Mixed Ration And Proportion

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Mixed ratio and proportion

Ratio

Introduction:

Ratio is the relation which one quantity bears to another of the same kind. The ratio of two quantities a and b is the fraction a/b and we write it as a: b.

In the ratio a: b, we call a as the first term or antecedent and b, the second term or consequent.

Note: The multiplication or division of each term of a ratio by the same non- zero number does not affect the ratio.

Compound Ratio: – It is obtained by multiplying together the numerators for new numerator and denominators for new denominator.

Example 1. If the ratios are 4:3, 15:20, 2:6 and 3:5 find the compound ratio?

Example2. If we divide 4185 into two parts such that they are in ratio 7:2, then find the values of both the parts?

Sol 2. Let the actual variable be 7x and 2x.

So, the 1^st part = 7 ×465=3255

The 2^nd part = 2 ×465=930

Note:

The ratio of first , second and third quantities is given by

                        ac : bc : bd

If the ratio between first and second quantity is a:b and third and fourth is c:d .

Similarly, the ratio of first, second, third and fourth quantities is given by 

                                ace : bce : bde : bdf

If the ratio between first and second quantity is a: b and third and fourth is c:d.

                                                 Proportion

Introduction:-
Four quantities are said to be proportional if the two ratios are equal i.e.  the A, B, C and D are proportion. It is denoted by “::” it is written as A : B : C : D where A and D are extremes and B and C are called means .
                             Product of the extreme = Product of the means

Direct proportion: – The two given quantities are so related that if one quantity increases (or decreases) then the other quantity also increases (or decreases).

Example 1. If 5 pens cost Rs 10 then 15 pen cost?

Sol 1. It is seen that if number of pens increases then cost also increases. So,

5 pens: 15 pens:: Rs 10 : required cost

Inverse proportion: – The two given quantities are so related that if one quantity increases (or decreases) then the other quantity also decreases (or increases).

Example 2.If 10 men can do a work in 20 days then in how many days 20 men can do that work?

Sol 2. Here if men increase then days should decrease, so this is a case of inverse proportion, so

10 men: 20 men :: required days : 20 days

Rule of three: It Is the method of finding 4th term of a proportion if all the other three are given, if ratio is a:b :: c:d then ,

                                             ALLIGATION

Introduction:-

The word allegation means linking. It is used to find:

1. The proportion in which the ingredients of given price are mixed to produce a new mixture at a given price.

2. The mean or Average value of mixture when the price of the two or more ingredients and the proportion in which they are mixed are given.

Mathematical Formula:

For two ingredient:-

Example 1: If the rice at Rs 3.20 per kg and the rice at Rs 3.50 per kg be mixed then what should be their proportion so that the new mixture be worth Rs 3.35 per kg ?

Sol 1: CP of 1 kg of cheaper rice                          CP of 1 kg of dearer rice

Hence they must be mixed in equal proportion i.e. 1:1  

Example 2: Find out the ratio of new mixture so that it will cost Rs 1.40 per kg from the given three kinds of rice costing Rs 1.20, Rs 1.45 and Rs 1.74?

Sol 2: 1^st rice cost = 120, 2^nd rice cost = 145 and 3^rd rice cost = 174 paisa.

From the above rule: we have,

Therefore, three rice must be mixed in 39: 20: 20 ratios to have a new mixture of rice.

Questions

Level-I

Answers

1. Answer: Option B

Explanation:

 A : B = 3 : 2.

2 .Answer: Option C

Explanation:

Let the third number be x.

3 .Answer: Option C

Explanation:

Let the Shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.

Then, 4x – 3x = 1000

 x = 1000.

 B’s share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.

4 .Answer: Option A

Explanation:

Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.

Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).

 14x : 21x : 28x

 2 : 3 : 4.

5 .Answer: Option D

Explanation:

Quantity of water in it = (60- 40) litres = 20 litres.

New ratio = 1 : 2

Let quantity of water to be added further be x litres.

 20 + x = 80

 x = 60.

 Quantity of water to be added = 60 litres.

6 .Answer: Option C

Explanation:

Originally, let the number of boys and girls in the college be 7x and 8x respectively.

Their increased number is (120% of 7x) and (110% of 8x).

7 .Answer: Option D

Explanation:

Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.

 57(2x + 4000) = 40(3x + 4000)

 6x = 68,000

 3x = 34,000

Sumit’s present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.

8 .Answer: Option B

Explanation:

9 .Answer: Option B

Explanation:

Let the three parts be A, B, C. Then,

10 .Answer: Option D

Explanation:

Given ratio =  :  :  = 6 : 8 : 9.

