**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, y – 2.**(c)** Given n students in the class like football, what may 2n show? What may 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) may indicate Sara’s age in future.

The expressions (y – 3), (y – 2) may indicate Sara’s past age.

(c) The expression 2n may show the number of students who like hockey. The expression may show the number of students who like basketball.