**Algebra**

**EXERCISE -11.4**

**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 two year 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 three 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 Reena 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.**

`**Solution:**

(a) (i) y + 5

(ii) y – 3

(iii) 6y

(iv) 6y – 2

(v) 3y + 5

(b) length = 3b

breadth = (3b – 4) metre

(c) Height of the rectangular box = h

Length = 5h cm

Breadth = 10 cm less than length

=(5h – 10) cm.

(d) Meena’s position = s

Beena’s position 8 step ahead = s + 8

Leena’s position 7 step behind = s – 7

Total number of steps = 4s – 10

(d) Speed of bus = v km/h

Distance travelled by Bus in 5 hours = 5v km.

Remaining distance = 20 km

∴ Distance from Daspur to Beespur = (5v + 20) km.

**EX 11.4 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 put 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 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) The number of marbles in the box is 8 times the marbles on the table.

(c) The school has 20 times the number of students in a class.

(d) Jaggu’s uncle’s age is 4 times the age of jaggu. and his aunt’s age is 3 years less than the age of his uncle.

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

**EX 11.4 QUESTION 3.**

**(a) Given Munnu’s age to 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, , **

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

**Solution:**

(a) Munnu’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) Sara’s today age= y years.

y + 7 shows her future age.

y – 3 shows her past age.

y + 4 show her future age i.e., the age after z

four and a half years.

y – 2 shows her past age i.e., the age before two and a half years.

(c) Number of students who like football = n

∴ 2n = twice the number of football players may like to play cricket.

and = half of the number of football 2

players may like to play basketball.