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Q.

If 2 kg of sugar contains $9 × 106$ crystals, then find the sugar crystal contained by 6 kg of sugar.

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a

2.25 × 105

b

2.70 × 106

c

2.70 × 107

d

2.25 × 108

answer is B.

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Detailed Solution

Given that,
2 kg of sugar contains

9 × 106

crystals.
We have to find the number of sugar crystals containing 6 kg of sugar.
We know that if two quantities

x

and

y

vary in the same way while maintaining a constant ratio between their respective values, then the two quantities are said to be in direct proportion.
i.e.

x y = k,

where k is a constant positive number.
Here, if the amount of sugar increases, then the number of sugar crystals also increases.
So, it is a case of direct proportion.
So, we can arrange a table as given below:

Amount of sugar(kg)	$x 1 = 2$	$x 2 = 6$
Number of sugar crystals	$y 1 = 9 × 106$	$y 2 =$ ?

Using the relation of direct proportion

x 1 y 1 = x 2 y 2

, we get,

x 1 y 1 = x 2 y 2

⇒ y 2 = y 1 x 2 x 1

⇒ y 2 = 9 × 106 × 6 2

∴ y 2 = 2.70 × 106

Therefore, the sugar crystal contained by 6 kg of sugar is

2.70 × 106

.
Hence, option 2 is correct.

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