Maharashtra Board Class 9 Maths Part I Chapter 4 Ratio and Proportion PDF Download

Ratio And Proportion

Let's Recall

In earlier standards, we have learnt about ratio and proportion. We have also solved examples based on it. Let us discuss following example.

Ex. The rawa ladoo prepared by Vimal are tasty, for which she takes 1 bowl of ghee, 3 bowls of rawa and 2 bowls of sugar.

Here proportion of rawa and sugar is 3 : 2 or \(\frac{3}{2}\).

If 12 units of rawa is used, how many units of sugar are required?

Let the number of bowls of sugar required be x.

From above information, \(\frac{3}{2} = \frac{12}{x}\) therefore \(3x = 24\) therefore \(x = 8\)

That is for preparation of ladoo, with 12 units of rawa requires 8 units of sugar.

Alternatively we can solve the above example in the following way.

3k bowls of rawa, 2k bowls of sugar is required because \(\frac{3k}{2k} = \frac{3}{2}\)

If \(3k = 12\) then \(k = 4\) therefore \(2k = 2 \times 4 = 8\) bowls of sugar is required.

Let's Learn

Ratio And Proportion

The concept of ratio of two numbers can be extended to three or more numbers. Let us see the above example of ladoos. The proportion of ghee, rawa and sugar is 1 : 3 : 2.

Here proportion of ghee and rawa is 1 : 3 and that of rawa and sugar is 3 : 2.

This means the proportion of ghee, rawa and sugar is 1 : 3 : 2.

Let us take k bowls of ghee, 3k bowls of rawa and 2k bowls of sugar.

Hence for 12 bowls of rawa, how much quantity of ghee and sugar is required can be found as follows.

Now \(3k = 12\) therefore \(k = 4\) and \(2k = 8\).

Therefore 4 bowls of ghee and 8 bowls of sugar is required.

Teacher's Note

Ratio is used to compare two things. In Indian cooking, we use ratios for recipes like 1:2:3 for sugar, flour, and butter in a cake.

Exam Trick

Remember: Ratio is always written in reduced form. If you find 6:4, reduce it to 3:2. Think of it like simplifying fractions.

Points to Remember

A ratio compares two quantities with the same unit.

When three numbers are in ratio like a:b:c, we use k method to find their values.

The second term of first ratio should equal the first term of second ratio to combine ratios.

Ratios stay the same if we multiply or divide both numbers by the same non-zero number.

Direct proportion means when one quantity increases, the other also increases in the same ratio.

The same concept can be extended for proportion of 4 or more entities.

If a, b, c, d are in the ratio 2 : 3 : 7 : 4 then let us assume that the numbers are 2m, 3m, 7m, 4m. From the given information, value of m can be determined.

For example if the sum of these four numbers is 48, we find these numbers.

\(2m + 3m + 7m + 4m = 16m = 48\)

therefore \(m = 3\)

therefore \(2m = 6, 3m = 9, 7m = 21, 4m = 12\)

therefore required numbers are 6, 9, 21, 12

Ex (1) The proportion of compounds of nitrogen, phosphorous and potassium in certain fertilizer is 18 : 18 : 10. Here compound of nitrogen is 18%, compound of phosphorous is 18% and that of potassium is 10%. Remaining part is of other substances. Find the weight of each of the above compounds in 20 kg of fertilizer.

Solution: Let the weight of nitrogen compound in 20 kg of fertilizer be x kg.

\(\therefore \frac{x}{20} = \frac{18}{100}\) \(\therefore x = \frac{18 \times 20}{100} = 3.6\)

therefore weight of nitrogen compound is 3.6 kg

The percentage of phosphorous compound is also 18%.

therefore Weight of compound of phosphorous is 3.6 kg

If we assume the weight of potassium compound y kg then

\(\frac{y}{20} = \frac{10}{100}\) therefore \(y = 2\) therefore weight of potassium compound is 2 kg.

Teacher's Note

Fertilizer needs nitrogen to help plants grow. India uses NPK ratios like 18:18:10 for different crops and soil types.

Exam Trick

When you see a percentage in a ratio, remember: percentage = ratio with second term as 100. So 18% means 18:100.

Points to Remember

A percentage is a ratio where the second number is always 100.

To find the actual quantity, multiply the total by the fraction of that percentage.

All quantities in a ratio must have the same units before you can use them.

Nitrogen, phosphorous, and potassium are three main nutrients in fertilizers.

Direct Proportion

A car covers a distance of 10 km consuming 1 litre of petrol.

It will cover a distance of \(20 \times 10 = 200\) km consuming 20 litre of petrol.

Consuming 40 litre of petrol, it will cover a distance of \(40 \times 10 = 400\) km.

Let us write this information in tabular form

The ratio of consumption of petrol (in litre) and distance covered by the car (in kilometres), is constant. In such case, it is said that the two quantities are in direct proportion or in direct variation.

Teacher's Note

Direct proportion is used in real life. If a car uses 1 litre for 10 km, then for 100 km it will use 10 litres.

Exam Trick

In direct proportion, when one thing increases, the other also increases. Think: more petrol = more distance.

Points to Remember

In direct proportion, the ratio of the two quantities always stays the same.

If x increases, y also increases in direct proportion.

Direct proportion is written as y = kx where k is a constant number.

This is a preview of the first 3 pages. To get the complete book, click below.