Let x, y and z are three positive numbers and P =x+y+z/2 if (p-x):(p-y):(p-z)=3: 5: 7 then the ratio of x:y:z is

Correct Answer is : 6:5:46: 5: 46:5:4

Correct Answer is : 6:5:46: 5: 46:5:4

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Ratio and Proportion

Question : 104 of 112

Marks: +1, -0

Let

x, y

z

P

=\frac{x+y+z}{2}

(p-x):(p-y):(p-z)=3: 5: 7

x:y:z

Solution:

Concept:

Express each difference

P-x

P-y

P-z

using a common multiple

k

, then use

P = \frac{x+y+z}{2}

to solve for

P

and the individual numbers.

Explanation:

Let

P-x = 3k

P-y = 5k

P-z = 7k

Add the three equations:

(P-x)+(P-y)+(P-z) = 3k+5k+7k = 15k

But the left side also equals

3P - (x+y+z)

Given

P = \frac{x+y+z}{2}

, so

x+y+z = 2P

Thus

3P - 2P = P

, hence

P = 15k

Now find each variable:

x = P - (P-x) = 15k - 3k = 12k

y = 15k - 5k = 10k

z = 15k - 7k = 8k

Therefore the ratio

x:y:z = 12k : 10k : 8k = 6:5:4

Answer:

6:5:4

(Option B)

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