Find the missing numbers in the following proportions in the table given below .
S. No. Proportion Product of extremes Product of means
(i) $1 : 2 :: 4 : 8$
(ii) $5 : 6 :: 75 : 90$
(iii) $3 : 4 :: 24 : 32$
(iv) $2 : 5 :: □ : 15$ 30
(v) $3 : 6 :: 12 : □$ 72

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Solution

S.No. Proportion Product of extremes product of means
$(i)$ $1 : 2 :: 4 : 8$ $1 \times 8 = 8$ $2 \times 4 = 8$
$(i i)$ $5 : 6 :: 75 : 90$ $5 \times 90 = 450$ $6 \times 75 = 450$
$(i i i)$ $3 : 4 :: 24 : 32$ $3 \times 32 = 96$
$4 \times 24 = 96$
$(i v)$ $2 : 5 :: x : 15$ $2 \times 15 = 30$ $5 x = 30$ or $x = 5$
$(v)$ $3 : 6 :: 12 : x$ $3 \times x$ or $3 x = 72 \Rightarrow x = \frac{72}{3} = 24$ $6 \times 12 = 72$

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