Question

At least how much money should a man earn so that he may be left with not less than Rs. 600 after giving half of his money to his wife and one – eighth to each of his two sons?
A) 2000
B) 2400
C) 2800
D) 3200

Answer 1

Hint: We will first assume the amount of money he should have and then apply all the given conditions as given in the question to form the required inequality and thus, we will have the answer.

Complete step-by-step solution:
Let us assume that the man had Rs. x initially. ……………..(1)
Now, since he gave half of the money to his wife, that means he gave Rs. $\dfrac{x}{2}$ to his wife and he is left with Rs. $x - \dfrac{x}{2} = \dfrac{x}{2}$. ……………(2)
Now, after this, he gave up one – eighth of the money he had to both of his sons, that means he gave Rs. $\dfrac{x}{8}$ to each of his sons.
$ \Rightarrow $ He gave Rs. $2 \times \dfrac{x}{8}$ to his sons which is equal to Rs. $\dfrac{x}{4}$. …………….(3)
Now, we are also given that he should have been left with more than Rs. 600 at end after giving the required amount to his wife and sons. Therefore, forming the inequality as per the conditions in the equations (1), (2) and (3), we will then obtain:-
$ \Rightarrow x - \dfrac{x}{2} - \dfrac{x}{4} \geqslant 600$
Simplifying the LHS of above expression by taking LCM, we will then obtain:-
$ \Rightarrow \dfrac{{4x - 2x - x}}{4} \geqslant 600$
Simplifying the numerator of LHS, we will then obtain the following expression:-
$ \Rightarrow \dfrac{x}{4} \geqslant 600$
Taking the 4 from division in the denominator in LHS to multiplication in RHS, we will then obtain:-
$ \Rightarrow x \geqslant 600 \times 4 = 2400$

$\therefore $ The correct option is (B).

Note: The students must note that we cannot use the assumption that she had Rs. 100 with us because that thing can only work if we have to find a ratio or percentage or anything like this which does not actually require the amount.
The students might make the mistake of forgetting to encounter the money given to both the sons and take only one son’s amount to get the answer which will lead to the wrong answer.