NCERT Solutions Class 6th Maths Chapter – 11 Algebra Exercise – 11.4

Question 1. Answer the following:
(a) Take Sarita’s present age to be y years.
Solution: Sarita’s age is given y years.

(i) What will be her age 5 years from now?
Solution: After 5 years from now, her age will be (y + 5) years.

(ii) What was her age 3 years back?
Solution: 3 years back from now, she was (y – 3) years of age.

(iii) Sarita’s grandfather is 6 times her age. What is the age of her grandfather?
Solution: Age of her grandfather = 6y years.

(iv) Grandmother is 2 years younger than grandfather. What is grandmother’s age?
Solution: Age of her grandmother = (6y – 2) years.

(v) Sarita’s father’s age is 5 years more than 3 times Sarita’s age. What is her father’s age?
Solution: Sarita’s father’s age = (3y + 5) years.

(b) The length of a rectangular hall is 4 metres less than 3 times the breadth of the hall. What is the length, if the breadth is b metres?

Solution: Let T be the length of the rectangular hall
∴ length = (3b – 4) metre
Where b represents the breadth.

(c) A rectangular box has height h cm. Its length is 5 times the height and breadth is 10 cm less than the length. Express the length and the breadth of the box in terms of the height.

Solution: Height of the rectangular box is ‘h’
∴ Length = 5h cm
and Breadth = (5h – 10) cm.

(d) Meena, Beena and Leena are climbing the steps to the hill top. Meena is at step s, Beena is 8 steps ahead and Leena 7 steps behind. Where are Beena and Meena? The total number of steps to the hill top is 10 less than 4 times what Meena has reached. Express the total number of steps using s.

Solution: Meena is at step s.
∴ Beena is at (s + 8) steps and Leena is at (s – 7) steps.
Total number of steps on to the hill top = (4s – 10)

(e) A bus travels at v km per hour. It is going from Daspur to Beespur. After the bus has travelled 5 hours, Beespur is still 20 km away. What is the distance from Daspur to Beespur? Express it using v.

Solution: Distance travelled by Bus in 5 hours = 5v km.
∴ Distance from Daspur to Beespur = (5v + 20) km.

Question 2. Change the following statements using expressions into statements in ordinary language.
(For example, Given Salim scores r runs in a cricket match, Nalin scores (r + 15) runs. In ordinary language – Nalin scores 15 runs more than Salim.
(a) A notebook costs ₹p. A book costs ₹3p.
Solution: A book costs 3 times the costs of a notebook.

(b) Tony puts q marbles on the table. He has 8q marbles in his box.
Solution: Tony’s box contains 8 times the number of marbles on the table

(c) Our class has n students. The school has 20n students.
Solution: Total number of students in the school is 20 times that of our class

(d) Jaggu is z years old. His uncle is 4z years old and his aunt is (4z – 3) years old.
Solution: Jaggu’s uncle is 4 times older than Jaggu and Jaggu’s aunt is 3 years younger than his uncle

(e) In an arrangement of dots there are r rows. Each row contains 5 dots.
Solution: The total number of dots is 5 times the number of rows

Question 3. (a) Given Mannu’s age to be x years, Can you guess what (x – 2) may show? (Hint: Think of Mannu’s younger brother) can you guess what (x + 4) may show? What (3x + 7) may show?

Solution: Given that Mannu’s age = x years.
∴ (x -2) years may be the age of her younger brother or younger sister.
(x + 4) years show the age of her elder brother or elder sister.
(3x + 7) years may be the age of her father, mother or uncle.

(b) Given Sara’s age today to be y years. Think of her age in the future or in the past. What will the following expression indicate? y + 7, y – 3, y + 4 ½ , y – 2 ½.

Solution: y represents the age of Sara in years.
∴ y + 7 shows her future age.
y – 3 shows her past age.
y + 4 ½ show her future age i.e., the age after z
four and half years.
y – 2 ½ shows her past age i.e., the age before two and half years.

(c) Given n students in the class like football, what may 2n show? What may n/2 show? (Hint: Think of games other than football).

Solution: Number of students who like football = n
∴ 2n = twice the number of football players may like to play cricket.
and n/2 = half of the number of football 2
players may like to play basketball.