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. x/y = y/z .
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., w/x = x/y = y/z, they are said to be in continued proportion.
Examples
Suppose that Rs. 74000 are to be divided among three friends A, B, C, such that
A : B = 4 : 5 and B : C = 3 : 2
Three partners invested Rs. 12500, 9000 and 7500 respectively. If the total profit earned is Rs. 5800, how much profit will each partner receive?
Solution:
Let A, B and C be three partners
Divide 60000 in ratio 5 : 7
Solution:
Let A and B be two people having a ratio of share 5 : 7
Sum of ratios = 5 + 7 = 12
Share of A = 5/12 x 60000 = 25000
Share of B = 7/12 x 60000 = 35000
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
⟹ k/8 = 8/16
⟹ k × 16 = 8²
⟹ 16k = 64
⟹ k = 64/16
⟹ 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
⟹ m/2 = 2/10 = 10/n
⟹ m/2 = 2/10 and 2/10 = 10/n
⟹ m × 10 = 2² and 2 × n = 10²
⟹ 10m = 4 and 2n = 100
⟹ m = 4/10 and n = 100/2
⟹ m = 0.4 and n = 50
Therefore, the value of m = 0.4 and n = 50.