Question

Present age of father and son are in the ratio 5:1 respectively. seven years later this ratio becomes 3:1.what is the son's present age in years?

Answer 1

Let present ages of A and B are x and y years respectively.

Therefore,

x/y=5/4

i.e.4x=5y

Now, (x−16)/(y−16)=27/20

20(x−16)=27(y−16)

20x−320=27y−432

27y−20x=112

Using 4x=5y, we get

27y−25y=112

2y=112

y=56

x=(5/4)y=(5/4)56=70

Hence, the present ages of A and B are 56 and 70 years respectively.

Answer 2

Answer:The present age of son is 7 years.

Step-by-step explanation:

Given:Present age of father and son are in the ratio 5:1 respectively. seven years later this ratio becomes 3:1.

To find:We have to find the present age of son.

Explanation:

Step 1:Let the present age of father be x years.

Step 2:Let the present age of son be y years.

Step 3:Seven years later father's age will be (x+7) years.

Step 4:Seven years later son's age will be (y+7) years.

Step 5:As the ratio of present age of father and son is 5:1.

i.e.                              x:y=5:1

⇒                                 $\frac{x}{y}=\frac{5}{1}$

On doing cross multiplication we have,

⇒                                 $x=5y$.......(1)

Step 6:As seven years later the ratio of their ages is 3:1.

i.e.                    (x+7):(y+7)=3:1

⇒                            $\frac{(x+7)}{(y+7)}=\frac{3}{1}$

On doing cross multiplication we have,

⇒                        $1(x+7)=3(y+7)$

⇒                             $x+7=3y+21$

Step 7:Substituting the value of x from equation on above equation we have,

⇒                            $5y+7=3y+21$

⇒                          $5y-3y=21-7$

⇒                                  $2y=14$

⇒                                    $y=\frac{14}{2}$

⇒                                    $y=7$

∴The present age of son is 7 years.

∴The father age will be $x=5y$

                                          $=5$×$7$

                                          $=35years$

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