What is Continued Proportion?
Three numbers are said to be in Continued Proportion if the ratio of first and second number is equal to the ratio of second and third number.
If three numbers a, b, c are in continued proportion
Then,
a : b : : b : c
Example 1
If 48, 24, a are in continued proportion, find the value of a?
Explanation:
Given – 48 , 24 , a are in continued proportion.
So,
48 : 24 :: 24 : a
(Product of extremes = Product of means)
Here, Extremes are 48 and a
Means are 24 and 24
48 x a = 24 x 24
Now, on simplifying we get a = (24 x 24)/48 = 12
Hence, the value of ‘a’ is 12
Example 2
If 12, 42, a are in continued proportion, find the value of a?
Explanation:
Given – 12 , 42 , a are in continued proportion.
So,
12 : 42 :: 42 : a
(Product of extremes = Product of means)
Here, Extremes are 12 and a
Means are 42 and 42
12 x a = 42 x 42
Now, on simplifying we get a = (42 x 42)/12 = 147
Hence, the value of ‘a’ is 147
Example 3
If 28, 14, a are in continued proportion, find the value of a?
Explanation:
Given – 28 , 14 , a are in continued proportion.
So,
28 : 14 :: 14 : a
(Product of extremes = Product of means)
Here, Extremes are 28 and a
Means are 14 and 14
28 x a = 14 x 14
Now, on simplifying we get a = (14 x 14)/28 = 7
Hence, the value of ‘a’ is 7
Example 4
If 48, 12, a are in continued proportion, find the value of a?
Explanation:
Given – 48 , 12 , a are in continued proportion.
So,
48 : 12 :: 12 : a
(Product of extremes = Product of means)
Here, Extremes are 48 and a
Means are 12 and 12
48 x a = 12 x 12
Now, on simplifying we get a = (12 x 12)/48 = 3
Hence, the value of ‘a’ is 3
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