Question

"Question 7 Suppose 2 kg of sugar contains 9 × 106 crystals. How many sugar crystals are there in (i) 5 kg of sugar? (ii) 1.2 kg of sugar?

Class 8 Direct and Inverse Proportions Page 208"

Answer 1

If two quantities increase or decrease together in such a manner that the ratio of their corresponding values remain constant, we say  that the two quantities vary  directly.

In other words x and y are said to vary directly if X/y = k , where k is a positive constant.

In direct Proportion
x/y= k

x=ky

So we can find value of k from known values, and then use the formula to calculate the unknown values.

When two quantities x and y are in direct proportion (or vary directly) they are also written as x∝y.
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Solution:

[Table is in the attachment]

I)

Let sugar crystal be ‘x’

Here weight of sugar and number of sugar crystals are in direct proportion.

2/9×10^6 = 5/x

X×2= 5×9×10^6

X= (5×9×10^6)/2

X= (45 × 10^6)/2= 22.5× 10^6

X= 2.25× 10^7

Hence, number of sugar crystal is  2.25× 10^7

 

 

 ii) Let sugar crystals be X.

Here weight of sugar and number of sugar crystals are in direct proportion.

2/9×10^6 = 1.2/x

X×2= 1.2×9×10^6

X= (1.2×9×10^6)/2

X= (0.6 × 9×10^6)

X= 5.4× 10^6

 

Hence, number of sugar crystal is  = 5.4× 10^6

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Hope this will help you...