## Using Equations to Solve Age Problems in Math, Problems on Ages - Aptitude Questions and Answers

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### Using Equations to Solve Age Problems in Math, Problems on Ages - Aptitude Questions and Answers

1. The sum of the age of father and a son is 50 years. 5 years ago, father age was seven times that age of a son. The present ages of father and son respectively are ???

Solution-

Let us be the age of father "X" The age of son be "Y"

So according to question

X + Y = 50------------------(1)

Next
Age of 5 years ago

(X-5)  = 7 ( Y-5)

Or X-5= 7Y-35

Or X-7Y =-30-----------------------(2)

Solving the equation of deduction from  NO -(1)  & NO-(2).

X  + Y = 50
X  -7Y = -30
(-) (+)    (+)
------------------
8Y = 80
Or Y = 10

Then the age of X is equal to

X + Y = 50

Or X + 10 = 50

Or X = 50-10

Or X = 40

Hence the age of Father is 40 years & the age of the son is 10 years.

2. A man's age is three times that of a son. In 12 years later father's age will be double the son' s age. Man's present age is ??

Solution:-

Let the age of father "x"
& the age of son "y"

So, according to question,

X= 3.Y.....................No(1)

Next to the age of 12 years of them

X+12 = 2 ( Y+ 12).........................No(2)
Or X+ 12= 2Y+24
or X- 2Y = 24 -12
Or X -2Y = 12..........................No(2)

Now let us put the value of  "X" into (No-2 ) equation.
X- 2Y = 12

Or 3Y - 2Y =12
Or Y = 12

Hence the age of Man will be  12× 3= 36 years of age. As mentioned in question the age of Man will be three times of that man' son. Here we get the age of son 12 years.

3. The difference between the ages of two men is 10 years. 15 years ago, the age of elder was twice as old as the younger one. What is the present age of elder?

Solution:-Let us suppose the age of two men

"X" & "Y"

Therefore, according to question

X -  Y = 10....................(1) No

The age of their 15 years back

(X-15) = 2 (Y-15)

Or X- 15= 2Y- 30
Or X-2Y= -30+15

X -2Y = -15.........................(2) No

We can get the age of  Y by deducting the question  No (1) - No (2).

X -  Y = 10

X - 2Y = -15
(-) (+)    (+)
_____________
Y = 25

Or Y = 25

Hence the present age of the elder person is (25+10)=35 years of age.

4.10 years ago the age of  DAVID  was thrice the age of his son. Ten years hence, David age will be twice that of his son. What is the ration of their present age ??

Solution:-

Let's be the age of David " X" & the age of his son is "Y".

So, 10 years ago the age of them

(X-10)= 3 (Y-10)
Or X-10= 3Y-30

X-3Y= -30+10

X- 3Y= -20...................(1)

10 Years after the age of them

X + 10 = 2( Y + 10)

Or
X+ 10 = 2Y + 20
Or X- 2Y = 20 - 10

Or X  - 2Y = 10....................(2)

We can get the ratio of "Y" by deducting the two equations( No-1 ) - (No-2).

X- 3Y= -20
X  - 2Y = 10
(-) (+)     (-)
-------------------------
-Y = - 30
Or Y  = 30

We can get the ration of " X " by putting the value of Y into ( No -1 ) equation.

X- 3Y= -20...................(1)

X- 3.30  = -20

Or  X - 90 = - 20

Or X = -20 + 90

Or  X = 70

X : Y =  70 : 30
=  7: 3

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