Complete the following table considering that the cost of apples and their number are in direct variation.

Number of apples (x) 1 4 ... 12 ...

Cost of apples (y) 8 32 56 ... 160

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Solution

It is given that the cost of apples (y) and number of apples (x) are in direct variation.

$∴ y \propto x \Rightarrow y = k x$ , where k is constant of variation

When x = 1, y = 8.

∴ 8 = k × 1

⇒ k = 8

So, the equation of variation is

y = 8x

When y = 56,

56 = 8x

⇒ x = 7

When x = 12,

y = 8 × 12 = 96

When y = 160,

160 = 8x

⇒ x = 20

The complete is given below.

Number of apples (x) 1 4 7 12 20

Cost of apples (y) 8 32 56 96 160

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Deposit (in Rs)	1000	2000	3000	4000	5000
Simple interest (in Rs)	80	160	240	320	400

(i) Does the graph pass through the origin?

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Type of fruit	Mangoes	Apples	Oranges	Coconuts	Pomegranates
Number	26	30	21	5	8

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