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Toggle## NCERT Solution For Class 6, Maths, Chapter 11, Algebra, Exercise 11.4

** Exercise 11.4**

**Q.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 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?**

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

** ****(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 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 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’.**

**Ans: ****(a) **(i) Sarita’s age after 5 years from now = Sarita’s present age + 5 = (y + 5) years

(ii) Sarita’s age 3 years back = Sarita’s present age – 3 = (y – 3) years

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

(iv) Grandmother’s age = grandfather’s present age – 2 = (6y -2) years

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

**(b)** Length = 3 × Breadth – 4

l = (3b – 4) metres

**(c)** Height of the box = h cm

Length of the box = 5 times the height = 5h cm

Breadth of the box = 10 cm less than length = (5h -10) cm

**(d)** Meena’s position = s

Beena’s position = 8 steps ahead = s + 8

Leena’s position = 7 steps behind = s – 1

Total steps = 4 × (step at which Meena is) – 10 = (4s – 10)

**(e)** Speed of the bus = v km/h

So, in 1 h bus cover the distance = v km

∴ Distance travelled in 5 hours = 5 x v = 5v km

Remaining distance = 20 km

Therefore, total distance = (5v + 20) km

**Q.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 ****₹**** 3 p.**

**(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 20 n students.**

**(d) Jaggu is z years old. His uncle is 4 z 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.**

**Ans: ****(a) **A book costs 3 times the costs of a notebook.

(b) Tony’s box contains 8 times the number of marbles on the table.

(c) Total number of students in the school is 20 times that of our class.

(d) Jaggu’s uncle’s age is 4 times the age of Jaggu. Jaggu’s aunt is 3 years younger

than his uncle.

(e) The total number of dots is 5 times the number of rows.

**Q.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 (3 x + 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? ** **.**

**(c) Given n students in the class like football, what may 2n show? What may n/2 show?**

**Ans: ****(a) **(x – 2) represents the age of his younger brother whose age is (x – 2) years and he is 2 years younger to Munnu.

(x + 4) represents His elder brother’s age which is 4 years more than his age = (x + 4) years

(3x + 7) represents the person whose age is (3x + 7) years, elder to Munnu and his age is 7 years more than the three times of the age of Munnu

**(b) **Sara’s age today = y years

Her age in past = ** $y-3,\,y-2\frac{1}{2}$**

Her age in future = ** $y+7,\,\,\,y+4\frac{1}{2}$**

**(c)** No. of students like cricket is twice the students liking football, i.e., 2n

No. of students like tennis is half the students like football, i.e., n/2