:
Steps: 2 Marks
Answer: 2 Marks
It is given that
Teslamakes a profit of Rs 100 on each car it sells
While it makes a loss of Rs 150 each time they send a rocket into space.
Teslawants to make a profit of Rs 3000.
Total number of rockets sent to space this year = 10
Total Loss due to the rockets = 10 $\times$ 1500 = Rs 1500
Let $x$ number of cars be sold, so as to make a profit of Rs 3000.
Net Profit = Profit from selling cars - loss due to sending of rockets
So on substituting the values, we get:
3000 = 100 $\times$ $x$ - 1500
$x$ = (3000 + 1500) $÷$ (100)
$x$ = 4500 $÷$ 100
$x$ = 45
So, the total number of cars that need to be sold to make a profit of Rs 3000 are 45.
It is given that, 10 cars have already been sold.
Number of cars that need to be sold to meet the target = 45 - 10 = 35
So, 35 more cars need to be sold to meet the target.

:
Steps: 2 Marks
Result: 1 Mark
(i) Profit earned by selling one pen = Re 1
Profit earned by selling 45 pens = Rs 45, which we denote by + Rs 45
Total loss= Rs 5, which we denote by (– Rs 5)
Profit earned + Loss incurred = Total loss
Therefore, Loss incurred = Total Loss – Profit earned
= Rs (– 5 – 45) = Rs (–50) = (– 5000 paise)
Loss incurred by selling one pencil = 40paise
which we write as (– 40paise)
So, number of pencils sold
$=(–5000)÷(–40)=125pencils$.
(ii) In the next month, there is neither profit nor loss.
So, Profit earned + Loss incurred = 0
i.e., Profit earned = – Loss incurred.
Now, profit earned by selling 70 pens = Rs 70
Hence, the loss incurred by selling pencils = Rs 70 which we indicate by (– Rs 70) or (– 7,000 paise).
Total number of pencils sold
$=(–7000)÷(–40)=175pencils$.

:
Steps: 2 Marks
Result: 2 Marks
As per the question
Loss incurred while selling 1 bag of grey cement = -Rs 5
Loss incurred while selling 6400 bags of grey cement = (- 5) $\times$ 6400 = - 32000
Let the number of bags of white cement to be sold be x.
Profit earned while selling 1 bag of white cement=Rs 8
Profit earned while selling x bags of white cement
= x $\times$ 8
=8x
In condition of no profit no loss,
Profit earned + Loss incurred = 0
8x + (-32000) = 0
8x = 32000
x = 4000
Therefore, 4000 bags of white cement must be sold.

Answer: Option C. -> -10
:
C
Here,
$(1-2)=-(2-1)=-1$
$(3-4)=-(4-3)=-1$
.
.
$(19-20)=-(20-19)=-1$.
There are 10 pairs having a value -1.
$\therefore 1-2+3-4+5-6+...........+19-20$
$=+10\times (-1)=-10[\because x\times (-y)=-xy]$

Answer: Option C. -> -480
:
C
Here,
Sum of 883 and -479
= 883 + (-479) =883 - 479
= 404
Now, subtracting the sum from -76
= -76 - 404
= -480

Answer: Option B. -> −5+1=4
:
B
Here,
$-7-6=-13,$
$-5+1=-4,$
$2-1=1,$
$8-9=-1$
$\therefore$ The second statement is false.

:
Ascending order : 1 Mark
Number Line : 1 Mark
Difference: 1 Mark
Marks obtained by the students = 12, 4, 6 , (-1), (-3 )
Marks arranged in ascending order = (-3) , (-1), 4, 6, 12

So, the difference between the highest scorer and the lowest scorer=12-(-3)=12+3=15.
Hence, the difference between the highest scorer and the lowest scorer is 15.

:
Writing the equation: 1 Mark
Steps: 2 Marks
Result: 1 Mark
Marks obtained for 1 right answer = +3
Marks obtained for 1 wrong answer = −2
Total marks scored by Rakesh = 18
Number of questions attempted = 16
(No. of correct ans)(3) + (No. of incorrect ans)(-2)
= 18
$\Rightarrow$ (No. of correct ans)(3) + (16 - No. of correct ans)(-2)
= 18
$\Rightarrow$ (No. of correct ans)(3) + -32 + 2(No. of correct ans)
= 18
$\Rightarrow$ (No. of correct ans)(5) + -32 = 18
$\Rightarrow$ (No. of correct ans)(5) = 18 + 32 = 50
$\Rightarrow$ No. of correct ans = 10
$\therefore$ No. of incorrect ans = 16 - 10 = 6
$\therefore$ Total number of correct and incorrect answers scored by Rakesh is 10 and 6 respectively.

:
Rule: 1 Mark
Value: 3 Mark
LHS ={10 × (5 + 2)}
= 10 × (7)
= 70
RHS = {(10 × 5 ) + (10 ×2 )}
= {50 + 20}
= 70
Hence , LHS = RHS
This rule is known asDistributivity of multiplication over addition.
We have to find out the value of
99$\times$101 = 99$\times$(100+1) = 9900 + 99 = 9999

:
Steps: 1 Mark
Temperature on Tuesday: 1 Mark
Temperature on Wednesday: 1 Mark
Temperature on Saturday: 1 Mark
Temperature on Monday =$-5^{\circ }C$
Temperature on Tuesday = Temperature on Monday $-2^{\circ }C$
$=-5^{\circ }C-2^{\circ }C=-7^{\circ }C$
Temperature on Wednesday = Temperature on Tuesday $+4^{\circ }C$
$=-7^{\circ }C+4^{\circ }C=-3^{\circ }C$
Therefore, the temperature on Tuesday and Wednesday was $-7^{\circ }C$ and $-3^{\circ }C$ respectively.
Given that
Thetemperaturedropsby$2^{\circ }$each dayafterWednesday
The temperature on Wednesday =$-3^{\circ }C$
The temperature on Saturday
$=-3-(2\times 3)=-3-6=-9^{\circ }C$
The temperature on Saturday is $-9^{\circ }C$