Name: Direct Proportion: Introduction
Uploaded: 2019-07-19
Duration: 2 min 34 s
Description: Suppose you increase the number of books in your bag. What will happen to its weight? It will also increase. This is direct proportionality. Let us explore more about it.

Question

The following ingredients are required to make Halwa for

5

persons: Suji/Rawa

= 250 g

, Sugar

= 300 g

, Ghee

= 200 g

, Water

= 500 ml

. Using the concept of proportion, estimate the changes in the quantity of ingredients to prepare for a class of

30

students.

Accepted Answer

Given: The amount of different ingredients required to make Halwa for $5$ persons are given.

To Find: The amount of ingredients required to make Halwa for a class of $30$ students.

Solution: The amount of ingredients will increase with the increase in the number of students.Thus, the amount of ingredients can be said to be directly proportional to the number of students.

For Suji/Rawa:

Number of Students $(x)$ $5$ $30$

Quantity of Ingredients $(y)$ $250 g$ $y_{2}$

Formula: $\frac{x_{1}}{y_{1}} = \frac{x_{2}}{y_{2}}$

Substituting $x_{1} = 5, y_{1} = 250$ and $x_{2} = 30$ in the formula,

$\frac{5}{250} = \frac{30}{y_{2}}$

$5 y_{2} = 250 \times 30$

$y_{2} = \frac{7500}{5}$

$y_{2} = 1500$

Hence, the quantity of Rawa/Suji required is $1500 g$ .

For sugar:

Number of Students $(x)$ $5$ $30$

Quantity of Ingredients $(y)$ $300 g$ $y_{2}$

Formula: $\frac{x_{1}}{y_{1}} = \frac{x_{2}}{y_{2}}$

Substituting $x_{1} = 5, y_{1} = 300$ and $x_{2} = 30$ in the formula,

$\frac{5}{300} = \frac{30}{y_{2}}$

$5 y_{2} = 300 \times 30$

$y_{2} = \frac{9000}{5}$

$y_{2} = 1800$

Hence, the quantity of sugar required is $1800 g$ .

For ghee:

Number of Students $(x)$ $5$ $30$

Quantity of Ingredients $(y)$ $200 g$ $y_{2}$

Formula: $\frac{x_{1}}{y_{1}} = \frac{x_{2}}{y_{2}}$

Substituting $x_{1} = 5, y_{1} = 200$ and $x_{2} = 30$ in the formula,

$\frac{5}{200} = \frac{30}{y_{2}}$

$5 y_{2} = 200 \times 30$

$y_{2} = \frac{6000}{5}$

$y_{2} = 1200$

Hence, the quantity of ghee required is $1200 g$ .

For water:

Number of Students $(x)$ $5$ $30$

Quantity of Ingredients $(y)$ $500 ml$ $y_{2}$

Formula: $\frac{x_{1}}{y_{1}} = \frac{x_{2}}{y_{2}}$

Substituting $x_{1} = 5, y_{1} = 500$ and $x_{2} = 30$ in the formula,

$\frac{5}{500} = \frac{30}{y_{2}}$

$5 y_{2} = 500 \times 30$

$y_{2} = \frac{15000}{5}$

$y_{2} = 3000$

Hence, the quantity of water required is $3000 ml$ .

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