Question

Ramdeen gave 40 % of his total property to his son. He gives 60% of the balance to his daughter and the remaining sum to his wife. If the wife got Rs. 1920 less than daughter. Find the value of his property.

Answer 1

Hint: Here first we will assume the total property to be x. Then we will evaluate the share of the son and daughter and wife and form a linear equation to evaluate the value of x.

Complete step-by-step answer:
Let us assume the total property to be x.
Now it is given that, the son gets 40% of the share
Hence the share of son is:-
\[ = 40\% {\text{of x}}\]
\[{\text{ = 0}}{\text{.40x}}\]
Now the remaining property is given by:-
\[ = x - {\text{0}}{\text{.40x}}\]
\[ = 0.60x\]
Now it is given that, the daughter gets 60% share of the remaining property
Hence, the share of daughter is given by:-
\[ = 60\% {\text{ of }}0.60x\]
\[ = 0.36x\]
Now the remaining balance is given by:-
\[ = 0.60x - 0.36x\]
\[ = 0.24x\]which is the wife’s share
Now it is given that, wife got Rs. 1920 less than daughter
Hence,
\[{\text{daughter's share}} - {\text{wife's share}} = {\text{1920}}\]
Putting in the respective values we get:-
\[0.36x - 0.24x = 1920\]
Simplifying it further we get:-
\[0.12x = 1920\]
Solving it for x we get:-
\[x = \dfrac{{1920}}{{0.12}}\]
\[x = 16000\]

Hence, the total property is 16000 Rs.

Note: In such questions we have to form the linear equation in one variable i.e. the equation has the highest power of the variable as 1 and then solve for the value of that variable to get the desired answer.
The linear equation in two variables has two variables each with highest power as 1.
Here students should take note that the share of daughter and the wife is from the remaining balance and not the total balance.