Question

The sum of one fifth, one third and one ninth of a number is 29. Find the numbers.
A) 45
B) 29
C) 54
D) None of these

Answer 1

Hint: Here we will first assume the unknown number, then form the equation. Solve the equation to get the required number.

Complete step-by-step solution:

Given: Sum of one fifth, one third and one ninth of a number is 29.
Let the required number is \[x\].
One fifth of the number be \[\dfrac{x}{5}\].
One third of the number is $\dfrac{x}{3}$.
And one ninth of the number be $\dfrac{x}{9}$.
According to the question, $\dfrac{x}{5} + \dfrac{x}{3} + \dfrac{x}{9} = 29$.
$ \Rightarrow \dfrac{{9x + 15x + 5x}}{{45}} = 29$
$ \Rightarrow \dfrac{{29x}}{{45}} = 29$ $ \Rightarrow 29x = 29 \times 45$
$ \Rightarrow x = \dfrac{{29 \times 45}}{{29}}\therefore x = 45$.

Hence, correct option be A.

Note:In such types of questions where a relation between terms is given and value is assigned to equate with expression. First assume unknown quantity which must relate with as many possible terms. Then form the equation and solve it to find the value of the required number.