Test Index

Ratio and Proportion

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Question : 52 of 112

Marks: +1, -0

If

(a+b):(b+c):(c+a)=6: 7: 8

a+b+c=

14, then the value of

c

is :

8
7
6
12 .

Solution:

Concept:

Given three sums in a continued proportion, we express each sum as a multiple of a common variable

k

, then use the total to find

k

and the desired variable.

Explanation:

Let

a+b = 6k

,

b+c = 7k

, and

c+a = 8k

.

Add the three equations:

(a+b)+(b+c)+(c+a) = 2(a+b+c) = 6k+7k+8k = 21k

.

We know

a+b+c = 14

, so

2 \times 14 = 28 = 21k

.

Thus

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

.

Now,

a+b = 6 \times \frac{4}{3} = 8

.

Since

a+b+c = 14

, we get

c = 14 - 8 = 6

.

Answer:

c = 6

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