Question

Mr. J left his entire estate to his wife, his daughter, his son, and the cook. His daughter and son got half the estate, sharing in the ratio of 4 to 3. His wife got twice as much as the son. If the cook received a bequest of Rs. 500, then the entire estate was:
A. Rs 3500
B. Rs 5500
C. Rs 6500
D. Rs 7000
E. Rs. 7500

Answer 1

Hint: In order to solve these questions, we need to extract the information given in the question and frame the equation. We will start with assuming the total cost is equal to a or some variable and in the same manner as conditions given in the question we will frame other equations and then solve them to reach our answer.

Complete step-by-step answer:
Let the worth of entire estate of Mr. J be a
Now we will frame the equations according to the conditions given in the question.
Cost of the entire estate = a
Since his son and daughter got the share in the ratio 4:3
Therefore
Let the share of son = 3x
And the share of daughter = 4x
It is given that the sum of the share of the daughter and son is equal to half of the total share
Therefore
$
   \Rightarrow 3x + 4x = \dfrac{a}{2} \\
   \Rightarrow 7x = \dfrac{a}{2} \\
   \Rightarrow x = \dfrac{a}{{14}} \\
$
Therefore the share of the daughter is \[\dfrac{{2a}}{7}\] and the share of the son is $\dfrac{{3a}}{{14}}$
It is given that the share of his wife is twice the share that his son got
Share of wife = 2 times share of son
Share of wife = $\dfrac{{3a}}{7}$
As the half share is divide between son and daughter, therefore the half share must be divided between the cook and the wife
Therefore the share that cook got is
Share of wife + share of cook = $\dfrac{a}{2}$
$
  \dfrac{{3a}}{7} + x = \dfrac{a}{2} \\
  x = \dfrac{a}{2} - \dfrac{{3a}}{7} \\
  x = \dfrac{a}{{14}} \\
 $
It is given that the cook got a bequest of Rs 500
Therefore the cost of entire estate is
$
  \dfrac{a}{{14}} = 500 \\
  a = 7000 \\
$
Hence, the cost of entire estate is Rs. 7000
Hence the correct option is D.

Note: In order to solve these types of questions, you need to have a good concept for solving linear algebraic equations or quadratic equations. In the above question we have only linear equations while in some questions we may encounter with quadratic equations. Also remember that in order to find the solution of an equation the number of variables of the equations must be equal to the number of equations.