Answer VerifiedHint: 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.
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. 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. |