Question

The ratio of the ages of the father and the son
at present is 19:5. After 4 years the ratio will
become 3:1. What is the sum of the present
ages of the father and the son?
(A) 40
(B) 42
(C)48
(D) 52​

Answer 1

let father's age=19x

let son's age=5x

After 4 years:

father's age=19x+4

son's age=5x+4

A.T.Q

19x+4/5x+4=3/1

19x+4=15x+12

4x=8

x=2

sum=19*2+5*2=38+10=48

Answer 2

Answer:

We should find the sum of the present ages of the father and the son using given data. Answer: Option c: sum of the present ages of the father and the son is 48.

Step-by-step explanation:

• Let as consider father's present age is F and son's present age is S.
• The ratio of the ages of the father and the son at present is 19:5.

        That is,             $\frac{F}{S}=\frac{19}{5}$  

                                $F=\frac{19S}{5}$  -----------------(1)

• After 4 years the ratio will become 3:1.  

                              $\frac{F+4}{S+4}=\frac{3}{1}$

                    $(F+4)(1)=(S+4)(3)$      

                           $F+4=3S+12$

                         $F-3S=12-4=8$ ----------------(2)

• Now apply equation(1) into equation(2). Then we will get the value of F and S.

                       $\frac{19S}{5}-3S=8$

• Take the L.C.M

                        $\frac{19S-15S}{5}=8$

                                $\frac{4S}{5}=8$

                                $4S=8*5=40$

                                  $S=\frac{40}{4}$

                 son's age $S=10$            

• Now son's age apply in equation(2).That is,

                      $F-3(10)=F-30=8$      

                                   $F=30+8$  

            father's age   $F=38$

• Sum of the present ages of the father and the son is add the father's age and son's age.

                             $F+S=38+10=48$

• Final Answer: Option c: 48