# 10.(iii) A water tank has steps inside it. A monkey is sitting on the topmost step (i.e., the first step). The water level is at the ninth step.(iii) If the number of steps moved down is represented by negative integers and the number of steps moved up by positive integers, represent his moves in part (i) and (ii) by completing the following; (a) – 3 + 2 – ... = – 8 (b) 4 – 2 + ... = 8. In (a) the sum (– 8) represents going down by eight steps. So, what will the sum 8 in (b) represent?

H Harsh Kankaria

If we represent the down steps by negative and up steps by positive then:

Moves in (i):

$- 3 + 2 - 3 + 2 - 3 + 2 - 3 + 2 - 3 + 2 - 3 = -8$

Also,

Moves in part (ii):

$4 - 2 + 4 - 2 + 4 = 8$

Therefore, the sum +8 represents going up by eight steps.

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