Question

The difference between a number and its three – fifth is 50. What is the number?
(a) 75
(b) 100
(c) 125
(d) None of these

Answer 1

Hint: Assume the required number as x. Now, form a linear expression in x by subtracting the fraction three – fifth of x from x and equate it with 50. Solve for the value of x by making its coefficient equal to 1 using simple arithmetic operations like addition, subtraction, multiplication and division to get the answer.

Complete step-by-step solution:
Here we have been given with the sentence that ‘the difference between a number and its three – fifth is 50’. We are asked to find the number but first we need to form an expression to solve for the variable.
Now, let us assume the unknown number as x. So we have its three – fifth values equal to $\dfrac{3x}{5}$. It is said the difference of x and $\dfrac{3x}{5}$ is equal to 50, so we get,
$\Rightarrow x-\dfrac{3x}{5}=50$
Clearly the above equation is a linear equation in x, so let us solve this equation using simple arithmetic operations. Multiplying both the sides with 5 we get,
$\begin{align}
  & \Rightarrow 5x-3x=250 \\
 & \Rightarrow 2x=250 \\
\end{align}$
Dividing both the sides with 2 and cancelling the common factors we get,
$\therefore x=125$
Hence, option (c) is the correct answer.

Note: Note that one can check the answer by substituting the obtained value of x in the equation formed according to the statement provided in the question. Solve the L.H.S part only and if it is equal to 50 then our answer is correct. Here we haven’t been told that we are squaring, cubing or changing the exponent of the variable and that is why a linear equation is formed.