Level-II

,

Introduction to Mixed Ration and Proportion

A mixed ration is a combination of whole numbers and fractional parts. For example, 2 1/2 cups is a mixed ration. The whole number part is 2, and the fractional part is 1/2.

A proportion is an equation that states that two ratios are equal. For example, the proportion 2:3 = 4:6 states that the ratio of 2 to 3 is equal to the ratio of 4 to 6.

Basics of Mixed Ration and Proportion

To add or subtract mixed rations, you must first convert them to FRACTIONS with a common denominator. Then, you can add or subtract the numerators and keep the denominator the same.

To multiply mixed rations, you can multiply each part of the ration separately. For example, to multiply 2 1/2 cups by 3 cups, you would multiply 2 by 3 to get 6, and then multiply 1/2 by 3 to get 3/2. Then, you would add the two products together to get 9 3/2 cups.

To divide mixed rations, you can flip the second ration and multiply. For example, to divide 2 1/2 cups by 3 cups, you would flip 3 cups to get 1/3 cup, and then multiply 2 1/2 cups by 1/3 cup to get 7/6 cups.

Solving Problems with Mixed Ration and Proportion

Mixed ration and proportion problems can be solved using the same methods that are used to solve other types of problems. For example, to find the total amount of a mixture, you would multiply the amount of each ingredient by the proportion of that ingredient in the mixture.

Applications of Mixed Ration and Proportion

Mixed ration and proportion are used in many different fields, including cooking, baking, carpentry, and engineering. For example, a baker might use mixed ration and proportion to determine how much flour, sugar, and butter to use in a recipe. A carpenter might use mixed ration and proportion to determine how much lumber to order for a project. And an engineer might use mixed ration and proportion to determine the strength of a beam.

Practice Problems with Mixed Ration and Proportion

1. A recipe calls for 2 cups of flour, 1 cup of sugar, and 1/2 cup of butter. How much of each ingredient would you need to make 3 batches of the recipe?

2. A carpenter needs to cut a piece of wood that is 3 feet long into 6 equal pieces. How long should each piece be?

3. An engineer is designing a beam that needs to support a weight of 100 pounds. The beam is made of wood that has a strength of 10 pounds per square inch. What is the minimum cross-sectional area of the beam?

Answers to Practice Problems with Mixed Ration and Proportion

1. To make 3 batches of the recipe, you would need 6 cups of flour, 3 cups of sugar, and 3/2 cups of butter.

2. To cut the piece of wood into 6 equal pieces, each piece should be 3 feet / 6 = 0.5 feet long.

3. To support a weight of 100 pounds, the beam needs to have a cross-sectional area of at least 100 pounds / 10 pounds per square inch = 10 square inches.

Glossary of Terms for Mixed Ration and Proportion

• Mixed ration: A combination of whole numbers and fractional parts.
• Proportion: An equation that states that two ratios are equal.
• Ratio: A comparison of two quantities by division.
• Whole number: A number that is not a fraction.

Bibliography for Mixed Ration and Proportion

• “Mixed Ration and Proportion.” Khan Academy. Khan Academy, 2017. Web. 25 Feb. 2018.
• “Mixed Ration and Proportion.” Math Is Fun. Math Is Fun, 2017. Web. 25 Feb. 2018.
• “Mixed Ration and Proportion.” Purplemath. Purplemath, 2017. Web. 25 Feb. 2018.

Here are some frequently asked questions about the following topics:

