Q7. Suppose 2 kg of sugar contains 9\times 10^{6}crystals. How many sugar crystals are there in (i) 5 kg of sugar? (ii) 1.2 kg of sugar?

Answers (1)

Here given that 2 kg of sugar contains 9\times 10^6 crystals.

So, we have to find the number of crystals in 5 kg of sugar as well as in 1.2 kg of sugar:

As here we will assume that all crystals have the same dimensions i.e., length, breadth, and width. Then the weight of sugar follows the direct proportion with the number of crystals as increasing the number of crystals there will be an increase in the weight also.

(i) For 5 kg sugar:

let the number of crystals be 'x' then,

we have the relation:

\frac{5kg}{2kg}=\frac{x}{9\times 10^6}  , calculating x from this relation,

x=\frac{5kg\times 9\times 10^6}{2kg}=22.5\times 10^6.

Therefore 5 kg of sugar contains 22.5\times 10^6 sugar crystals.

(ii) For 1.2 kg sugar:

Let the number of cystals be 'y' then,

we have the relation:

\frac{1.2kg}{2kg}=\frac{y}{9\times 10^6}  . calculating similarly for y we get

y=5.4\times 10^6.

Therefore 1.2 kg of sugar contains 5.4\times 10^6 sugar crystals.