Question

A has Rs. 9 and B has Rs. 4.20. After B has won a certain sum from A, A has five sixth of what B has. How much did B win?
Rs. 2
Rs. 3
Rs. 4
Rs. 5

Answer 1

Hint: We will observe the given data and form a linear equation to get the required answer. A linear equation is any equation that can be written in the form
\[ax + b = 0\]
where a and b are real numbers and $x$ is a variable.
Use a linear equation to solve the question.

Complete step by step answer:
To solve this question, we will form equations by using the above statement. So we can assume that B has won = Rs $x$. Now B has Rs. (4.20 + $x$). And A is left with Rs. $(9 - x)$ which is equal to Rs. $\dfrac{5}{6}\left( {4.20 + x} \right)$.
Step by step solution:
Let B has win = Rs $x$
According to the statement,
B has won a certain sum from A, So, after winning,
B has Rs. 4.20 + $x$
Now,
A has = Rs (9 - $x$) because A has lose some money which is equal to Rs $x$
Which can also be calculated as $\dfrac{5}{6}\left( {4.20 + x} \right)$. That means
$(9 - x)$ = $\dfrac{5}{6}\left( {4.20 + x} \right)$
Cross multiply by 6
$6\left( {9 - x} \right) = 5\left( {4.20 + x} \right)$
On simplifying the above equation,
$54 - 6x = \left( {5 \times 4.20} \right) + 5x$
$54 - 6x = 21 + 5x$
On simplifying the above equation,
$\Rightarrow$ $54 - 21 = 5x + 6x$
$\Rightarrow$ $33 = 11x$
On further simplification, we get
$\Rightarrow$ $x = \dfrac{{33}}{{11}} = 3$

$\therefore$ B has won Rs.3. Hence, the correct option is B

Note:There is one more way to do the calculation. We can change Rs. into Paisa. We can write Rs 9 as 900 paise and Rs.4.20 can be taken as 420 paise. Else everything is the same. Only we need to replace the values.