If x, y, z are three positive numbers such that (A - x): (A - y): (A - z) = 1: 7: 4 and 2A = x+y+z, then x:y:z= ?Options12: 4: 99: 4: 128: 5: 1111: 5: 8
Question
If x, y, z are three positive numbers such that (A - x): (A - y): (A - z) = 1: 7: 4 and 2A = x+y+z, then x:y:z= ?
Options:
- 12: 4: 9
- 9: 4: 12
- 8: 5: 11
- 11: 5: 8
Solution
To solve this problem, we need to use the concept of ratios and proportions. Here are the steps:
-
We are given that (A - x): (A - y): (A - z) = 1: 7: 4. This means that A - x, A - y, and A - z are in the ratio 1:7:4.
-
We are also given that 2A = x + y + z.
-
We can express x, y, and z in terms of A using the given ratios. From the first ratio, we can write: x = A - 1k (where k is a constant representing the common difference in the ratio), y = A - 7k, z = A - 4k.
-
Substituting these values into the second equation gives: 2A = (A - 1k) + (A - 7k) + (A - 4k) Simplifying this gives: 2A = 3A - 12k Solving for A gives: A = 12k.
-
Substituting A = 12k into the equations for x, y, and z gives: x = 12k - 1k = 11k, y = 12k - 7k = 5k, z = 12k - 4k = 8k.
-
Therefore, the ratio x:y:z is 11k:5k:8k, which simplifies to 11:5:8.
So, the correct option is 11:5:8.
Similar Questions
If x:y = 3:4 and y:z = 8:9, z:a is 15:16, find x:y:z:a (a) 30:40:45: 48 (b) 78:82:65:45 (c) 76:90:56:80 (d) None of these Options : a b c d
If x, y, z are positive integers, such that xy + x + y = 215, yz + y + z = 161 and zx + z + x = 107, then (y – z)/(x – z) =
If a : (b+c)=1:3 ; c : (a + b) = 5 : 7, then b:(a+c) is equal to?Options1 : 32 : 32 : 11 : 2
Select the correct answerIf x:y=3:4 then (7x+3y): (7x-3y) is equal to:Options5 : 211 : 337 : 194 : 3
If a : b = 5 : 2 and b : c = 7 : 9, then find the value of a : c. Ops: A. 25 : 24 B. 35 : 18 C. 35 : 24 D. 25 : 18
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.