Question

If a number exceeds $20$ of itself by 40. Then the number is
(a) 500
(b) 50
(c) 25
(d) 10

Answer 1

Hint:Let the number be x. Then 20% of x will be $\dfrac{20x}{100}$. Also the number exceeds itself by 40, therefore forming the equation from the given condition, we get $x-$\dfrac{20x}{100}$=40$. We will now solve this equation to find the number x.

Complete step-by-step answer:
It is given in the question that a number exceeds 20% of itself by 40, then we have to find the number.
Let us assume that the required number is x. Then 20% of x will be $\dfrac{20}{100}\times x=\dfrac{20x}{100}=\dfrac{x}{5}$.
So from the question statement we get the difference between the first number x and the second number $\dfrac{x}{5}$ which is 20% of x is 40. Therefore, we get,
$x-\dfrac{x}{5}=40$
Solving the equation by taking LCM in LHS as 5, we get
$\dfrac{5x-x}{5}=40$
$\dfrac{4x}{5}=40$
On cross multiplying LHS and RHS, we get,
$4x=40\times 5=200$
$x=\dfrac{200}{4}=50$
Therefore the required number is 50 and option b) is the correct answer.

Note: Students may miss-understand this question as 20% of x is 40 and they may solve the question completely wrong by forming a totally incorrect equation. Also, 20% of x will result in $x=200$, which is not correct because the question asked is different thus it is recommended to understand the question carefully prior to jumping on the solution to solve the question early. Also, students have to understand the question statement properly to avoid any mistake of + and – sign in the equation.