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Aman gave $40\% $ of the amount he had to Rohan. Rohan in turn gave one-fourth of what he received from Aman to Sahil. After paying Rs. $200$ to the taxi driver out of the amount he got from Rohan, Sahil now has Rs. $600$ left with him. How much will Aman have.
(A) 4000
(B) 8000
(C) 12000
(D) Data inadequate
Answer
![Verified]()
Verified
Verified
Hint: In this type of question we have to choose one person’s amount as variable “$X$” and rest are calculated by converting all in the form of variable $X$.
Complete step-by-step answer:
Let the amount with Aman be Rs. $X$, because we have to find how much money Aman will have.
Now according to the question Aman gave $40\% $ of the amount he had to Rohan.
Amount received by Rohan = $40\% $ of $X$
That is $\dfrac{{40 \times X}}{{100}}$
Now amount received by Sahil is $\dfrac{1}{4}$of Rohan’s amount
So total amount received by Sahil = $\dfrac{1}{4} \times \dfrac{{40 \times X}}{{100}}$
Total amount received by Sahil = $\dfrac{X}{{10}}$
Now the question says that after giving Rs.$200$ to the taxi driver Sahil have Rs.$600$as remaining amount
So $600 + 200 = \dfrac{X}{{10}}$
$800 = \dfrac{X}{{10}}$
By using cross-multiplication in above equation
From this we get $X = 8000$
And we choose $X$ as the amount of Aman, therefore we get an amount of Aman as Rs.$8000$.
Option B is the correct answer.
Note:This is the basic question of linear equations in one variable. Linear equations in one variable are always in the form of \[ax + b = c\]. In this type of question do not take more than one variable that creates a solution complicated.
Complete step-by-step answer:
Let the amount with Aman be Rs. $X$, because we have to find how much money Aman will have.
Now according to the question Aman gave $40\% $ of the amount he had to Rohan.
Amount received by Rohan = $40\% $ of $X$
That is $\dfrac{{40 \times X}}{{100}}$
Now amount received by Sahil is $\dfrac{1}{4}$of Rohan’s amount
So total amount received by Sahil = $\dfrac{1}{4} \times \dfrac{{40 \times X}}{{100}}$
Total amount received by Sahil = $\dfrac{X}{{10}}$
Now the question says that after giving Rs.$200$ to the taxi driver Sahil have Rs.$600$as remaining amount
So $600 + 200 = \dfrac{X}{{10}}$
$800 = \dfrac{X}{{10}}$
By using cross-multiplication in above equation
From this we get $X = 8000$
And we choose $X$ as the amount of Aman, therefore we get an amount of Aman as Rs.$8000$.
Option B is the correct answer.
Note:This is the basic question of linear equations in one variable. Linear equations in one variable are always in the form of \[ax + b = c\]. In this type of question do not take more than one variable that creates a solution complicated.
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