Question

Shuba got three fourth of what Alka had. Alka gave half of what remained with her to Mohini. If Mohini got Rs 625 how much did Alka have in the beginning?
A.Rs 3750
B.Rs 7000
C.Rs 5000
D.Rs 5625

Answer 1

Hint: To solve this question first thing we should assume some value to what Alka had and then whatever is given in the question, we should proceed accordingly. The linear equation solutions will produce values which make the equation true when the unknown values are replaced. There is only one solution in the case of one variable, such as $ x + 1 = 0 $ .

Complete step-by-step answer:
Given, Shuba got three fourth of what Alka had. Alka gave half of what remained with her to Mohini and Mohini got Rs 625.
Let, Alka is having Rs x in the beginning.
As, Shubha got three-fourth of what Alka had, so this means, Shubha got $ \dfrac{{3x}}{4} $ .
Now, let us calculate how much Alka is having after giving three-fourth to Shubha, that is $ \dfrac{{3x}}{4} $ .
So,
Alka is having x and giving three-fourth to Shubha, so the difference between these two gives in result what Alka is having.
 $ x - \dfrac{{3x}}{4} = \dfrac{{4x - 3x}}{4} = \dfrac{x}{4} $
Therefore, Alka has $ \dfrac{x}{4} $ , after giving three-fourth to Shubha.
Now, Alka gave half of what remained with her to Mohini and Mohini got Rs 625.
As Alka is having $ \dfrac{x}{4} $ , so half of it is given to Mohini.
So,
 $
\Rightarrow \dfrac{x}{4} \times \dfrac{1}{2} = 625 \\
\Rightarrow \dfrac{x}{8} = 625 \\
\Rightarrow x = 625 \times 8 \\
\Rightarrow x = 5000 \;
 $
Therefore, Alka has Rs 5000 in the beginning.
So, the correct answer is “5000”.

Note: This question is based on linear equations in one variable, If there is a homogeneous variable (i.e. just one variable) in the equation, then this type of equation is defined as a single variable linear equation. A line equation is obtained in various terms by comparing zero to a linear polynomial over some field from which the coefficients are taken.