GSEB Solutions Class 6 Maths Chapter 11 Algebra Ex 11.4

Gujarat Board GSEB Textbook Solutions Class 6 Maths Chapter 11 Algebra Ex 11.4 Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 6 Maths Chapter 11 Algebra Ex 11.4

Question 1.
Answer the following:
(a) Take Sarita s present age to be y years
(i) What will be her age 5 years from now?
(ii) What was her age 3 years back?
(iii) Sarita’S grandfather is 6 times her age. What is the age of her grandfather?
(iv) Grandmother is 2 years younger than grandfather. What is a grandmother’s age?
(v) Sarita’s father’s age is 5years more than 3 times Sarita’s age. What is her father’s age?
(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?
(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.
(d) Meena, Beena and Leena are climbing the steps to the hilltop. 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 hilltop is 10 less than 4 times what Meena has reached. Express the total number of steps using s.
(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: (a)
(i) Her age 5 years from now
= [Present age of Sarita] + 5 years
= (y + 5) years

(ii) Her age 3 years back
= [Present age of Sarita] – 3 years
= (y – 3) years

(iii) Age of grandfather
= [Present age of Sarita] × 6
= 6y years

(iv) Age of grandmother
= [Present age of grandfather] – 2
= (6y – 2) years

(v) Father’s age
= [Sarita’s present age] × 3 + 5 years
= (3y + 5) years

(b) ∵ Breadth of the rectangular hall = b metres
∴ Length of the rectangular hall
= 3 (Breadth) – 4 metres = 3b – 4 metres

(c) Height of the box = h cm
∴ Length of the box = 5 × height = 5 h cm
Breadth of the box = (Length – 10) cm
= (5 h – 10) cm

(d) ∵ Meena is at ‘s’ step
∴ Beena’s position = (8 + s) steps
Leena’s position = (s – 7) steps
∵ Total number of steps to the hill top
= 4 × [Number of steps at which Meena has reached] – 10
= 4 × [s] – 10 = 4s – 10

(e) Speed of the bus = v km/hr
Distance travelled after 5 hours = 5 × v km = 5v km
∴ Distance of Beespur = (5v + 20) km
Thus, distance between 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.
(b) Tony puts q marbles on the table. He has 8q marbles in his box.
(c) Our class has n students. The school has 20n students.
(d) Jaggu is z years old. His uncle is 4z years old and his aunt is (4z – 3) years old.
(e) In an arrangement of dots there are r rows. Each row contains 5 dots.
Solution:
(a) A book costs 3 times the cost of a notebook.
(b) Tony’s box contains 8 times the number of marbles on the table.
(c) The strength of the school is 20 times that of our class.
(d) Jaggu’s uncle is 4 times older than Jaggu and Jaggu’s aunt is 3 years younger than his uncle.
(e) Total number of dots in a row is 5 times the number of rows.

Question 3.
(a) Given Munnu s age to be x years, can you guess what (x – 2) may show?
Hint: Think of Munnu s younger brother.
Can you guess what (x + 4) may show? What (3x + 7) may show?
(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\(\frac { 1 }{ 2 }\), y – 2\(\frac { 1 }{ 2 }\).
(c) Given n students in the class like football, what may 2n show? What may \(\frac { n }{ 2 }\) show?
Hint: Think of games other than football
Solution:
(a) (x – 2): Munnu’s younger sister is (x – 2) years old. Age of Munnu’s younger sister is 2 years less than his age.
(x + 4): The age of Munnu’s brother is 4 years more than his age.
(3x + 7): The age of Munnu’s mother is 7 years more than 3 times his age.

(b) (i) y + 7 indicates Sara’s age after 7 years
(ii) y – 3 indicates Sara’s age 3 years ago.
(iii) y + 4\(\frac { 1 }{ 2 }\) indicates Sara’s age after 4\(\frac { 1 }{ 2 }\) years.
(iv) y – 2\(\frac { 1 }{ 2 }\) indicates Sara’s age 2\(\frac { 1 }{ 2 }\) years ago.

(c) Since, the number of students who like football is ‘n’.
∴ 2n (twice the number of football players) like to play cricket and \(\frac { n }{ 2 }\) (half the number of football players) like to play hockey.