Question

A father divides his property among his 3 sons such that the eldest son's share is double the second son's share and the share of the second son is triple the third son's share. If the second son gets Rs.4000 more than the third, find the value of the total property.
A. $Rs.10000$
B. $Rs.20000$
C. $Rs.5000$
D. $Rs.2000$

Answer 1

Hint: The sum of all the three son’s shares is the value of the total property of the father. If the share of three sons is x, y, and z. According to question, \[2y = z,y = x + 4000\] and $y = 3x.$ We further have to find the sum of $x,y$ and $z.$

Complete step-by-step answer:
Let the share of three sons be $x,y$ and $z$
Given, the eldest son's share is double the second son's share.
$
   \Rightarrow 2y = z \\
    \\
 $
And, the share of the second son is triple the third son's share.
$ \Rightarrow y = 3x$
The second son gets Rs.4000 more that the third son, this gives
$ \Rightarrow y = x + 4000$
Putting $y = 3x$ in the above equation, we get
$
   \Rightarrow 3x = x + 4000 \\
   \Rightarrow 2x = 4000 \\
   \Rightarrow x = 2000 \\
 $
Hence, the share of the third son we get is $x = Rs.2000$
The share of second son is $y = $ $3x = Rs.6000$
The share of third son is $z = 2y = Rs.12000$
The value of the total property of the father is $x + y + z$
$ \Rightarrow x + y + z = 2000 + 6000 + 120000 \\
   \Rightarrow Rs.20000 \\
$

So, the correct answer is “Option B”.

Note: An important aspect to notice and keep in mind is that the elder son is the first son. When in question it says that the eldest son's share is double the second son's share. It means that the first son’s share is double the second son’s share.