When the son age will be as old as his father?

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Question 954041: When the son will be as old as his father today, the sum of their ages then will be 126 years. When the father was as old as his son is today, the sum of their ages then was 38 years. Find their present ages.
Answer by hemu_da(13)
When the son age will be as old as his father?
 
When the son age will be as old as his father?
 
When the son age will be as old as his father?
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Let the present ages of son and his father are x and y respectively. The difference of their ages is- (y-x). Hence, it will take (y-x) more years for son to reach his father's present age. After (y-x) years sum of their ages will be - (which is given 126) . . [ x + (y-x) ] + [ y + (y-x) ] = 126 . . 3y-x = 126. ........ eq-1 Similarly (y-x) before father's age was equal his son's present age. (y-x) years before sum of their age was- ( which is given 38)-- [ x - (y-x) ] + [ y - (y-x) ] = 38 . . 3x - y = 38................. eq-2 by multiplying eq-2 with 3 and then adding to the eq-1 3y - x = 126 9x - 3y = 114 -------------------- 8x = 240 x = 30 Putting x =30 to the eq-2 Y= 52 So son's age is 30 years and father's age is 52 years.



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When the son age will be as old as his father?
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Hint: In these types of questions use the given information to form the equation such as make one equation while considering the previous age of father and son then make a second equation using the new age of father and son use this information to get a better approach in this question.


Complete step-by-step solution:

In this question we have asked their present age, So, let us take the son’s current age” x “and father’s current age” y”. The question says that the son is going to be as old as the father is today, meaning the son has to live a certain number of years. How many years will he be aging? The difference between his current age and the current age of his father. So, to calculate a son’s age the son has to live certain years to reach his current age which means that if the son is 20 years old and the father was 50 years old, it would take the son 30 years to reach his current age which means the equation which will form will be : (y-x).

According to the question,

So, $\text{[father’s new age]} + \text{[son’s new age]}$ = 126

Therefore the equation will be $[y + (y - x)] + [(x + (y - x))] =126$

$ \Rightarrow 2y - x + y=126$

$ \Rightarrow 3y - x =126 $ ……………….(equation 1)

Similarly, $\text{[father’s previous age]} + \text{[son’s previous age]}$ =38

Thus the equation is $[y - (y - x)] + [x - (y - x)] =38$

$ \Rightarrow – x – y =38$

$ \Rightarrow y = 3x – 38 $ …………………..(equation 2)

Now substituting the value of y in equation (1)

$ \Rightarrow 3(3x – 38) - x =126$

$ \Rightarrow 9x -114 - x=126$

Therefore the son’s present age is 30

Now for father’s age substituting the value of x in equation 2

Hence, the son is 30 years old and the father is 52 years old.

Note: The equations we made using the given information in the above solution are linear equations, but what is a linear equation so the linear equation can be explained as equations that have only 2 variables the general form of a linear equation is $ax + by + c = 0$, for example, $2x + 3y + 6 = 0$.

When the son age will be as old as his father?

Text Solution

Solution : Let the present age of father be `x` years and that of his son be `y` years. <br> After `(x-y)` years son's age will be x years. i.e. he will be as old as his father. <br> After `(x-y)` years father's age will be <br> `x+(x-y)=(2x-y)` years <br> From the first condition. <br> `x+2x-y=126` i.e. `3x-y=126`...............1 <br> `(x-y)` years ago father's age was `y` years. <br> i.e. the father was as old as his son today. <br> `(x-y)` years ago, son's age was <br> `y-(x-y)=(2y-x)` years <br> From the second condition. <br> `y+2y-x=38` i.e. `-x+3y=38`.............2 <br> Multiplying equation (2) by 3, <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/NVT_21_MAT_P1_X_C07_E01_006_S01.png" width="80%"> <br> `:.y=30` <br> Substituting `y=30` in equation 1 <br> `3x-30=126 :.3x=156 :.x=52` <br> Ans. The present ages of father and son are 52 years and 30 years respectively.

Let son 's current age is x and his father 's current age is y.

Where does the(y-x) term come from? Well, it says 'when the son will be as old as the father is today, which means that the son has to age a certain amount of years. How many years does he have to age? The difference between his current age and his father 's current age.

For example, if the son was 10 and the father was 40, it would take the son 30 years (or y-x = 40-10) to reach his current age. In the meantime, the father would age the same amount (y - x = 40 - 10 = 30 years).

[Father 's new age] + [Son 's new age] = 126

[y+(y-x)] + [(x + (y-x))] = 126

⇒ 2y - x + y = 126

∴ 3y - x = 126 ----------(1)

[Father 's previous age] + [Son 's previous age] = 38

⇒ [y - (y-x)] + [x - (y-x)] = 38

⇒ x + x - y + x = 38

⇒ 3x - y = 38

∴ y = 3x - 38 -----------(2)

Now sub equ(2) into equation 1

⇒ 3(3x-38) - x = 126

⇒ 9x - 114 - x = 126

⇒ 8x = 240

∴ x = 30 

Now y = 3x - 38

⇒ y = 3(30) - 38

∴ y = 52 

The son is 30 years old, and the father is 52 years old.