**Question 1:**

**The temperature (in degree Celsius) of different places on a particular day is represented using a number line.**

**i) Write the temperature of the places marked on the number line by observing it.**

**ii) Calculate temperature difference between the hottest place and the coldest place on the number line.**

**iii) Calculate the temperature difference between Lachung and Gangtok.**

**iv) Is the temperature of Gangtok and Majhitar taken together is less than the temperature at Majhitar? Is it also less than the temperature at Gangtok?**

**Answer:**

i) Following are the temperature of the places marked on the number line:

Places |
Temperature |

Shillong | 22^{o}C |

Siliguri | 14^{o}C |

Majhitar | 5^{o}C |

Gangtok | -2^{o}C |

Lachung | -8^{o}C |

ii) Temperature difference between the hottest and the coldest place =

Temperature of the hottest place (Shillong) â€“ Temperature of the coldest place (Lachung)

= 22^{o}C â€“ (-8^{0}C) = 22^{o}C + 8^{o}C = 30^{o}C

iii) Difference between Lachung and Gangtok = Temperature at Gangtok â€“ Temperature at Lachung

= -2^{o}C â€“ (-8^{o}C) = -2^{o}C + 8^{o}C = 6^{o}C

iv) Temperature of Gangtok and Majhitar taken together = -2^{o}C + 5^{o}C = 3^{o}C

Temperature at Majhitar = 5^{o}C

Therefore, 3^{o}C < 5^{o}C

Yes, the temperature of Gangtok and Majhitar taken together is less than the temperature at Majhitar.

Now, the temperature of Gangtok = -2^{o}C

Therefore, 3^{o}C > -2^{o}C

No, it is not less than the temperature at Gangtok.

**Question 2:**

**In a quiz, positive marks and negative marks are given for correct answers and incorrect answers respectively. If Sangamâ€™s scores in five successive round were 20, -2, -8, 12, and 15, what was his total at the end?**

**Answer:**

Given, Sangamâ€™s scores in five successive rounds are 20, -2, -8, 12, and 15.

Total marks obtained by Sangam = 20 + (-2) + (-8) + 12 + 15 = 37

Thus, Sangam obtained 37 marks in a quiz.

**Question 3:**

**At Gangtok, temperature on Monday was -5 ^{o}C. On Tuesday, the temperature dropped by 3^{o}C and on Wednesday it rose by 3^{o}C. Calculate the temperature on Tuesday and Wednesday.**

**Answer:**

At Gangtok, temperature on Monday = -5^{o}C

On Tuesday, temperature dropped by 3^{o}C

Therefore, Temperature on Tuesday = -5^{o}C â€“ 3^{o}C = -8^{o}C

On Wednesday, temperature rose up by = 3^{o}C

Therefore, Temperature on Wednesday = -8^{o}C + 3^{o}C = -5^{o}C

Thus, temperature on Tuesday was -8^{o}C and on Wednesday was -5^{o}C.

**Question 4:**

**The plane is flying at the height of 5000 m above sea level. A submarine is floating 1200 m below the sea level. Calculate the vertical distance between them when at a particular point the plane is exactly above the submarine.**

**Answer:**

Height of the plane above the sea level = 5000 m

Position of submarine below sea level = 1200 m

Therefore, the vertical distance between the plane and the submarine = 5000 + 1200 = 6200 m.

**Question 5:**

**Reuben deposits Rs 3,000 in his bank account. On the next day, he withdraws Rs 1,560. Find the balance in Reubenâ€™s account after the withdrawal.**

**Answer:**

Deposit amount = Rs 3,000 and Withdrawal amount = Rs 1,560

Therefore, Balance = 3,000 â€“ 1,560 = Rs 1,440

Thus, the balance in Reubenâ€™s account after withdrawal is Rs 1,440.

**Question 6:**

**From a point P, Priyanka goes 40 km towards east, to the point Q. From Q, she moves 60 km towards west along the same road. If the distance towards east is represented by a positive integer then, how will you represent the distance traveled towards west? By which integer will you represent her final position from P?**

**Answer:**

According to the number line, Priyanka moving towards east is represented by a positive integer. When she moves in the opposite direction, i.e. when she moves west, it is represented by a negative integer.

Distance from P to Q = 40 km

Distance from Q to R = 60 km

Distance from P to R = 40 â€“ 60 = -20 km

Thus, Priyanka is at a final position from P to R is -20 km.

**Question 7:**

**Check whether the following is a magic square (each row, column and diagonal have the same sum) or not.**

**Answer:**

Taking the first square box,

a) Taking rows

1 + (-10) + 0 = 1 â€“ 10 = -9

(-4) + (-3) + (-2) = -4 â€“ 3 â€“ 2 = -9

(-6) + 4 + (-7) = -6 + 4 â€“ 7 = -9

b) Taking columns

1 + (-4) + (-6) = -9

(-10) + (-3) + 4 = -9

0 + (-2) + (-7) = -9

c) Taking diagonals

1 + (-3) + (-7) = -9

0 + (-3) + (-6) = -9

This box is a magic square because all the sums are equal, i.e., -9.

