Question 78

If a : (b + c) = 1 : 3 and c : (a + b) = 5 : 7, find the value of b : (c + a).

Solution

Let say,

a=k & (b+c)=3k ....................(1)

and c=5x & (a+b)=7x.................(2)

So,

$$b=\left(3k-5x\right).$$ (from (1) and (2))

and

$$b=\left(7x-k\right).$$ (from (1) and (2))

So, $$7x-k=3k-5x.$$

or, $$4k=12x.$$

or,$$k=3x.$$

So, $$a=3x,\ b=4x\ and\ c=5x.$$

So,

$$\frac{b}{\left(c+a\right)}=\frac{4x}{\left(3x+5x\right)}=\frac{4x}{8x}=\frac{1}{2}.$$

C is correct choice.

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