# NCERT Solutions Class 8 Mathematics Solutions for Exercise 13.1 in Chapter 13 - Direct and Inverse Proportions

Question 14 Exercise 13.1

Suppose 2 kg of sugar contains 9 x 10^6 crystals. How many sugar crystals are there in

(i) 5 kg of sugar? (ii) 1.2 kg of sugar?

Solution:

(i) Let sugar crystals be x.

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

\begin{array}{c} \frac{2}{9 \times 10^{8}}=\frac{5}{x} \\ \Rightarrow x \times 2=5 \times 9 \times 10^{5} \\ x=\frac{5 \times 9 \times 10^{6}}{2} \\ =22.5 \times 10^{6}=2.25 \times 10^{7} \end{array}

Hence the number of sugar crystals is

(2.25 \times 10^{7}

(ii) Let sugar crystals be x.

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

\begin{array}{l} \frac{2}{9 \times 10^{5}}=\frac{1.2}{x} \\ \Rightarrow x \times 2=1.2 \times 9 \times 10^{6} \\ x=\frac{1.2 \times 9 \times 10^{6}}{2} \end{array}

=0.6 \times 9 \times 10^{4}=5.4 \times 10^{6}

Hence the number of sugar crystals is 5.4 x 10^6

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