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If x and y are in direct proportion, then find the value of a, b, c and d from the given table.

x
7.5
a
15
c
45
y
4.5
3
b
24
d

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a = 5, b = 9, c = 40, d = 27

a = 9, b = 5, c = 27, d = 40

a = 40 b = 27, c = 5, d = 9

a = 27, b = 40, c = 9, d = 5

answer is A.

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Detailed Solution

Given a table.

x	7.5	a	15	c	45
y	4.5	3	b	24	d

Finding the ratio of x and y from second column of the table.

\frac{x}{y} = \frac{7.5}{4.5}

\Rightarrow \frac{x}{y} = \frac{5}{3}

Using the fact that the ratio of x and y is a constant and in direct proportion.
Hence equating the ratio of a and 3 with

\frac{5}{3}

\frac{a}{3} = \frac{5}{3}

\Rightarrow a = 5

Repeat the same fact again and now equate the ratio of 15 and b We need to find b.

\frac{15}{b} = \frac{5}{3}

\Rightarrow b = 9

Repeat same procedure to find value of c and d.

\frac{c}{24} = \frac{5}{3}

\Rightarrow c = 40

And,

\frac{45}{d} = \frac{5}{3}

\Rightarrow d = 27

Values are, a = 5, b = 9, c = 40, d = 27.
Hence, the correct option is 1.

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