A dumpy level was set up at mid-point between pegs A and B, 80 m apart and the staff readings were 1.32 and 1.56. When the level was set up at a point 10 m from A on BA produced, the staff readings obtained at A and B were 1.11 and 1.39. The correct staff reading from this set up at S should be

ANS:B - 1.345

1.32+1.56=2.88/2=1.44,
1.11+1.39=2.50/2=1.25,
Now 1.44+1.25=2.69/2= 1.345 ans. For mid point station { 1.56-1.32=.24} for second station {1.39-1.11=.28}.
The difference in reading shows collimation error , which is .28-.24=.04,
.04 is collimation error in 80 m.therefore in 90m = (.04/80)*90=.045,
Now correct reading at B = 1.39 - .045 = 1.345. The difference in level b/w A and B:1.56-1.32=.24.
Apparent difference = 1.39-1.11 = .28,
True difference = 1.11 + .24 = 1.35,
Collimation error in 80m = 1.39-1.35 = 0.04.
Collimation error in 90m=(.04 * 90)÷80 = .045m.
Nd correction =.045m.
Correct staff reading on B=1.390-.045=1.345m.