# Suppose 2 kg of sugar contains 9 × 10^{6} crystals

How many sugar crystals are there in (i) 5 kg of sugar? (ii) 1.2 kg of sugar?

**Solution:**

Given that, 2 kg of sugar contains 9 × 10^{6} crystals

(i) Let the amount of sugar be x and the number of crystals be y

Amount of sugar |
Number of crystals |

2 | 9 × 10^{6} |

5 | ? |

More the amount of sugar more will be the number of crystals. Hence this is a direct proportion.

Two numbers x and y are said in direct proportion if, the relationship between two quantities is such that if we increase one, the other will also increase, and if we decrease one the other quantity will also decrease.

x/y = k, x = ky

where k is a constant.

Thus, x₁_{ }/ y₁ = x₂ / y₂

2 / (9 × 10^{6}) = 5 / y₂

2 × y₂ = 9 × 10^{6} × 5

y₂ = (9 × 10^{6}^{ }× 5) / 2

y₂ = 22.5 × 10^{6}

y₂ = 2.25 × 10^{7}

Hence there are 2.25 × 10^{7} crystals.

(ii)

Amount of sugar |
Number of crystals |

2 | 9 × 10^{6} |

1.2 | ? |

x₁/y₁ = x₂/y₂

2/(9 × 10^{6}) = 1.2/y₂

2 × y₂ = 9 × 10^{6} × 1.2

y₂ = (9 × 10^{6}^{ }× 1.2)/2

y₂ = 5.4 × 10^{6}

Hence there are 5.4 × 10^{6} crystals.

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 13

**Video Solution:**

## 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?

NCERT Solutions Class 8 Maths Chapter 13 Exercise 13.1 Question 7

**Summary:**

Suppose 2 kg of sugar contains 9 × 106 crystals. The number of sugar crystals that are there in (i) 5 kg of sugar is 2.25 × 10^{7} (ii) 1.2 kg of sugar is 5.4 × 10^{6}

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