}$
By cross multiplying, we get
$40 \times 24 = y \times 16 y = \frac{4 0 \times 2 4}{1 6} = 60 ∴ \frac{1 6}{4 0} = \frac{2 4}{6 0}$

$∴ Missing numbers in the given ratio are 18 and 60$

Answer 2

Part 1: Find the missing number in the first two ratios

Consider first two ratios
Let the missing number be x

\frac{x}{4 5} = \frac{1 6}{4 0}

By cross multiplying, we get

16 \times 45 = x \times 40 x = \frac{1 6 \times 4 5}{4 0} = 18 ∴ \frac{1 8}{4 5} = \frac{1 6}{4 0}

Part 2: Find the missing number in the last two ratios

Consider last two ratios
Let the missing number be y

\frac{1 6}{4 0} = \frac{2 4}{y}

By cross multiplying, we get

40 \times 24 = y \times 16 y = \frac{4 0 \times 2 4}{1 6} = 60 ∴ \frac{1 6}{4 0} = \frac{2 4}{6 0}

∴ Missing numbers in the given ratio are 18 and 60