UPSEE Solved Model Paper 7

Given
5 (x) = x + [x] ... (i)
and [x] - (x) =

1

2

... (ii)
where (x) and [x] are fractional part function and greatest integer function.
We have to find the value of x .
Consider, equation (i)
5 (x) = x + [x]
⇒ 5 (x) = [x] + (x) + [x] [Since, x = [x] + (x)]
⇒ 5 (x) = 2 [x] + (x)
⇒ 4 (x) = 2 [x]
⇒ (x) =

[x]

2

Substituting the value in (i), we get
[x] = 1 and (x) =

1

2

Now, x = (x) + [x]
⇒ x =

1

2

+1
⇒ x =

3

2

Hence , option 'B' is correct.