Question

The sum of weights of father and son is 85 kg. The weight of the son is $\dfrac{1}{4}$ of the weight of the father. Find their weights.

Answer 1

Hint:
Let us consider the weight of father is x and that of son is y. Then we get two equations from the question as \[x + y = 85\] and \[y = \dfrac{1}{4}x\]. We will put the value of one variable in the form of another in another equation and then find the value of their weights.

Complete step by step solution:
Given that the sum of weights of father and son is 85 kg. So let father’s weight be x kgs and son’s weight be y kgs.
So the equation will be
  \[x + y = 85\]……eq1
But one more condition given is the weight of the son is \[\dfrac{1}{4}\] of the weight of the father. So it can be written as \[y = \dfrac{1}{4}x\]…..eq2
From eq1 we get \[x = 85 - y\]. Putting this in eq2,
\[y = \dfrac{1}{4}\left( {85 - y} \right)\]
Multiplying the terms by \[\dfrac{1}{4}\] we get
\[ \Rightarrow y = \dfrac{{85}}{4} - \dfrac{y}{4}\]
Taking terms with y on one side,
\[ \Rightarrow y + \dfrac{y}{4} = \dfrac{{85}}{4}\]
Taking LCM on right side we get,
\[ \Rightarrow \dfrac{{4y + y}}{4} = \dfrac{{85}}{4}\]
Cancelling 4 from both sides,
\[ \Rightarrow 4y + y = 85\]
\[ \Rightarrow 5y = 85\]
Dividing 85 by 5 we get,
\[ \Rightarrow y = \dfrac{{85}}{5} = 17\]
This is the weight of my son \[17kgs\]. Now to find the weight of father we will use eq1.
\[x = 85 - y\]
Putting the value of y in above equation
\[ \Rightarrow x = 85 - 17 = 68\]
This is the weight of my father \[68kgs\].

Thus the weights of father and son are 68 and 17 respectively.

Note:
In this problem if we have to cross verify we can use eq1 or eq2.These are equations with 2 variables and thus it needs 2 equations to be formed. Only write the conditions carefully because if they get revered we will get the wrong answer. Like here the weight of the son is $\dfrac{1}{4}$ of father and not reverse.