Question

10 years hence, the age of the father is 2 times the age of his son. 10 years ago
the age is 6 times the age of his son. Find the present ages.
Aathinte​

Answer 1

Step-by-step explanation:

Let the present ages of the father and son be x and y respectively.

10 years ago:

We know that the age of the father was 4 times the age of his son. So, we can express this relationship in terms of x and y ;

x−10=4(y−10)

x−10=4y−40

x=4y−30 ——(1)

This equation will come in handy later on.

10 years after;

Now we know that the age of the father will be 2 times the age of his son.

x+10=2(y+10)

x+10=2y+20

x−2y=20−10

x−2y=10 ——(2)

So, in the end we have two equations (1) and (2), in terms of x and y , so we have two simultaneous equations and we can solve this by using substitution.

Substitution Method:

The two equations are:

x=4y−30 ——(1)

x−2y=10 ——(2)

In the substitution method, one variable is expressed in terms of another. This would allow the number of variables to be reduced to one, and so we can solve for that one variable. Once we get the value of that variable, we use it to solve for the other variable. Let’s see how this works;

So, since we have x=4y−30 , I will choose to substitute (“replace”) every instance of x with 4y−30 , and so reducing the number of variables to just one, namely y . We can substitute this in equation (2);

x−2y=10

(4y−30)−2y=10

2y=10+30=40

y=20

We have found the value of y to be 20. Now, we can substitute this back into equation (1), to solve for x ;

x=4y−30

x=4(20)−30=50

We have successfully found the values of x and y to be 50 and 20 respectively. Finally, just to check our answer, we see if these values satisfy the question.

Checking

10 years ago:

x=4y−30

50=4(20−30)

50=50

Since LHS = RHS, our values satisfy the first part of the question.

Present day:

x+10=2(y+10)

50+10=2(20+10)

60=60

Since LHS = RHS, our values satisfy the second part of the question too.

Thus, we can conclude that our values are correct. Therefore;

Present age of father = 50 years old

Present age of son = 20 years old

Answer 2

Answer:

∴ Required ratio =(3x+10):(x+10)=70:30=7:3

Step-by-step explanation:

Let the ages of father and son 10 years ago be 3x and x years respectively.

Then, (3x+10)+10=2[(x+10)+10]

⇒3x+20=2x+40

⇒x=20

∴ Required ratio =(3x+10):(x+10)=70:30=7:3

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