# Exercise – 1.1

Q1. Following number line shows the temperature in degree Celsius  (0C) at different places on a particular day .

SOLUTION:-

(A) Observe this number line and write the temperature of the places marked on it .

SOLUTION:-

By observing the number line we can find the temperature of the cities as follows,

Temperature at the lahulspiti is -80C

Temperature at the Srinagar is -2oC

Temperature at the shimla is 50C

Temperature at the bengaluru is 22oC

(B)  What is the temperature difference between hottest and coldest places among the above?

SOLUTION:-

From the number

line we observe that ,

The temperature at the hottest places bengaluru  is 220C

The temperature at the coldest places lahulspiti -80C

Temperature difference between hottest and coldest place is = 22oC – (-8oC)

= 22OC + 8OC

= 300C

(C)  What is the temperature difference between lahulspiti and Srinagar ?

SOLUTION:-

From the given number line

The temperature at the Srinagar is -20C

The temperature at the lahulspiti  -80C

The temperature difference between lahulspiti and Srinagar is = -20C – (-80C)

=  -2OC + 8OC

=  6OC

(D) Can we say temperature of Srinagar taken together is less than the the temperature at shimla ? Is it also less than the temperature at Srinagar ?

SOLUTION:-

From the given number line

The temperature at Srinagar = -20C

The temperature at shimla  = 50C

The temperature of srinagar   and shimla taken together is = – 2oC + 5OC

= 30C

50C  > 30C

So the temperature of Srinagar and shimla taken together is less than the temperature at shimla.

Then,

30C > -20C

No , the temperature of Srinagar  and shimla taken together is not less than the temperature of Srinagar .

Q2. In a quiz positive marks are given for correct answers and negative marks given for the wrong answers . If JACK scores in five successive rounds were 25,-5,-10,15 and 10 ,what was his total at the end ?

ANS –   FROM THE QUESTION

JACK SCORED IN FIVE SUCCESSIVE ROUNDS 25,-5,-10,15 and 10

2+(-5) +(-10)+15+10 = 35

Jack score a total at the end is 35

Q3. At Srinagar temperature was -5 degree   Celsius on Monday and then it dropped by 2 degree Celsius on Tuesday  .What was the temperature of Srinagar on Tuesday ? On Wednesday ,it rose by 4 degree Celsius . What was the temperature on this day ?

Ans-  From the question

The temperature on Monday at Srinagar -5degree Celsius

Temperature on Tuesday at Srinagar dropped by 2 degree Celsius =Temperature on Monday  -2 degree Celsius

= -5 degree Celsius – 2 degree Celsius

= -7 degree Celsius

Temperature on Wednesday at Srinagar is rose by 4 degree Celsius = Temperature on Tuesday + 4 degree Celsius

=-7 degree Celsius + 4 degree Celsius

=-3 degree celsius

Thus  the temperature on Tuesday and wednesday  was -7 degree Celsius and -3 degree celsius  respectively

Q4. A plane is flying at the height of 5000m above the sea level . At a particular point, it is exactly  above a submarine floating 1200m below the sea level . What is the vertical distance between them ?

Ans – From the question ,

Plane is flying at the height =5000m

Depth of submarine = -1200m

The vertical height between plane and submarine =5000m-(-1200)m

=5000m+1200m

=6200m

Q5. Mohan deposit Rs 2000 in his bank account and withdraws Rs 1642 from it ,the next day . If withdrawl of amount from the account is represented by the negative integer ,then how will you represent the amount deposited? Find the balance in mohan account after the withdrawal .

Ans – Withdrawl of amount  is represented by a negative integer .

Then, deposits of amount to the account is represented by a positive integer.

From the questions ,

Total amount deposited in bank account by the mohan = Rs= 2000

Total Amount withdrawn from the bank account by the mohan  =-1642

Balance in mohan account after the withdrawl =amount deposited +amount withdrawn =Rs2000 +(-Rs 1642)

=Rs 2000 –Rs 1642

=Rs 358

Hence, the balance in Mohan account after the withdrawal is Rs 358

Q6. Rita goes 20 km towards east from a point A to the point B. From B ,she moves 30km towards west along the same road .If the distance towards east is represented by the positive integers then, how will you represent the distance travelled towards west ? By which integer will you represents her final position from A?

Ans – From the questions , it is given that

Then , distance travelled towards the west will be represented by a negative integer.

Rita travels a distance in east direction =20km

Rita travels a distance in west direction =-30km

Distance travelled from A

= 20 + (-30)

=20-30

= -10Km

Hence ,we will represents the distance travelled by rita from point A by a negative integer , i.e. -10km

Q7. In a magic square each row , column and diagonal have the same sum. Check which of the following is a magic square.

 5 -1 -4 -5 -2 7 0 3 -3

 1 -10 0 -4 -3 -2 -6 4 -7

Ans – First  we consider the square .

(i)By adding the numbers in each rows we get ,

=5 +(-1)+(-4)= 5-1-4

=5-5=0

= -5 +(-2)+7 = -5-2+7

=-7+7 =0

= 0+3+(-3)=3-3 =0

By adding the numbers in each columns we get  ,

= 5+(-2)+(-3)=5-2-3

=5-5=0

=-4+(-2)+0=-4-2=-6

Because sum of one diagonal is not equal to zero,

So,(i) is not a magic square

Now , we consider the square (ii)

By adding the numbers in each row we get ,

=1+(-10)+0 =1-10+0=-9

= (-4) +(-3)+(-2)=-4-3-2=-9

By  adding the numbers in each column we get,

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

=1-10=-9

=(-10)+(-3)+4=-10-3+4=-13+4

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

=-9

By adding the numbers in diagonals we get ,

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

=1-10=-9

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

=-9

This (iii) square is a magic square ,because sum of each row each column and diagonal is equal to -9.

Q8.Verify  a-(-b)=a+b for the following values of a and b.

(i) a=21 , b=18

Solution :

From the questions ,

A = 21   b=18

To verify a-(-b)=a+b

Let us take left hand side (LHS) =  a-(-b)

=21-(-18)

=21+18

=39

Now right hand side (RHS)

=A+B

=21+18

=39

By comparing LHS and RHS

LHS=RHS

39=39

Hence, the value of a and b is verified.

(ii)  a=118   ,  b=125

Solution :- From  the question ,

A=118 and b = 125

To verify a-(-b)=a+b

Let us take left hand side (LHS)=a-(-b)

=118-(-125)

=118+125

=243

Now , right hand side (RHS)=a+b

=118+125

=243

By comparing LHS and RHS

LHS=RHS

243=243

Hence , the value of a and b  is verified