Exercise 8.1 consists of topics like the use of letters to denote numbers and basic operations like addition, subtraction, multiplication and division on literals and numbers. RD Sharma Solutions Class 6 are prepared by teachers at BYJUâ€™S having vast experience in the education industry. To know more about the concepts explained in this exercise students can download RD Sharma Solutions for Class 6 Maths Chapter 8 Introduction to Algebra Exercise 8.1 PDF which are given below.

## RD Sharma Solutions for Class 6 Chapter 8: Introduction to Algebra Exercise 8.1 Download PDF

### Access RD Sharma Solutions for Class 6 Chapter 8: Introduction to Algebra Exercise 8.1

**1. Write the following using numbers, literals and signs of basic operations. State what each letter represents:**

**(i) The diameter of a circle is twice its radius.**

**(ii) The area of a rectangle is the product of its length and breadth.**

**(iii) The selling price equals the sum of the cost price and the profit.**

**(iv) The total amount equals the sum of the principal and the interest.**

**(v) The perimeter of a rectangle is two times the sum of its length and breadth.**

**(vi) The perimeter of a square is four times its side.**

**Solution:**

(i) Consider d as the diameter and r as the radius of the circle

Hence, we get d = 2r.

(ii) Consider A as the area, l as the length and b as the breadth of a rectangle

Hence, we get A = l Ã— b.

(iii) Consider S.P as the selling price, C.P as the cost price and P as the profit

Hence, we get S.P = C.P + P

(iv) Consider A as the amount, P as the principal and I as the interest

Hence, we get A = P + I

(v) Consider P as the perimeter, l as the length and b as the breadth of a rectangle

Hence, P = 2 (l + b)

(vi) Consider P as the perimeter and a as the side of a square

Hence, P = 4a

**2. Write the following using numbers, literals and signs of basic operations:**

**(i) The sum of 6 and x.**

**(ii) 3 more than a number y.**

**(iii) One-third of a number x.**

**(iv) One-half of the sum of number x and y.**

**(v) Number y less than a number 7.**

**(vi) 7 taken away from x.**

**(vii) 2 less than the quotient of x and y.**

**(viii) 4 times x taken away from one-third of y.**

**(ix) Quotient of x by 3 is multiplied by y.**

**Solution:**

(i) The sum of 6 and x can be written as 6 + x.

(ii) 3 more than a number y can be written as y + 3.

(iii) One-third of a number x can be written as x/3.

(iv) One-half of the sum of number x and y can be written as (x + y)/ 2.

(v) Number y less than a number 7 can be written as 7 â€“ y.

(vi) 7 taken away from x can be written as x â€“ 7.

(vii) 2 less than the quotient of x and y can be written as x/y â€“ 2.

(viii) 4 times x taken away from one-third of y can be written as y/3 â€“ 4x.

(ix) Quotient of x by 3 is multiplied by y can be written as xy/3.

**3. Think of a number. Multiply by 5. Add 6 to the result. Subtract y from this result. What is the result?**

**Solution:**

Consider x as the number.

Multiplying the number by 5 = 5x

Again add 6 to the number = 5x + 6

By subtracting y from the above equation = 5x + 6 â€“ y.

Hence, the result is 5x + 6 â€“ y.

**4. The number of rooms on the ground floor of a building is 12 less than the twice of the number of rooms on first floor. If the first floor has x rooms, how many rooms does the ground floor has?**

**Solution:**

Consider y as the number of rooms on the ground floor

We know that

The number of rooms on the first floor = x

It is given that number of rooms on the ground floor of a building is 12 less than the twice of the number of rooms on first floor

So we get

y = 2x â€“ 12

Hence, the rooms on the ground floor is y = 2x â€“ 12.

**5. Binny spend Rs a daily and saves Rs b per week. What is her income for two weeks?**

**Solution:**

Amount spent by Binny = Rs a

Amount saved by Binny = Rs b

Amount spent by Binny in one week = 7a

So the total income for one week = Amount spent by Binny in one week + Amount saved by Binny

Substituting the values

Total income for one week = 7a + b

We get Binnyâ€™s income for 2 weeks = 2 (7a + b) = Rs 14a + 2b

Hence, the income of Binny for two weeks is Rs 14a + 2b.

**6. Rahul scores 80 marks in English and x marks in Hindi. What is his total score in the two subjects?**

**Solution:**

Marks scored by Rahul in English = 80

Marks scored by Rahul in Hindi = x

So the total scores in the two subjects = x + 80

Hence, the total score of Rahul in two subjects is x + 80.

**7. Rohit covers x centimetres in one step. How much distance does he cover in y steps?**

**Solution:**

Distance covered by Rohit in one step = x cm

So the distance covered by Rohit in y steps = xy cm

Hence, Rohit covers xy cm in y steps.

**8. One apple weighs 75 grams and one orange weighs 40 grams. Determine the weight of x apples and y oranges.**

**Solution:**

Weight of one apple = 75 g

Weight of one orange = 40 g

So the weight of x apples = 75x g

So the weight of y oranges = 40y g

We get the weight of x apples and y oranges = (75x + 40y) g

Hence, the weight of x apples and y oranges is (75x + 40y) g.

**9. One pencil costs Rs 2 and one fountain pen costs Rs 15. What is the cost of x pencils and y fountain pens?**

**Solution:**

Cost of one pencil = Rs 2

Cost of one fountain pen = Rs 15

Cost of x pencils = 2x

Cost of y fountain pens = 15y

So the cost of x pencils and y fountain pens = Rs (2x + 15y)

Hence, the cost of x pencils and y fountain pens is Rs (12x + 15y).