Ratio & Proportion

Ratio:The ratio of two quantities in the same units is a fraction that one quantity is of the other.

The Ration a : b represents a fraction a/b,

The First term of a ratio is called antecedent while the second term is known as consequent.

Thus, the ratio 5 : 7 represents 5/7 with antecedent 5 and consequent 7.

Proportion : The equality of two ratios is called proportion

If a : b = c : d, we say that a,b,c,d are in proportion

In a proportion, the first and fourth terms are known as extremes , while second and third terms are known as means

we have Product of Means = Product of Extremes.

Fourth Proportional : If a : b = c : d then d is called the fourth proportional to a, b, c,

Compound Ratio :The compound ratio of the ratios

(a : b), (c : d), (e : f) is (ace : bdf)

Problems :

1.A mixes contains alcohol and water in the ratio 4 : 3. If 5 liters of water is added to the mixture, the ratio becomes 4 : 5. Find the quantities of alohol in the given mixture.

Sol :Let the quantity of alcohol & water be 4x , 3x respectively.

Then (4x/(3x + 5) 20x = 12x + 20, i.e. x = 2.5

Alcohol in the given mixture= 4x Liters = 10 liters

2. Five bananas and four apples cost as much as three banas and seven apples. The ratio of the cost one banana to that of one apple is :

Sol : Let the cost of each banana be x paise and that of each apple be y paise, Then

5x + 4y = 3x + 7y 2x = 3y x/y = 3/2

Required Ratio is 3 : 2

3. A sum of money is to be devided among P, Q and R in the ratio of 2 : 3 : 5. If the total share of P and R together is Rs 400 more than that of Q, what is R's share in it?

sol: Let P=2x, Q=3x, and R=5x,

Now Z - X=27 i.e 16x - 7x = 27 i.e x=3

Total Money =31x = Rs. 93

4. The ratio of ages of mother and son is 7 : 3, if the sum of their ages is 60 years, What is the difference in their ages ?.

Sol : Mothers age = {60 x (7/10)} = 42 years

Son's age = (60 - 42) = 18 years

Difference of thier ages = (42 - 18)years = 24 years

5. Pencils, Pens and Exercise books in a shop are in the ratio of 10 : 2 : 3 If there 120 pencils, the number of exercise books in the shop is :

Sol : Let Pencils = 10x, Pens = 2x & Exercise books = 3x

Now 10x = 120 and x = 12

Therefore Number of exercise books = 3x = 3

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