Question

If one-fourth of two-fifths of a number is $36$, what is the number?
A. $340$
B. $720$
C. $240$
D. $360$

Answer 1

Hint: Here, in the given question, we are given a statement and we need to solve it to find the number. We can let the required number equal to a variable (A variable is a symbol (usually a letter) standing for an unknown numerical value in an equation), then make an equation according to the statement. By solving this equation, we will get the value of the variable and thus the required answer.

Complete step by step answer:
We are required to find the number that satisfies the given statement. Let the required number be $x$. We are given, one- fourth of two-fifths of a number is $36$.One-fourth is written as, $\dfrac{1}{4}$. Two-fifths of a number is written as, $\dfrac{2}{5} \times x$.The given statement is: One- fourth of two-fifths of a number is $36$. This statement can be written as:
$ \Rightarrow \dfrac{1}{4} \times \dfrac{2}{5} \times x = 36$
On multiplication of terms written in denominator, we get
$ \Rightarrow \dfrac{2}{{20}} \times x = 36$
On division of terms written is left hand side, we get
$ \Rightarrow \dfrac{1}{{10}} \times x = 36$
Multiply both sides by $10$.
$ \Rightarrow \dfrac{{10}}{{10}} \times x = 36 \times 10$
On canceling-out common terms, we get
$ \Rightarrow x = 36 \times 10$
On multiplication of terms, we get
$ \therefore x = 360$

Therefore, the correct option is D.

Note: Remember that, OF in algebra means to multiply and BY in algebra means to divide. Remember that if we add the same number to both sides, or subtract the same number from both sides, or multiply both sides by the same non-zero number, or divide both sides by the same non-zero number, the balance remains undisturbed. Transporting means moving from one side to the other. When a term is transposed from one side of the equation to the other side, its sign gets changed. We should take care of the calculations so as to be sure of our final answer.