In our everyday lives we are often required to mix two different substances for practical purposes- for example, we mix phenyl with water or dettol with water to wipe floors, tea manufacturers often mix tea from different regions like Assam and Darjeeling in different proportions to produce a blended tea. The substance obtained by this process of mixing is called a mixture. Sometimes two or more components are mixed in specific proportions in terms of weight to form a new substance called mixed substances. The main difference between a mixture and a mixed substance is that while preparing a mixture one can increase or decrease the proportion of components as he wishes but while preparing a mixed substance the proportions of components are fixed. For example, soda water is a mixed substance constituting of water and carbon dioxide in a specific proportion. Similarly, syrup is a mixed substance of water and sugar in fixed proportions. When we are dealing with mixtures instead of mixed substances proportion of components changes and this creates mathematical problems. Such problems can be solved using the concept ratio and proportion.

**Note:** A mixture can be a combination of more than two substances. For example, a lot of fertilizers contain more than two minerals, `a lot of metal alloys are made up of more than two metals.

**Example 1: A mixed fertilizer contains urea and cow manure in the proportion 2:5. Find out the weight of the components required to produce 28 quintals of mixed fertilizer.**

**Solution:**

Urea: Cow manure=2:5

Proportion of urea in the mixed fertilizer

Proportion of cow manure in the mixed fertilizer

In mathematical language the problem is (i)

(ii)

Weight of urea=8 quintals and weight of cow manure=20 quintals.

**Example 2: Two different types of washing powders contain soda and soap powder in the ratio at 2:19 and 1:11 respectively. What will be the ratio of soda and soap powder in a mixture prepared by mixing 7 Kg of the 1st powder with 4 Kg of the 2nd powder?**

**Solution:**

In 1st washing powder, soda: soap powder= 2:19

Weight of soda in 7 Kg

Weight of soap powder in 7 Kg

In the 2nd washing powder, soda: soap powder=1:11

Weight of soda in 4 Kg

Weight of soap powder in 4 Kg

The problem in mathematical language is,

**Example 3: There are three similar glasses filled with juice. The ratio of water and syrup in the three juices are 5:1, 5:3 and 5:7 respectively. If the juices are poured into a big container; what will be the ratio of water and syrup in it?**

** Solution:**

In the 1st glass, water:syrup=5:1

Proportion of water

Proportion of syrup

In the 2nd glass, water:syrup=5:3

Proportion of water

Proportion of syrup

In the 3rd glass, water:syrup=5:7

Proportion of water

Proportion of syrup

The problem in mathematical language is,

## Exercise:

- The ratio of Copper and Zinc in a type of brass is 5:3. What will be the ratio of Copper and Zinc in 24 Kg of brass, if 3Kg Copper is added to it?
- 49 Kg of a blended tea contains Assam tea and Darjeeling tea in the ratio 5:2. What weight of Darjeeling tea should be added to it, so that the ratio of Assam tea and Darjeeling tea becomes 2:1?
- A fertilizer used in paddy fields contains ammonia, phosphate and potash in the ratio of 11:5:2. A farmer wants to use 16 Kg of such a mixed fertilizer on 9 bigha of farm land. Find out the weights of different types of fertilizers that he should buy.
- A mason mixed sand and cement in the ratio 7:1 to prepare a masonry mixture. 72 Kg of the mixture remained unused after the brick work was over. he then mixed some cement to the mixture to make it a6:1 mixture and used it for plastering. What quantity of cement did he add?
- The ratios of Soda and Soap powder in two different washing powders are 2:3 and 4:5 respectively. If 18 Kg of the second washing powder is mixed with 10 Kg of the first washing powder, what proportion of soda and soap powder will be there in the new mixture?
- A glass of drink contains syrup and water in the ratio 3:1. What volume of the drink should be removed and equal volume of water should be added so that volume of syrup and water becomes equal?
- Two similar vessels had and parts respectively filled with fruit juice. The remaining empty part of these vessel, were filled with water. The content of both the vessels were poured into another vessel. What will be the ratio of fruit juice and water in the new vessel?
- Three similar (of equal size) glasses are completely filled with a beverage. The ratio of water and syrup in the first, second and third glasses are 3:1, 5:3 and 9:7 respectively. the contents of the three glasses are poured into a bigger vessel. What will be the ratio of water and syrup in the new vessel?
- Two different types of stainless steel contain Chromium and steel in the ratio of 2:11 and 5:21 respectively. In what proportion should these two types of steel be mixed so that the ratio of chromium and steel becomes 7:32?
- The proportion of 1st and 2nd liquids in a mixture is 2:3 while in another mixture their ratio is 5:4. In what ratio should the two mixtures be mixed, so that the new mixture contain equal amounts of the two liquids?

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