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Definition of Continued Proportion


Definition of Continued Proportion:

Three quantities are said to be in continued proportion if the ratio of the first term and second term be equal to the ratio of the second term and third term.

Suppose, the three quantities x, y and z are said to be in continued proportion if x : y = y : z, i.e., xy = yz.

Similarly, four quantities are said to be in continued proportion if the ratio of the first term and second term be equal to the ratio of the second term and third term be equal to the ratio of the third term and fourth term.

If w, x, y and z are four quantities such that w : x = x : y = y : z, i.e., wx = xy = yz, they are said to be in continued proportion.

For example,

(i) The numbers 4, 6 and 9 are in continued proportion because

46 = 69

or, 62 = 4 × 9.


(ii) The numbers 2, 4 and 6 are not in continued proportion because

2446 .


(iii) The numbers 2, 4, 8 and 16 are in continued proportion because

24 = 48  = 816.



Solved examples on continued proportion of three or four quantities:

1. If k, 8, 16 are in continued proportion then find k.

Solution:

k, 8 and 16 are in continued proportion.

⟹ k : 8 = 8 : 16

k8 = 816  

⟹ k × 16 = 82

⟹ 16k = 64

⟹ k = 6416

⟹ k = 4

Therefore, the value of k = 4.


2. Quantities m, 2, 10 and n are in continued proportion then find the values of m and n.

Solution:

m, 2, 10 and n are in continued proportion.

 ⟹ m : 2 = 2 : 10 = 10 : n

m2 = 210 = 10n   

m2 = 210 and 210 = 10n 

⟹ m × 10 = 22 and 2 × n = 102

⟹ 10m = 4 and 2n = 100

⟹ m = 410 and n = 1002

⟹ m = 0.4 and n = 50

Therefore, the value of m = 0.4 and n = 50

 

● Ratio and proportion












10th Grade Math

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