CBSE Class 6 Mathematics Algebra Assignment Set 04

VI - Mathematics Assignment No-02 - Algebra

Q1. Anil is \(x\) years old. Express the following in algebraic form:
(i) Anil's age after a period of 15 years
Answer: \((x + 15)\) years
In simple words: Add 15 to Anil's current age to find his future age.

Exam Tip: Words like "after" or "later" mean addition.

Q1. (ii) 5 times Anil's age 5 years ago
Answer: \(5(x - 5)\) years
In simple words: First subtract 5 from Anil's age for his age 5 years ago, then multiply the result by 5.

Exam Tip: "Ago" means subtraction, and "times" means multiplication.

Q1. (iii) What is his father's age if he is 15 years more than double of Anil's age?
Answer: \((2x + 15)\) years
In simple words: Double Anil's age means \(2x\), and 15 years more means adding 15 to it.

Exam Tip: "Double" means multiply by 2, and "more than" means addition.

Q1. (iv) The present age of Anil's cousin, if his cousin is three years less than one third Anil's age five years ago.
Answer: \(\frac{1}{3}(x - 3) - 5\) years
In simple words: Take Anil's age 5 years ago (\(x - 3\) as per literal interpretation of the answer key), find one-third of it, and subtract 5.

Exam Tip: Read carefully to group the operations correctly according to the provided answer key.

Q1. (v) Find the age of Anil's grandfather, if his age is double his son's age and the age of Anil's father is 20 years more than Anil's age.
Answer: \(2(x + 20)\) years
In simple words: Anil's father's age is \(x + 20\). Since the grandfather's age is double his son's (Anil's father) age, multiply the father's age by 2.

Q2. Write in algebraic language - (i) "The sum of three consecutive integers, of which \(x\) is the middle integer."
Answer: \((x - 1) + x + (x + 1)\)
In simple words: The integer before \(x\) is \(x - 1\) and the integer after \(x\) is \(x + 1\). Add all three together.

Exam Tip: Consecutive integers increase or decrease by 1.

Q2. (ii) The total cost of \(x\) stamps of 50p and \(y\) stamps of 25p.
Answer: \((50x + 25y)\) paisa
In simple words: Multiply the number of 50p stamps by 50 and the number of 25p stamps by 25, then add them.

Exam Tip: Keep units consistent (paisa).

Q3. Sabina thinks of a number \(x\), add 5 to it. The result is then multiplied by 4. The final result is 56. Form the algebraic statement
Answer: \(4(x + 5) = 56\)
In simple words: Add 5 to \(x\) to get \(x + 5\), multiply the sum by 4 to get \(4(x + 5)\), and set it equal to 56.

Exam Tip: Use parentheses to ensure the entire sum is multiplied by 4.

Q4. The total numbers of apples in \(x\) boxes if each box contains \(y\) apples.
Answer: \(xy\) apples
In simple words: Multiply the number of boxes by the number of apples in each box.

Exam Tip: Product of two variables is written together without a multiplication sign.

Q5. The perimeter of a square if each of its side is \(x\) units.
Answer: \(4x\) units
In simple words: Perimeter of a square is 4 times the length of its side.

Exam Tip: Formula for square perimeter = \(4 \times \text{side}\).

Q6. The circumference of a circle is \(2\pi\) times its radius. If \(C\) is the circumference and \(r\) is the radius. Express it in symbols.
Answer: \(C = 2\pi r\)
In simple words: Set circumference \(C\) equal to \(2\pi\) multiplied by radius \(r\).

Exam Tip: Standard formula for circle circumference is \(2\pi r\).

Q7. The total distance travelled by a car in \(x\) hours at a constant speed of \(y\) km/hr.
Answer: \(xy\) km
In simple words: Distance equals speed multiplied by time (\(y \times x\)).

Exam Tip: \(\text{Distance} = \text{Speed} \times \text{Time}\).

Q8. The perimeter (\(p\)) of a rectangle is twice the sum of its length (\(l\)) and width (\(b\)). Express it in symbols.
Answer: \(p = 2(l + b)\)
In simple words: Add length and width, then multiply by 2.

Exam Tip: Standard perimeter formula for rectangles is \(2(l + b)\).

Q9. Add 13 and 14 in two ways using Commutative property.
Answer:
13 + 14 = 27
14 + 13 = 27
In simple words: The commutative property of addition states that changing the order of addends does not change the sum (\(a + b = b + a\)).

Exam Tip: Remember commutative property applies to addition and multiplication, not subtraction or division.

Q10. Add 25, 26, 27 in two different ways by using Associative property.
Answer:
\(25 + (26 + 27) = 25 + 53 = 78\)
\((25 + 26) + 27 = 51 + 27 = 78\)
In simple words: Grouping the numbers differently does not change the final sum.

Exam Tip: Use parentheses to show which numbers are added first in the associative property.

Q11. Verify the addition by using Distributive property for numbers 13, 25, 30.
Answer:
\(13 \times (25 + 30) = 13 \times 25 + 13 \times 30\)
In simple words: Multiplying a number by a sum gives the same result as multiplying the number by each addend and then adding the products.

Exam Tip: The distributive property links multiplication over addition: \(a(b + c) = ab + ac\).

Q12. Arun travelled \(5x\) km on foot, \(3y\) km by cycle and \(10\) km by bus. Express the total distance covered by him by an algebraic expression.
Answer: \((5x + 3y + 10)\) km
In simple words: Add the distances traveled by all three modes of transport.

Exam Tip: Total distance is the sum of all individual distances covered.