Test Index

Ratio and Proportion

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Question : 112 of 112

Marks: +1, -0

If

x+y, y+z, z+x

are in the ratio

6:7:8

x + y + z=14

then the value of x is

6
14/3
8
10

Solution:

Concept:

Use a common multiplier

k

to express the given sums, then use the total to find

k

and solve for

x

.

Explanation:

Given

x+y:y+z:z+x = 6:7:8

.

Let

x+y = 6k

,

y+z = 7k

,

z+x = 8k

.

Add all three equations:

(x+y)+(y+z)+(z+x) = 2(x+y+z) = 6k+7k+8k = 21k

.

We know

x+y+z = 14

, so

2 \times 14 = 21k

gives

28 = 21k

.

Thus

k = \frac{28}{21} = \frac{4}{3}

.

Now

x+y = 6 \times \frac{4}{3} = 8

.

Since

x+y+z = 14

, we get

z = 14 - 8 = 6

.

Also

z+x = 8 \times \frac{4}{3} = \frac{32}{3}

.

Therefore

x = \frac{32}{3} - 6 = \frac{32}{3} - \frac{18}{3} = \frac{14}{3}

.

Answer:

x = \frac{14}{3}

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