Question

Number of natural number satisfying the equation $\left[\frac{x}{49}\right]=\left[\frac{x}{51}\right]$ are (where $[.]$ denotes greatest integer function)

• A. $464$
• B. $575$
• C. $675$
• D. $624$

Answer 1

The correct option is D $624$

$\begin{array}{c}\left[\frac{x}{49}\right]=\left[\frac{x}{51}\right]\\ formx=1to48\left[\frac{x}{49}\right]=\left[\frac{x}{51}\right]=0numberofsolutions=48\\ fromx=51to97\left[\frac{x}{49}\right]=\left[\frac{x}{51}\right]=1numberofsolutions=47\\ fromx=102to146\left[\frac{x}{49}\right]=\left[\frac{x}{51}\right]=2numberofsolutions=45\\ fromx=153to195\left[\frac{x}{49}\right]=\left[\frac{x}{51}\right]=3numberofsolutions=43\\ numberofsolutions=48+47+45+43+...........\\ =48+\left(A.P.witha=47,d=-2and48+576=624n=24\right)\end{array}$