RBSE Solutions for Class 6 Maths Chapter 11 Algebra Ex 11.4

Rajasthan Board RBSE Solutions for Class 6 Maths Chapter 11 Algebra Ex 11.4 Textbook Exercise Questions and Answers.

RBSE Class 6 Maths Solutions 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 after 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 grandmother's age?
(v) Sarita's father's age is 5 years more than 3 times Sarita's age. What is her father's age?
Answer:
(a) (i) Given, Sarita's present age to bey years.
Sarita's age after 5 years
= Present age + 5 years = (y + 5) years

(ii) Sarita's age 3 years ago
= Present age - 3 years 
= (y - 3) years

(iii) Grandfather's age
= 6 × (Sarita's present age) = 6y

(iv) Grandmother's age
= Grandfather's present age - 2 years
From, Question (iii), we get grandfather's present age to be 6y Therefore, grandmother's age
= Grandfather's present age - 2 years 
= (6y - 2) years

(v) Father's age
= 3 × (Sarita's present age) + 5 
= (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?
Answer: 
Breadth of rectangular hall = b metres. 
Then, length of hall = (36 - 4) 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.
Answer: 
Height of the box = h cm
Length of the box = 5 times the height = 5 h cm
Breadth of the box = 10 cm less than length = 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.
Answer:
Meena's position = s
Beena's position = 8 steps ahead = s + 8
Leena's position = 7 steps behind = s - 7
Total number of steps = 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.
Answer:
Speed of the bus = v km/h 
Distance travelled in 5 hours = 5v km 
∵ Remaining distance = 20 km 
Therefore, total distance = (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.
Answer:
A hook costs 3 times the cost of a notebook.

(b) Tony puts q marbles on the table. He has 8q marbles in his box.
Answer:
The number of marbles in box is 8 times the marble on the table.

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

(d) Jaggu is z years old. His uncle is 4z years old and his aunt is (4z - 3) years old.
Answer:
Jaggu's uncle's age is 4 times the age of Jaggu. 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.
Answer:
The total number of dots is 5 times the number of rows.

Question 3. 
(a) Given Munnu’s age to be * 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?
Answer:
Munnu's age = x years 
His younger brother is 2 years younger than him = (x- 2) years
His elder brother's age is 4 years more than his age = (x + 4) years 
His father is 7 years more than thrice of his age = (3x + 7) years

(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\(\frac{1}{2}\).
Answer:
After n years from now, Sara's age will be (y + n) years
In past:
n years ago, Sara's age was (y - n) years. 
y + 7 indicates her age 7 years from now. 
y - 3 indicates her age 3 years back. 
y + 4\(\frac{1}{2}\) indicates her age 4\(\frac{1}{2}\) years from now.
y - 2\(\frac{1}{2}\) indicates her age 2\(\frac{1}{2}\) years back.

(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?)
Answer:
Number of students who like hockey is twice the number of students who like football, i.e. 2n.
Number of students who like tennis is half the number of students who like football, i.e. n/2.