Taking the second square box,

a) Taking rows

8 + 0 + (-8) = 0

(-5) + 5 + 0 = 0

(-3) + (-5) + 8 = 0

b) Taking columns

8 + (-5) + (-3) = 0

0 + 5 + (-5) = 0

(-8) + 0 + 8 = 0

c) Taking diagonals

8 + 5 + 8 = 21

(-8) + 5 + (-3) = -6

This box is not a magic square because not all the sums are equal.

**Question 8:**

**Verify x â€“ (-y) = x + y for the following values of x and y:**

**i) x = 22, y = 17**

**ii) x = 119, y = 124**

**iii) x = 76, y = 83**

**iv) x = 29, y = 10**

**Answer:**

i) Given: x = 22, y = 17

We have x â€“ (-y) = x + y

Putting the values in L.H.S. = x â€“ (-y) = 22 â€“ (-17) = 22 + 17 = 39

Putting the values in R.H.S. = x + y = 22 + 17 = 39**Â Â **

Since, L.H.S = R.H.S.

Hence, verified.

ii) Given: x = 119, y = 124

We have x â€“ (-y) = x + y

Putting the values in L.H.S. = x â€“ (-y) = 119 â€“ (-124) = 119 + 124 = 243

Putting the values in R.H.S. = x + y = 119 + 124 = 243

Since, L.H.S = R.H.S.

Hence, verified.

iii) Given: x = 76, y = 83

We have x â€“ (-y) = x + y

Putting the values in L.H.S. = x â€“ (-y) = 76 â€“ (-83) = 76 + 83 = 159

Putting the values in R.H.S. = x + y = 76 + 83 = 159

Since, L.H.S = R.H.S.

Hence, verified.

iv) Given: x = 29, y = 10

We have x â€“ (-y) = x + y

Putting the values in L.H.S. = x â€“ (-y) = 29 â€“ (-10) = 29 + 10 = 39

Putting the values in R.H.S. = x + y = 29 + 10 = 39

Since, L.H.S = R.H.S.

Hence, verified.

**Question 9:**

**Use the sign >, < or = in the blank spaces to make the statement correct:**

**i) (-7) + (-5) ______ (-7) â€“ (-5)**

**ii) (-2) + 6 â€“ (-18) ______ 14 â€“ 6 â€“ (-8)**

**iii) 22 â€“ 43 + 11 ______ 22 â€“ 43 â€“ 11**

**iv) 40 + (-23) â€“ 15 ______ 20 + (-22) + 54**

**v) (-230) + 80 + 50 ______ (-299) + 160 + 80**

**Answer:**

i) (-7) + (-5) ______ (-7) â€“ (-5)

-7 â€“ 5 ______ -7 + 5

-12 ______ -2

-12 < -2

ii) (-2) + 6 â€“ (-18) ______ 14 â€“ 6 â€“ (-8)

-2 +6 +18 ______ 14 â€“ 6 + 8

22 ______ 16

22 > 16

iii) 22 â€“ 43 + 11 ______ 22 â€“ 43 â€“ 11

-10 ______ -32

-10 > -32

iv) 40 + (-23) â€“ 15 ______ 20 + (-22) + 54

40 â€“ 23 â€“ 15 ______ 20 â€“ 22 +54

2 ______ 52

2 < 52

v) (-230) + 80 + 50 ______ (-299) + 160 + 80

-230 + 80 +50 ______ -299 +160 +80

-100 ______ -59

-100 < -59

**Question 10:**

**A monkey is sitting on the topmost step (i.e., the first step) of a water tank. The level of water is at the ninth step:**

**a) The monkey jumps 3 steps down and then jumps back 2 steps up. In how many jumps he can reach the water level.**

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

**c) If the number of steps moved down and the number of steps moved up is represented by negative integers and positive integers respectively, represent his moves in parts (a) and (b) by completing the following:**

**i)-3 + 2 â€“ ______ = -8Â Â Â Â Â Â Â **

**ii) 4 â€“ 2 + ______ = 8**

**Â Â Â Â Â In (i) the sum (-8) represent going down by eight steps. So, what will the sum 8 in (ii) represent?**

**Â **

**Answer:**

a) Monkey jumps 3 steps down and jumps back 2 steps up. The jumps of monkey can be represented by following number ray:

First jump = 1 + 3 = 4 steps

Second jump = 4 â€“ 2 = 2 steps

Third jump = 2 + 3 = 5 steps

Fourth jump = 5 â€“ 2 = 3 steps

Fifth jump = 3 + 3 = 6 steps

Sixth jump = 6 â€“ 2 = 4 steps

Seventh jump = 4 + 3 = 7 steps

Eighth jump = 7 â€“ 2 = 5 steps

Ninth jump = 5 + 3 = 8 steps

Tenth jump = 8 â€“ 2 = 6 steps

Eleventh jump = 6 + 3 = 9 steps

He will reach ninth steps in 11 jumps.

b)Â Thus monkey reach back on the first step in fifth jump.

c)

i) -3 + 2 â€“ 3 + 2 â€“ 3 + 2 â€“ 3 + 2 â€“ 3 + 2 â€“ 3 + 2 -3 + 2 â€“ 3 + 2 = -8

ii) 4 â€“ 2 + 4 â€“ 2 + 4 â€“ 2 + 4 â€“ 2 = 8

Thus, sum 8 in (ii) represents going up by eight steps.