Q 1 – Solve for x : 0.35x – 0.025 = 0.32x + 0.023
Given 0.35x – 0.025 = 0.32x +0.023
0.35x – 0.32x = 0.023 + 0.025
0.03x = 0.048
x = 0.048/0.03 = 1.6
Q 2 – The sum of the two consecutive odd numbers is 36. Find the larger number.
Let the two consecutive odd numbers be x and x + 2.
Given that Sum of 2 consecutive odd numbers = 36.
x + x + 2 = 36
2x + 2 = 36
2x = 34
x = 17
Then the other number = x + 2
= 17 + 2
= 19.
Therefore the integers are 17 and 19.
Q 3 – The sum of a two-digit number and the number obtained by reversing its digits is 121.
Find the number if its unit place digit is 5.
Given units digit is x and tens digit is y
Hence the two digit number = 10y + x
Number obtained by reversing the digits = 10x + y
Given that sum of a two digit number and the number obtained by reversing the order of its digits is 121.
Then (10y+x)+(10x+y)=121
⇒10y+x+10x+y=121
⇒11x+11y=121
⇒x+y=11
Thus the required linear equation is x + y = 11.
x given (unit place) = 5
putting 5 in equation:- 5 + y = 11
Hence y = 6
x = 5 y = 6
Required number is = 56
Q 4 – A road divider of certain length is painted one–sixth yellow, three–fifth black and there remaining 28m is painted white. Find the length of the divider.
Let total length of pencil be x cm.
Then, black part = x/8
Remaining part pencil after black part = x – x/8 = 7x/8
then White part = 1/2 (7x/8)
= 7x/16
Now Remaining part of pencil is blue = total length of pencil – (length of black part + length of white part)
length of blue part of pencil = x – (x/8 + 7x/16)
length of blue part of pencil = x – (2x + 7x)/16
length of blue part of pencil = x – 9x/16
length of blue part of pencil = (16 x – 9x)/16
∴ Length of blue part = 7x/16;
According to question
Length of blue part = 31/2
7x/16 = 31/2
⇒ 7x/16 = 7/2
⇒ x/16 = 1/2
⇒ x = 16/2
∴ x = 8 cm
Q 5 – A boy gets 3 marks for each correct sum and loses 1 mark for each incorrect sum. He does 25 sums and obtains 67 marks. Then how many correct sums were there?
Q 6 – Ram and Mohan have Rs 60000 together. If Ram has Rs 8000 more than Mohan, then find how much money Ram has?
Let the amount with Rahim be x So, the amount with Ram is x + 8000 x+8000 ∴ X + x + 8000 = 60 , 000 ∴X+x+8000=60,000 ⇒ x = 26 , 000 ⇒x=26,000 ∴ ∴ The amount with Ram = 8000 + 26 , 000 = R s 34 , 000
Q 7 – I have Rs 1000 in ten and five rupee notes. If the number of ten rupee notes that I have is
ten more than the number of five rupee notes, how many notes do I have in each denomination?.
Let no. of five rupee notes = x
no. of ten rupee notes = x+10
Cost of 5 rupee notes = Rs. 5x
Cost of 10 rupee notes = Rs. 10x +100
Total Cost = Rs. 1000
Therefore,
5x + 10x + 100 = 1000
15x = 1000 – 100
15x = 900
x = 900/15 = 60
Therefore, No. of five rupee notes = 60
No. of ten rupee notes = 60 + 10 = 70
Q 8 – If the side of chess board is smaller than its perimeter by 21 cm, then find the side of the
chess board.
If the side of a chess board is smaller than its
perimeter by 21 cm, then find the side of the chess
board.
P – s = 21
4s – s = 21
S = 7
Q 9 – Find the value of x in the equation 
Q 10 – If 
then what would be the value of y?
Q 11 – Solve for 
Q 12 – The angles of a triangle are in the ratio 2 : 3 : 4. Find the angles of the triangle.
It is given that the angle of triangle are in the ratio 2 : 3 : 4. Let the angles are 2x, 3x and 4x.
According to the angle sum property, the sum of interior angles of a triangle is 180 degree.
The value of x is 20.
Therefore the angles of triangle are 40, 60 and 80.
Q 13 – If the sum of two consecutive numbers is 11, find the numbers.
According to the problem
Let the two consecutive integers are and
.
so,
The first integer is and second integer is
Q 14 – The difference between two positive numbers is 40 and the ratio of these integers is 1: 3. Find the integers.
Let two numbers are x and y .
According to question ,
y – x = 40…… (i)
x/y = 1/3.
or , y = 3x….. (ii)
Put the value of y from equation (ii) on the equation (i).
3x-x=40.
or , 2x=40.
or , x = 20.
So , y = 3*x
or , y = 3 * 20.
or , y = 60.
The integers are 60 and 20.