When two ratios are equal, then it is called as a proportion. It is an equation that can be solved. It is a case where two fractions are equal. It can be written in two ways:
There are four quantities in proportions where the first and fourth terms are known as extremes and the second and third terms are called means. It shows or tells two fraction or ratios are equal.
Terms are the four different quantities in the proportion. In proportion a: b: :c: d, a, b, c, and d are its first term, second term, third term& fourth terms. The fourth term is called the fourth proportional to the numbers a, b, and c.
In a proportion, the first and fourth terms are called extremes and the second and third terms are called means.
Examples
Solution:
Let the required third proportion be x.
2 : 22 = 22 : x
or, \(\frac{2}{22}\) = \(\frac{22}{x}\)
or, 2x = 22\(\times\) 22
or, x = \(\frac{22 \times 22}{2}\)
\(\therefore\) x = 242
Solution:
Let the required mean proportion be x. Then,
2 : x = x : 32
or, \(\frac{2}{x}\) = \(\frac{x}{32}\)
or, x^{2} = 64
or, x = \(\sqrt{64}\)
\(\therefore\) x = 8
Solution:
Let x be the proportional to 5, 7 and 8
Then, \(\frac{5}{7}\) = \(\frac{8}{x}\)
or, 5x =7 \(\times\) 8
or, x = \(\frac{56}{5}\)
\(\therefore\) x = 11.2
Solution:
16 : 8 = x : 5
or, \(\frac{16}{8}\) = \(\frac{x}{5}\)
or, 8x =16 \(\times\) 5
or, x = \(\frac{80}{8}\)
\(\therefore\) x = 10
Solution:
The ratio of first two numbers = \(\frac{7}{9}\)
The ratio of second two numbers = \(\frac{z}{18}\)
Now,
\(\frac{7}{9}\) = \(\frac{z}{18}\)
or, z = \(\frac{7\times18}{9}\)
or, z = 7\(\times\)2
\(\therefore\) z = 14
Solution:
Given, x:5 = 10:25
or, \(\frac{x}{5}\) = \(\frac{10}{25}\)
or, 25x = 5 \(\times\) 10
or, x = \(\frac{50}{25}\)
\(\therefore\) x = 2
Solution:
Given, 3:7 = 21:x
or, \(\frac{3}{7}\) = \(\frac{21}{x}\)
or, x = \(\frac{21\times7}{3}\)
\(\therefore\) x = 49
Solution:
The first two number of ratio = \(\frac{3}{a}\)
Second two number of ratio = \(\frac{9}{21}\)
given numbers are in proportion, so
\(\frac{3}{a}\) = \(\frac{9}{21}\)
or, a = \(\frac {3\times21}{9}\)
\(\therefore\) a = 7
Solution:
Given,
25 : 15 = x : 3
or, \(\frac{25}{15}\) = \(\frac{x}{3}\)
or, x = \(\frac{25\times3}{15}\)
or, x = \(\frac{75}{15}\)
\(\therefore\) x = 5
Solution:
The ratio of first and second numbers = \(\frac{7}{8}\) = 7:8
The ratio of third and fourth numbers = \(\frac{14}{20}\) = 7:10
Hence, the first ratio 7:8 and the second ratio 14:20 = 7:10 are not not in the proportional form.
Find the value of x?
x, 2, 6, 4
Find the value of x?
x:5 = 10:25
Find the value of x?
3 : 7 = 21 : x
Find the value of x?
10 : x = 2 : 11
Find the value of y?
16, 4, 4, y
Find the value of a?
3, a, 9, 21
Find the value of x in 16 : 8 = x : 5
Find the fourth proportional to :
5, 7 ,8
If 5 pens cost Rs 150, what is the cost of 12 pens ?
Find the third proportional to 2 and 32.
Find the mean proportion between :
0.9 and 2.5
Find the mean proportional between:
0.6 and 9.6
If x : y = 2 : 3 and y : z = 5 : 7, find x : y : z.
If m : n = 4 : 9 and n : s = 3 : 7, find m : s.
Find x in the following proportions:
4 : 8 : : x : 16
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Sanjiv
If the distance beteen two places is 18000 and thw ratio of two places is1:200000.find the distance
Jan 30, 2017
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