**Rd Sharma Solutions Class 6 Chapter 8 Introduction to Algebra**

Welcome to NCTB Solution. Here with this post we are going to help 6th class students for the Solutions of Rd Sharma Class 6 Mathematics, Chapter 8, Introduction to Algebra. Here students can easily find Exercise wise solution for chapter 8, Introduction to Algebra. Students will find proper solutions for Exercise 8.1 and 8.2. Our teachers solved every problem with easily understandable methods so that every students can understand easily. Here all solutions are based on the CBSE latest curriculum.

**Introduction to Algebra Exercise 8.1 Solution**

**Question no – (1)**

**Solution :**

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

Let, diameter = d,

radius = r

∴ d = 2r

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

Let, Area = A,

length = l

breadth = b

**∴** A = l × b

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

S.P = C.P + P

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

Let, A = Amount,

P = principal,

I = Interest

**∴** A = P + I

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

Let, P = Perimeter,

l = Length,

b = breadth

**∴** P = 2 (l + b)

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

Let, P perimeter,

a = side of square

**∴** P = 4a

**Question no – (2)**

**Solution :**

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

= 6 + x

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

= Y + 3

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

= x/3

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

= X + Y/2

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

= 7 – Y

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

= x – 7

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

= x/y – 2

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

= y/3 – 4x

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

= xy/3

**Question no – (3)**

**Solution :**

Let, The number = x

**∴** The result,

= 5x + 6 – y

Hence, the result is 5x + 6 – y

**Question no – (4)**

**Solution :**

Let, y = the no of rooms on the ground floor

x = the no of rooms on the 1st floor

Therefore, y = 2x – 12

Thus, the ground floor will have y = 2x – 12 rooms.

**Question no – (5)**

**Solution :**

Let, Binny spent amount = a Rs

Binny spent = b Rs

**∴** Total income of two weeks,

= 2 (7a + b) Rs

= 14a + 2b Rs

Therefore, Binny’s income in two weeks will be 14a + 2b Rs.

**Question no – (6)**

**Solution :**

Let, Rahul’s score in Hindi = x

Rahul’s score in English = 80

**∴** Total score of Rahul,

= (x + 80)

Therefore, total score in the two subject will be (x + 80).

**Question no – (7)**

**Solution :**

Let, Distance curved in one steps c cm by Rohit .

**∴** Distance curved by Rohit in y steps,

= xy cm

Therefore, Rohit will cover xy cm.

**Question no – (8)**

**Solution :**

According to the question,

One apple weighs = 75 grams

One orange weighs = 40 grams

**∴** Weight of x apples and y oranges,

= (75x + 40y) gm

**Question no – (9)**

**Solution :**

According to question,

One pencil costs = Rs 2

One fountain pen costs = Rs 15

**∴** Cost of x pencils and y fountain pens,

= (2x + 15y) Rs

Therefore, the cost will be (2x + 15y) Rs.

**Introduction to Algebra Exercise 8.2 Solution**

**Question no – (1) **

**Solution : **

**(i)** a × a × a × a ×…15 times

= a^{15}

**(ii)** 8 × b × b × b × a × a × a × a

= 8a^{4}b^{3}

**(iii)** 5 × a × a × a × b × b × c × c × c

= 5a^{3}b^{2}c^{3}

**(iv)** 7 × a × a × a … 8 times × b × b × b × … 5 times

= 7a^{8}b^{5}

**(v)** 4 × a × a × … 5 times × b × b × … 12 times × c × c … 15 times

= 4a^{5}b^{12}c^{15}

**Question no – (2) **

**Solution : **

**(i)** a^{2}b^{5}

= a × a × b × b × b × b × b

**(ii)** 8x^{3}

= 8 × x × x × x

**(iii)** 7a^{3}b^{4}

= 7 × a × a × × × b × b × b × b

**(iv)** 15a^{9}b^{8}c^{6}

15 × a × a × a × a …9 times

× b × b …8 times x × c × c …6 times

**(v)** 30x^{4}y^{4}z^{5}

= 30 × x × x × x × x × y × y × y × y × z × z × z × z × z

**(vi)** 43p^{10}q^{5}r^{15}

= 43 × p × p …× 10 times,

× q × q × …5 times

× r × r × …15 times

**Previous Chapter Solution : **

👉 Chapter 7 👈