Class 6 Maths NCERT Solutions for Chapter 11 Algebra Ex – 11.4

Algebra

Question 1.
Answer the following:

(a) Take Sarita’s present age to be y years

  • What will be her age 5 years from now?
  • What was her age 3 years back?
  • Sarita’s grandfather is 6 times her age. What is the age of her grandfather?
  • Grandmother is 2 years younger than grandfather. What is grandmother’s age?
  • Sarita’s father’s age is 5 years 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 io 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.
(e) A bus travels at v km per hour. It is going from L>aspur to Beespur. After the bus has travelled 5 hours, Beespuris still 20 km away. What is the distance from Daspur to Beespur? Express it using v.

Solution:
(a) Let Santa’s present age be y years.

  • Her age 5 years from now = (y + 5) years.
  • Her age 3 years back = (y – 3) years.
  • Since Sarita’s grandfather’s age is 6 times that of Sarita’s age.
    ∴ Her grandfather’s age = 6y years.
  • Since grandmother is 2 years younger than grandfather. Therefore,
    Grandmother’s age = (6 y – 2) years.
  • Since Sarita’s father’s age is 5 years more than 3 times Sarita’s age.
    Therefore, her father’s age = (3y + 5) years.

(b) Let the breadth of the hall be b metres
Since its length is 4 metres less than 3 times the breadth of the hall.
∴ Length of the hall = (3b – 4) metres

(c) Let the height of the rectangular box = h cm
It is given that its length is 5 times the height and breadth is 10 cm less than the length. Therefore,
Its length = 5h cm
and, breadth = (5h-10) cm

(d) Let Meena be at step s while climbing the steps to the hill top.
Since Beena is 8 steps ahead and Leena 7 steps behind Meena.
∴ Beena is at step (s + 8) and Leena is at step (s – 7)
Also, the total number of steps to the hill top is 10 less than 4 times what Meena has reached. .
∴ Total number of steps to the hill top = 4s-10

(e) Speed of the bus = v km per hour
Distance travelled by the bus in 5 hours = 5v km
According to question,
Distance from Daspur to Beespur
= Distance travelled by bus in 5 hours +20 km
= 5 km +20 km = (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 8 q 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 marbles on the table.
(c) Total number of students in 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) The number of dots in a row is 5 times the number of rows.

Question 3.
(a) Given, Munn’s age %p be x years, can you guess what (x – 2) may show?
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?

Solution:
(a) (x – 2) may show the age of his younger sister.
(x + 4) may show the age of his elder brother.
(3x + 7) may show the age of his grandfather.
(b) The expressions (y + 7), (y + 4\frac { 1 }{ 2 } ) may indicate Sara’s age in future.
The expressions (y – 3), (y – 2\frac { 1 }{ 2 } ) may indicate Sara’s past age.
(c) The expression 2n may show the number of students who like hockey. The expression \frac { n }{ 2 }  may show the number of students who like basketball.

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