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46 vote

The sum of the ages of father and a son presently is 70 years. After 10 years, the son's age is exactly half that of the father. What are their ages now?

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The sum of the ages of father and a son presently is 70 years. After 10 years, the son's age is exactly half that of the father. What are their ages now?
1). 45 years, 25 years
2). 50 years, 20 years
3). 47 years, 23 years
4). 50 years, 25 years


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2 answers

43 vote
Answered by on | Votes 43 |
it from previous year ssc papers, option 2 is the right answer

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33 vote
Answered by on | Votes 33 | | Last Updated: 2021-08-04 15:59:28

Let us take the son's and father's present age as 'x' and 'y'.

It is given that, $x + y = 70$ --------> 1

After $10$ years, son's age will be $(x + 10)$ and father's age will be

$( y + 10)$. It is also given that,

$x + 10 = ( y + 10 )/2$ ----------> 2 

From equation 1 we get, $x = 70 - y $

Substituting 'x' in equation 2 we get,

$70 - y + 10 = ( y + 10 )/2$

$2 (70 - y + 10 ) = ( y + 10 )$

$140 - 2y + 20 = y + 10$

Rearranging the equation we get,

$y + 2y = 140 + 20 - 10$

$3y = 160 - 10$

$3y = 150$

$y = 150/ 3$

$y = 50$

Substituting the value of 'y' in eqn 1 we get,

$x + 50 = 70$ 

$x = 70 - 50$

$x = 20 $

So, son's age is $20$ years and father's age is $50$ years.

The correct option is 2). 50 years ,20 years

 

 

 

Accepted Answer




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