Question: In the equation x=10y24, sum of the coefficients of dependent and independent variables is ___.

: The value of x depends on the value of y. So the dependent variable is x and the independent variable is y. Sum of the coefficients of dependent and independent variable =(10+1)=11

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Question 1. The sum of a number and its half is five less than twice the number. Which of the following equations represents given statement mathematically?
  1.    x+x2 = (2x−5)
  2.    x+a2 = (5−2x)
  3.    x+a2 = (5−2a)
  4.    a+x2 = 2x−5
Answer: Option A
: A

Let the number be 'x'.

Half of the number isx2.

Similarly, twice of the number=2x.

Sum of the number and its half=x+x2

5 less than twice the number=2x5

Given: Sum of the number and its half is five less than twice of the number.

The required equation isx+x2=2x5
Question 2. The sum of three consecutive numbers is 36. Find the numbers.
  1.    12,13,14
  2.    10,11,12
  3.    11,12,13
  4.    13,12,11
Answer: Option C
: C

Let the first number be a.
So the three consecutive numbers will be a,a+1,a+2.

a +a +1 +a +2 = 36
3a +3 = 36
3a = 36 -3 = 33

So, the three consecutive numbers will be 11,12,13.
Question 3. Pavani has a certain number of chocolates; she gave one-third of the chocolates to her brother Arjun, one-sixth to her friend Preeti. She was then left with 30 chocolates. What is the sum of the number of chocolates did she give to Arjun and Preeti?

: Let the number of chocolates Pavani has be x.
x3 are given to Arjun. So now she is left with xx3=2x3 chocolates

She gave x6 to Preeti. So, she is left with 2x3 - x6 = 4x6 - x6 = 3x6 = x2
So, x2=30

Initially, Pavani had 60 chocolates. She gave 13rd i.e. 603 =20 to Arjun.
16th i.e. 10 chocolates to Preeti.

Sum = 10 + 20 = 30
Question 4. After buying a toy from the shop, I am left with 15 from my 100 rupees of pocket money. Then, the cost of toy (in rupees) is:
  1.    15
  2.    100
  3.    85
  4.    75
Answer: Option C
: C

Let the cost of the toy be x as it is the unknown.
x + 15 = 100

x = 100 - 15 =₹85

So, the cost of the toy=₹85

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