Q1: Keeping the instrument height as 1.5 m, length of staff 4 m, the slope of the ground as 1 in 10, the sight on the down-slope, must be less than

ANS:B - 25 m

In a simple way we can say that;
Let consider the slope is downward which 1 in 10.
So at 10m, the staff reading becomes 1. 5+1=2. 5m (staff reading).
At 20 m distance reading becomes 3. 5m.
Similarly, at 25 m distance, the reading becomes 4m. Which is the full length of the staff? By similar triangles;
1/10 = (4-1.5)/X
X = 2.5(10) = 25m. If we are levelling on the sloped surface then we need to keep staff near the instrument, otherwise, it will not be visible inside the instrument because of the slope (if the distance is more).
so here is the formula, UNDER WHICH DISTANCE WE MUST KEEP STAFF,
Sight= (Staff ht.- instrument ht.)/(1/10)
= (4 - 1.5) /0.1,
= 2.5/0.1,
= 25m.

If you will keep the staff more than 25m away from the instrument , IT WILL NOT BE VISIBLE INSIDE THE INSTRUMENT, The Hi is 1.5m so when and staff 4m.
The reading will be 2.5m on staff on plane. The slope being 1 in 10.
2.5 * 10 = 25 on down slope. Slope = 1/10.
HI = 1.5m.

Height of staff = 4.0 m.
Sight = (4-1.5)/(1/10) = 25 m.