Ratio
The ratio shows the relative sizes of two or more values. The ratio compares two or more quantities of the same unit. It tells how many times quantity is less or more than another quantity of the same unit.
For example, The ratio of a to b = a:b or \(\frac{a}{b}\). Similarly ratio of b to a = b:a or\(\frac{b}{a}\). The quantities of a ratio are called the terms of the ratio. The term in the numerator is called antecedent and the denominator is called consequent.
Proportion
If there is the equality between two ratios then it can be known as the proportion. Let a, b, c and d are called first, second, third and fourth proportional respectively, The first and fourth proportional are called Extremes. The second and third proportional are called Means.
Types of proportion
Solution:
Let, the required cost be Rs x.
Here, the quantities of apples and their cost are in direct proportion.
\(\therefore\) 8:5 = 180:x
or, \(\frac{8}{5}\) = \(\frac{280}{x}\)
8x = 5 × Rs 280
x = \(\frac{5 ×Rs 280}{8}\) = Rs 175.
So the required cost is Rs 175.
Solution:
Here, Rs 2 is the tax for the income of Rs 100
Re 1 is the tax for the income of Rs \(\frac{100}{2}\) = Rs 50
Rs 525 is the tax for the income of Rs 525 × 50 = 26250.
So, the required income of the man is Rs 26250.
Solution:
In 8 days, Hari can do 1 work.
In 1 day, Hari can do \(\frac{1}{8}\) part of the work.
In 6 days, Hari can do \(\frac{6}{8}\) parts of work = \(\frac{3}{4}\) parts of the work.
Now, remaining parts of the work = (1 - \(\frac{3}{4}\)) = \(\frac{1}{4}\) part of the work.
So, Gopal finished \(\frac{6}{8}\) parts of the work.
A ratio is equal to 5 : 7. If the antecedent is 25, what will be its consequent?
If the terms 2, 3 and 14 are in proportion, then what will be its fourth proportional?
If the terms 6, 8, and 24 are in proportion, find the third proportional?
What will be the value of x if 8 : 10 = x : 50
If the 12, 60, 40 terms are in proportion, what will be its second proportional?
Find the ratios and reduce 2kg and 250g in their lowest terms.
What will be the results when dividing Rs 60 in the ratio of 1 : 4?
The ratio of two numbers is 7 : 2. If the greater number is 28, what will be smaller one?
If the pair of complementary angles are in the ratio 2 : 3, find them?
60 boys in a hostel have provisions for 30 days. How long would the provisions last to 72 boys?
ASK ANY QUESTION ON Ratio and Proportion
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