Question

[Subject :- Maths]
[Class 7 Maths Chapter 1 Integers]

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.

(i) He jumps 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level?

(ii) After drinking water, he wants to go back. For this, he jumps 4 steps up and then jumps back 2 steps down in every move. In how many jumps will he reach back the top 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?

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Answer 1

Solution :-

→ In first jump money goes down = (-3) steps

then,

→ In second jump Money goes up = 2 steps

so,

→ In 2 Jumps he cover = (-3) + 2 = (-1) steps .

then,

→ (-1) step = in 2 jumps

→ (-6) steps = 6 * 2 = 12 jumps .

now, the monkey is in 6th step and water is at 9th step .

therefore,

→ In next Jump he goes to = (-6) + (-3) = 9th step and Drinks the water.

Hence, in 13 jumps he will reach the water level .(Ans.i)

now,

→ In first jump money goes up = 4 steps

then,

→ In second jump Money goes down = 2 steps

so,

→ In 2 Jumps he cover = 4 - 2 = 2 steps. (sum)

then,

→ 2 step = in 2 jumps

→ 5 steps = 5 jumps .

now, the monkey is in 6th jump he goes 4 steps up and reached at the topmost (5 + 4 = 9 steps) .

therefore,

→ Total jumps needed to reach back on top = 5 + 1 = 6 jumps (Ans.)

Answer 2

(i)$1st jump 1+3=4th\ step1+3=4th step$

$2nd jump 4-2=\ 2nd\ step\4−2= 2nd step$

$3rd jump 2+3=5th\ step\2+3=5th step$

$4th jump 5-2=\ 3rd\ step\5−2= 3rd step$

$5th jump 3+3=6th\ step3+3=6th step$

$6th jump 6-2=4th\ step6−2=4th step$

$7th jump 4+3=7th\ step\4+3=7th step$

$8th jump 7-2\ =\ 5th\ step\7−2 = 5th step$

$9th jump 5+3=\ 8th\ step\5+3= 8th step$

$10th jump 8-2=\ 6th\ step\8−2= 6th step$

$11th jump 6+3=\ 9th\ step\6+3= 9th step$

he will reach 9th step in 11th jumps.

$(ii) 1st jump = 9-4=\ 5th\ step\9−4= 5th step$

$2nd jump = 5+2=\ 7th\ step5+2= 7th step$

$3rd jump = 7-4=\ 3rd\ step\7−4= 3rd step$

$4th jump = 3+2=\ 5th\ step\3+2= 5th step$

$5th jump = 5-4=\ 1st\ step\5−4= 1st step$

he reach back on the first step in fifth steps.

(iii)

$(a) -3+2-3+2-3+2-3+2-3+2-3+2-3+2-3+2=\ -8−3+2−3+2−3+2−3+2−3+2−3+2−3+2−3+2= −8$

$(b) 4-2+4-2+4-2+4-2=\ 84−2+4−2+4−2+4−2= 8$

thus, sum 8 in (b) represents going up by eight steps.