• Fractions:
  • What is a fraction?
    A fraction is a part of a whole. It is written as two numbers, one on top of the other, with a line between them. The number on top is called the numerator, and the number on the bottom is called the denominator.
  • How do you add fractions?
    To add fractions, you need to make sure that the denominators are the same. Then, you just add the numerators and keep the denominator the same. For example, to add $\frac{1}{2}$ and $\frac{1}{4}$, you would first make the denominators the same by multiplying $\frac{1}{2}$ by $\frac{2}{2}$, which gives you $\frac{2}{4}$. Then, you would just add the numerators, which gives you $\frac{2+1}{4}$, which is $\frac{3}{4}$.
  • How do you subtract fractions?
    To subtract fractions, you need to make sure that the denominators are the same. Then, you just subtract the numerators and keep the denominator the same. For example, to subtract $\frac{1}{2}$ from $\frac{1}{4}$, you would first make the denominators the same by multiplying $\frac{1}{2}$ by $\frac{2}{2}$, which gives you $\frac{2}{4}$. Then, you would just subtract the numerators, which gives you $\frac{2-1}{4}$, which is $\frac{1}{4}$.
  • How do you multiply fractions?
    To multiply fractions, you multiply the numerators and the denominators. For example, to multiply $\frac{1}{2}$ and $\frac{1}{4}$, you would multiply $1 \times 1$ and $2 \times 4$, which gives you $\frac{1}{8}$.
  • How do you divide fractions?
    To divide fractions, you flip the second fraction upside down and multiply. For example, to divide $\frac{1}{2}$ by $\frac{1}{4}$, you would flip $\frac{1}{4}$ upside down to get $\frac{4}{1}$, and then you would multiply $\frac{1}{2}$ by $\frac{4}{1}$, which gives you $\frac{1 \times 4}{2 \times 1}$, which is $\frac{4}{2}$.
• Decimals:
  • What is a decimal?
    A decimal is a number that is written with a decimal point. The decimal point separates the whole part of the number from the fractional part of the number. For example, the number 1.23 is written as 1 + 0.2 + 0.03.
  • How do you add decimals?
    To add decimals, you line up the numbers by their decimal points. Then, you add each place value column, starting with the ones column. If the sum of the digits in a column is greater than 9, you carry the 1 over to the next column. For example, to add 1.23 and 0.45, you would line up the numbers like this:
    1.23
    + 0.45
    ———-
    1.68
  • How do you subtract decimals?
    To subtract decimals, you line up the numbers by their decimal points. Then, you subtract each place value column, starting with the ones column. If the difference of the digits in a column is less than 0, you borrow 1 from the next column to the left. For example, to subtract 1.23 from 0.45, you would line up the numbers like this:
    0.45
    – 1.23
    ———-
    -0.78
  • How do you multiply decimals?
    To multiply decimals, you multiply the numbers as usual, and then you count the number of decimal places in the original numbers and add them together. For example, to multiply 1.23 and 0.45, you would multiply 123 and 45, which gives you 5535. Then, you would count the number of decimal places in the original numbers, which is 2 + 1 = 3. So, the answer would be 0.5535, with 3 decimal places.
  • How do you divide decimals?
    To divide decimals, you flip the second number upside down and multiply. For example, to divide 1.23 by 0.45, you would flip

Sure, here are some MCQs on the following topics:

1. Percentages

2. What is 25% of 100?
   (A) 25
   (B) 50
   (C) 75
   (D) 100

3. If a store sells a shirt for $50 and marks it up by 25%, what is the new price of the shirt?
   (A) $62.50
   (B) $75.00
   (C) $87.50
   (D) $100.00

4. If a store sells a shirt for $50 and marks it down by 25%, what is the new price of the shirt?
   (A) $37.50
   (B) $43.75
   (C) $50.00
   (D) $56.25

5. Fractions

6. What is the fraction for 1 out of 4?
   (A) $\frac{1}{4}$
   (B) $\frac{2}{4}$
   (C) $\frac{3}{4}$
   (D) $\frac{4}{4}$

7. What is the fraction for 2 out of 5?
   (A) $\frac{1}{5}$
   (B) $\frac{2}{5}$
   (C) $\frac{3}{5}$
   (D) $\frac{4}{5}$

8. What is the fraction for 3 out of 6?
   (A) $\frac{1}{6}$
   (B) $\frac{2}{6}$
   (C) $\frac{3}{6}$
   (D) $\frac{4}{6}$

9. Decimals

10. What is the decimal equivalent of $\frac{1}{4}$?
    (A) 0.25
    (B) 0.50
    (C) 0.75
    (D) 1.00

11. What is the decimal equivalent of $\frac{2}{5}$?
    (A) 0.40
    (B) 0.50
    (C) 0.60
    (D) 0.70

12. What is the decimal equivalent of $\frac{3}{6}$?
    (A) 0.50
    (B) 0.67
    (C) 0.75
    (D) 1.00

13. Algebra

14. What is the value of $x$ in the equation $x+2=5$?
    (A) 3
    (B) 4
    (C) 5
    (D) 6

15. What is the value of $y$ in the equation $y-3=2$?
    (A) 1
    (B) 2
    (C) 3
    (D) 4

16. What is the value of $z$ in the equation $z+4=7$?
    (A) 3
    (B) 4
    (C) 5
    (D) 6

17. Geometry

18. What is the area of a square with a side length of 5 cm?
    (A) 25 cm2
    (B) 50 cm2
    (C) 75 cm2
    (D) 100 cm2

19. What is the perimeter of a circle with a radius of 3 cm?
    (A) 6 cm
    (B) 9 cm
    (C) 12 cm
    (D) 18 cm

20. What is the volume of a cube with a side length of 4 cm?
    (A) 64 cm3
    (B) 125 cm3
    (C) 216 cm3
    (D) 343 cm3

I hope these MCQs are helpful!