Question

Six more than one-fourth of a number is two-fifth of the same number. Then the number is
A) 40
B) 35
C) 25
D) 45

Answer 1

Hint: We can let the required number equal to a variable, then make an equation according to the given statement. By solving this equation, we will get the value of the variable and thus the required number.

Complete step-by-step answer:
We are required to find the number that satisfies the given statement. Let the required number be x.
One-fourth of this number is given as:
 $ \dfrac{1}{4} \times x \Rightarrow \dfrac{x}{4} $
Two-fifth of this number is given as:
 $ \dfrac{2}{5} \times x \Rightarrow \dfrac{{2x}}{5} $
The given statement is:
Six more than one-fourth of this number is equal to two-fifth of the same number. According to this statement, the equation obtained is given as:
 $
  \dfrac{x}{4} + 6 = \dfrac{{2x}}{5} \\
  \Rightarrow \dfrac{{2x}}{5} - \dfrac{x}{4} = 6 \;
  $
LCM of 5 and 4 will be their product i.e. 20. So, by taking LCM:
 $
  \Rightarrow \dfrac{{2x \times 4 - x \times 5}}{{20}} = 6 \\
  \Rightarrow \dfrac{{8x - 5x}}{{20}} = 6 \\
  \Rightarrow 8x - 5x = 6 \times 20 \\
  \Rightarrow 3x = 120 \\
   \Rightarrow x = \dfrac{{120}}{3} \\
   \Rightarrow x = 40 \;
  $
Thus the required number is $ 40 $.
Therefore, the number which satisfies the given statement is 40 and the correct option is A).
So, the correct answer is “Option A”.

Note: Instead of taking LCM by making a common base, we can follow another route that is:
We can directly multiply all the terms present on RHS and LHS of the equation by the LCM of the two denominators present on LHS like:
 \[
  \dfrac{{2x}}{5} \times 20 - \dfrac{x}{4} \times 20 = 6 \times 20 \\
   \Rightarrow 8x - 5x = 120 \;
 \]
As we had only one variable in this equation whose maximum power is 1, it is known as linear equation in one variable.