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All questions of Algebra for Grade 6 Exam

Ramu's father is thrice as old as Ramu. If father's age is 45 years, how old is Ramu?
  • a)
    45 years
  • b)
    30 years
  • c)
    15 years
  • d)
    10 years
Correct answer is option 'C'. Can you explain this answer?

Let, Ramu's age be x years
∴ Ramu's father's age will be 3x years
Father's age is 45
∴3x = 45
⟹  x = 45/3 = 15
∴ Ramu's age is 15 years

Write an equation for the statement 'thrice the length of a room is 340 metres'.
  • a)
    3l = 430
  • b)
    3l = 340
  • c)
    3+l = 340
  • d)
    340 − 3l
Correct answer is option 'B'. Can you explain this answer?

Coachify answered
⇒ The length of room is l.
⇒ So, thrice the length means 3l.
∴ According to the statement given in question,
⇒ 3l = 340

The length of a rectangle is twice its breadth. If its area is 72 sq. m, find the breadth of the rectangle.
  • a)
    12 m
  • b)
    24 m
  • c)
    6 m
  • d)
    72 m
Correct answer is option 'C'. Can you explain this answer?

Let the breadth of the rectangle be b units. The length is twice its breadth. 
⇒ Its length = 2b units 
∴  Area = b × 2b sq units 
⇒2×b×b = 72 b × b=  72/2 ⇒b × b = 36 = 6 × 6
⇒ b = 6m

In a piggy bank the number of 25 paise coins is five times the number of 50 paise coins. If there are 120 coins, find the amount in the bank.
  • a)
    Rs. 25
  • b)
    Rs. 10
  • c)
    Rs. 35
  • d)
    Rs. 40
Correct answer is option 'C'. Can you explain this answer?

Arshiya Sen answered
Let the number of 50 paise coins be x. 
⇒ 25 paise coins = 5x
Given that total coins = 120 
⇒ x + 5x = 120 
⇒ 6x = 120 
⇒ x = 120/6 = 20 
∴ 50 paise coins = 20
⇒ Amount = 20×50 p = Rs. 10
Value of 25 paise coins = 25p × 5 × 20
= 25p × 100 = Rs. 25
Total amount Rs. (25 + 10) = Rs. 35

What is the co-efficient of m in –7 l2 mn ?
  • a)
    –7
  • b)
    –7l2
  • c)
    –7l2 n
  • d)
    None of these 
Correct answer is option 'C'. Can you explain this answer?

Coachify answered
In the expression -7l2 mn, the coefficient of a variable is the constant factor that multiplies that variable.
The term involving m is -7l2 mn. The coefficient of m is everything multiplying m, which in this case is -7l2 n.
Thus, the correct coefficient of m is -7l2 n.

Determine the value ofxgiven6x−1 = 2x+9.
a) 1(1/2)
b) -2(1/2
c) 1(3/12)
d) 5/2
Correct answer is option 'D'. Can you explain this answer?

Kunal Ghosh answered
To determine the value of x in the given equation 6x - 1 = 2x + 9, we can solve for x by isolating it on one side of the equation.

Step 1: Simplify the equation
Start by simplifying both sides of the equation.

6x - 1 = 2x + 9

Step 2: Combine like terms
Combine the x terms on one side and the constant terms on the other side.

6x - 2x = 9 + 1

4x = 10

Step 3: Solve for x
To solve for x, divide both sides of the equation by 4.

4x/4 = 10/4

x = 5/2

Therefore, the value of x is 5/2, which is option D - 5/2.

The rule, which gives the number of matchsticks required to make the matchstick pattern L, is
  • a)
    2n
  • b)
    3n
  • c)
    4n
  • d)
    5n
Correct answer is option 'A'. Can you explain this answer?

Lavanya Menon answered
from the figure it is confirmed that we need 2 matchstick minium for a 'L' shape. so matchsticks will be multiple of 2. so, we need 2n matchsticks

The length of a rectangular field is 5m more than its breadth. If the perimeter of the field is 74 m what is its length?
  • a)
    16m
  • b)
    17m
  • c)
    21m
  • d)
    23m
Correct answer is option 'C'. Can you explain this answer?

