Question

One-fourth of a number exceeds one-fifth of the succeeding number by 3. Find the number.

Answer 1

★ Given : One-fourth of a number exceeds one-fifth of the succeeding number by 3.

$\rule{140}1$

★ To Find : the number = ?

$\rule{140}1$

★ Solution :

$\begin{lgathered}\bullet\:\:\textsf{Let the number be \textbf{x}}\\\\\bullet\:\:\textsf{Succeeding number = \textbf{x + 1}}\end{lgathered}$

$\rule{170}2$

☯$\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies\sf \dfrac{1}{4}\big\{x \big\} - \dfrac{1}{5}\big\{x + 1\big\} = 3\\\\\\:\implies\sf \dfrac{5x - 4\big\{x + 1\big\}}{20} = 3 \\\\\\:\implies\sf 5x - 4x - 4 = 3 \times 20 \\\\\\:\implies\sf 5x - 4x - 4 = 60\\\\\\:\implies\sf 5x - 4x = 60 + 4 \\\\\\:\implies\underline{\boxed{\textsf{x = 64}}}\:\:\:\:\:\Bigg\lgroup \textbf{ Required number} \Bigg\rgroup$

$\therefore\:\underline{\textsf{The required number is \textbf{64}}}.$

$\rule{170}2$