Continued Proportion
Continued Proportion
Continued Proportion:
Three quantities are said to be in continued proportion; if the ratio between the first and the second is equal to the ratio between the second and the third.
Suppose, if we have three qualities such that the ratio of first to second is equal to the ratio of second to third, we say that the three qualities are in continued proportion. The middle term is called the mean proportional between the first the third terms.
i.e. a, b and c are in continued proportion, if a : b = b : c
The second quantity is called the mean proportional between the first and the third
i.e. in a : b = b : c; b is the mean proportional between a and c.
The third quantity is called the third proportional to the first and the second
i.e. in a : b = b : c; c is the third proportional to a and b.
Illustration: Check whether the numbers 6, 12, 24 are in continued proportion or not.
Solution: Here the ratio of first quantity to the second = 6 : 12 = 1 : 2
And ratio of second quantity to the third = 12 : 24 = 1 : 2
We see that 6 : 12 = 12 : 24
Thus, 6, 12, 24 are in continued proportion.
The second quantity 12 is the mean proportional and third quantity 24 is the third proportional.
Illustration: Find the mean proportion between 4 and 9.
Solution: Let the mean proportion be x
Therefore, 4 : x = x : 9
⇒ x × x = 4 × 9
⇒ = 36
⇒ =
⇒ x = 6
The first three terms of a proportion are 3 , 5 and 21 respectively . Find its fourth term ? | |||
| Right Option : D | |||
| View Explanation | |||
The mean proportional of 9 and 16 is ? | |||
| Right Option : A | |||
| View Explanation | |||
The mean proportional of 6 and 24 is ? | |||
| Right Option : B | |||
| View Explanation | |||
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