Let the breadth be x m.
Length = (x + 5)
Perimeter of rectangle = 74
⇒ 2(x + 5 + x) = 74
⇒ 2x + 5 = 37 ⇒ 2x = 37 - 5
⇒ 2x = 32

Length = 16 + 5 = 21m

A man is thrice as old as his daughter. 5 years ago the man was four times as old as his  daughter, what is the age of the daughter?
  • a)
    10 years
  • b)
    12 years
  • c)
    14 years
  • d)
    15 years
Correct answer is option 'D'. Can you explain this answer?

Let the age of daughter be x years.
∴ Man's age = 3x.
and 5 years ago, daughter's age = x-5
∴ Man's age = 3x —5
⇒ 3x —5= 4x —20 = 4x —3x = — 5 + 20
⇒ x =15 years 

If 8 is subtracted from three times a number the result is 13. What is number?
  • a)
    7
  • b)
    5
  • c)
    8
  • d)
    9
Correct answer is option 'A'. Can you explain this answer?

Rounak Patel answered
Understanding the Problem
To solve the problem, we need to translate the words into a mathematical equation. The statement "If 8 is subtracted from three times a number the result is 13" can be broken down as follows:
- Three times a number: If we denote the unknown number as x, then three times this number is 3x.
- Subtracting 8: When we subtract 8 from 3x, it becomes 3x - 8.
- The result is 13: This means that 3x - 8 equals 13.
Putting this all together, we can form the equation:
3x - 8 = 13
Solving the Equation
Now, let's solve for x:
1. Add 8 to both sides:
- 3x - 8 + 8 = 13 + 8
- This simplifies to 3x = 21.
2. Divide both sides by 3:
- 3x / 3 = 21 / 3
- This gives us x = 7.
Conclusion
The number we are looking for is x = 7.
- Final Answer: The correct answer is option 'A' (7).
By translating the given problem into an equation and solving it step by step, we find that the number is indeed 7.

What is the next step to solve the equation 3y - 4 = 8?
  • a)
    Add 4 to both sides
  • b)
    Subtract 4 from both sides
  • c)
    Multiply both sides by 3
  • d)
    Divide both sides by 3
Correct answer is option 'A'. Can you explain this answer?

Shanaya Desai answered
Understanding the Equation
The equation we need to solve is 3y - 4 = 8. Our goal is to isolate the variable y on one side of the equation.
Identifying the Next Step
To solve for y, we want to eliminate the -4 from the left side. The best way to do this is to perform the opposite operation. Since -4 is being subtracted, we can add 4 to both sides of the equation.
Options Analysis
- a) Add 4 to both sides: This is the correct step. Adding 4 will cancel out the -4 on the left side.
- b) Subtract 4 from both sides: This would make the equation more complicated, as it would lead to 3y - 8 = 8, which is not helpful.
- c) Multiply both sides by 3: This is unnecessary at this stage and would complicate the equation further.
- d) Divide both sides by 3: Similar to multiplication, this does not help in isolating y effectively right now.
Performing the Operation
By adding 4 to both sides, we get:
3y - 4 + 4 = 8 + 4
This simplifies to:
3y = 12
Now, we can easily solve for y by dividing both sides by 3 in the next step.
Conclusion
Therefore, the next step to solve the equation 3y - 4 = 8 is indeed option 'A'—add 4 to both sides. This will help us move closer to finding the value of y.

If 9 is added to twice of a certain number, the result is 57, what is that number?
  • a)
    38
  • b)
    24
  • c)
    46
  • d)
    84
Correct answer is option 'B'. Can you explain this answer?

Palak Nair answered
Problem Analysis

To solve this problem, we need to find a number that satisfies the given condition. Let's assume the number as 'x'. According to the problem, if we add 9 to twice the number, the result is 57. So, we can write the equation as:
2x + 9 = 57

Solution

To find the value of 'x', we can solve the above equation using algebraic operations.

Adding -9 to both sides of the equation:
2x + 9 - 9 = 57 - 9
2x = 48

Now, we can isolate 'x' by dividing both sides of the equation by 2:
2x/2 = 48/2
x = 24

Therefore, the number that satisfies the given condition is 24.

