Question

The ratio of the present ages of two brothers is $$1:2$$ and $$5$$ years back the ratio was $$1:3$$. What will be the ratio of their ages after $$5$$ years?

Answer 1

Correct option is C. $$3:5$$
Let the age of the two brothers be $$x$$ and $$y$$ respectively

Given

At present

$$\dfrac { x }{ y } =\dfrac { 1 }{ 2 } \Rightarrow y=2x$$

Five years ago

$$\dfrac { x-5 }{ y-5 } =\dfrac { 1 }{ 3 }$$

substitute $$y=2x$$

$$\dfrac { x-5 }{ 2x-5 } =\dfrac { 1 }{ 3 }$$

$$\Rightarrow 3x-15=2x-5\Rightarrow x=10$$

$$\Rightarrow y=2x=2(10)=20$$

$$\therefore\ x=10$$ and $$y=20$$

Required ratio:

$$\displaystyle \frac { x+5 }{ y+5 } =\frac { 10+5 }{ 20+5 } =\frac { 15 }{ 25 } =\frac { 3 }{ 5 }$$

Hence option (C) is the correct option.