CAT Exam Model Paper 5 with solutions for free online practice

{x} = x - [x]
or {x} + [x] = x
The given equation
5[x] + 3{x} = 6 + x ⇒ 2[x] + 3([x] + {x}) = 6 + x
reduces to
2[x] + 3x = 6 + x
or 2[x] + 2x = 6
or [x] + x = 3
Since 3 and [x] are both integers, in the above equation x must also be an integer.
⇒ [x] = x
Hence, 2x = 3 or x = $\frac{3}{2}$
This contradicts what we assumed above.
So no real value of x satisfies the given equation.