Answer

The correct answer is option B) 24.

In the given figure, what are the magnitudes of the angles shown? 
  • a)
    40, 135∘ 
  • b)
    45, 130
  • c)
    45,135
  • d)
    180
Correct answer is option 'C'. Can you explain this answer?

Rajat Menon answered
From the figure,x + 3x = 180 (straight angle) 
⇒ 4x∘ =180
⇒x = 45
∴ 3x∘ = 3×45∘ = 135

The sum of three consecutive natural numbers is 114. Which is the greatest number?
  • a)
    37
  • b)
    38
  • c)
    39
  • d)
    41
Correct answer is option 'C'. Can you explain this answer?

Muskaan Joshi answered
Understanding Consecutive Natural Numbers
Consecutive natural numbers are numbers that follow each other in order without any gaps. If we denote the first of these three consecutive natural numbers as 'x', then the next two can be expressed as 'x + 1' and 'x + 2'.
Setting Up the Equation
According to the problem, the sum of these three consecutive numbers equals 114. We can set up the equation as follows:
- x (first number)
- x + 1 (second number)
- x + 2 (third number)
The equation can be written as:
- x + (x + 1) + (x + 2) = 114
Simplifying the Equation
Let's simplify the equation:
- Combine like terms:
- 3x + 3 = 114
Next, we need to isolate 'x':
- Subtract 3 from both sides:
- 3x = 111
Now, divide by 3:
- x = 37
Identifying the Consecutive Numbers
Having found 'x', we can now identify the three consecutive numbers:
- First number (x) = 37
- Second number (x + 1) = 38
- Third number (x + 2) = 39
Conclusion: The Greatest Number
The greatest of these three consecutive natural numbers is:
- 39
Thus, the correct answer is option 'C', which is 39.

By how much is 2x – 3y + 4z greater than 2x + 5y – 6z + 2?
  • a)
    8y – 10z + 2
  • b)
    – 8y + 10z + 2
  • c)
    8y – 10z – 2
  • d)
    –8y + 10z – 2
Correct answer is option 'D'. Can you explain this answer?

Ananya Das answered
Understanding the Problem
To find how much one expression is greater than another, we need to subtract the second expression from the first. Here, we will evaluate the difference between the two expressions:
1. First Expression: 2x – 3y + 4z
2. Second Expression: 2x + 5y – 6z + 2
Step-by-Step Calculation
Let's perform the subtraction:
1. Subtraction Setup:
(2x - 3y + 4z) - (2x + 5y - 6z + 2)
2. Distributing the Negative Sign:
2x - 3y + 4z - 2x - 5y + 6z - 2
3. Combining Like Terms:
- The terms with x:
2x - 2x = 0
- The terms with y:
-3y - 5y = -8y
- The terms with z:
4z + 6z = 10z
- The constant term:
-2
Putting it all together, we get:
Final Expression
The result from the subtraction is:
-8y + 10z - 2
This is the expression that tells us how much 2x - 3y + 4z is greater than 2x + 5y - 6z + 2.
Conclusion
Therefore, the correct answer is option 'D':
-8y + 10z - 2.

Convert  in the simplest form.
  • a)
     
    1:4
  • b)
    3:2
  • c)
    4:1
  • d)
    7:3
Correct answer is option 'A'. Can you explain this answer?

On multiplying both sides of the ratio by 8, we get 1 on left sids and 4 on right side.
Hence, 1:4.

What is the value of xy – [yz – zx –{yx – (3y – xz) – (xy – zy)}]?
  • a)
    xy – xz – 3y
  • b)
    xy + 2xz – 3y
  • c)
    xy – xz + 3y
  • d)
    None of these 
Correct answer is option 'B'. Can you explain this answer?

Pragati Khanna answered
xy – [ yz – zx – {yx – (3y – xz) – (xy – zy)}]
=  xy – [ yz – zx – {yx – 3y + xz– xy + zy}]
=  xy – [ yz – zx – yx + 3y – xz + xy – zy]
=  xy + 2xz –3y

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