Which of the following numbers are in proportion?

2, 3, 4, 5

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4, 5, 12, 15

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3, 1, 9, 1

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3, 4, 6, 4

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Solution

The correct option is B 4, 5, 12, 15
In any proportion, the product of means equals the product of extremes.
product of means = $5 \times 12 = 60$
roduct of extremes = $4 \times 15 = 60$ ,
hence, 4, 5, 12 and 15 are in proportion.
Or in other words, we have 4:5::12:15.
Now consider the numbers 2, 3, 4 and 5.
$2 \times 5 \neq 3 \times 4$ .i.e., $10 \neq 12$ , and thus these numbers are not in proportion.
Similarly, 3, 1, 9 and 1 are not in proportion ( $3 \times 1 \neq 1 \times 9$ ),
3, 4,6, and 4 are not in proportion( $3 \times 4 \neq 4 \times 6$ )

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Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$