**Selina Concise Mathematics Class 6 ICSE Solutions – Framing Algebraic Expressions (Including Evaluation)**

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**EXERCISE 21**

**Question 1.**

Write in the form of an algebraic expression :

(i) Perimeter (P) of a rectangle is two times the sum of its length (l) and its breadth (b).

(ii) Perimeter (P) of a square is four times its side.

(iii) Area of a square is square of its side.

(iv) Surface area of a cube is six times the square of its edge.

**Solution:**

(i) Let P be the perimeter and / be the length, and b be the breadth.

P = 2 (l + b)

(ii) Let P be the perimeter and a be the side of the square.

P = 4a

(iii) Let A be the area of the square and a be the sides of the square.

A = (a)^{2}

(iv) Let S be the surface area and a be the edges of the cube.

S = 6a^{2}

**Question 2.**

Express each of the following as an algebraic expression :

(i) The sum of x and y minus m.

(ii) The product of x and y divided by m.

(iii) The subtraction of 5m from 3n and then adding 9p to it.

(iv) The product of 12, x, y and z minus the product of 5, m and n.

(v) Sum of p and 2r – s minus sum of a and 3n + 4x.

**Solution:**

(i) x + y – m

(ii)

(iii) 3n – 5m + 9p

(iv) 12xyz – 5mn

(v) p + 2r – s – (a + 3n + 4x)

**Question 3.**

Construct a formula for the following :

Total wages (₹ W) of a man whose basic wage is (₹ B) for t hours week plus (₹ R) per hour, if he Works a total of T hours.

**Solution:**

Wages for t hours = ₹ B

Wages for overtime = R(T – t)

=> Total wages = Wages for t hours + wages for overtime of (T – t) hours

=> ₹ W = ₹ B + ₹ R (T – t)

**Question 4.**

If x = 4, evaluate :

(i) 3x + 8

(ii) x^{2} – 2x

(iii)

**Solution:**

**Question 5.**

If m – 6, evaluate :

(i) 5m – 6

(ii) 2m^{2} + 3m

(iii) (2m)^{2}

**Solution:**

**Question 6.**

If x = 4, evaluate :

(i) 12x + 7

(ii) 5x^{2} + 4x

(iii)

**Solution:**

**Question 7.**

If m = 2, evaluate :

(i) 16m – 7

(ii) 15m^{2} – 10m

(iii)

**Solution:**

16m – 7

= (16 x 2) – 7

= 32 – 7 = 25

**Question 8.**

If x = 10, evaluate :

(i) 100x + 225

(ii) 6x^{2} – 25x

(iii)

**Solution:**

**Question 9.**

If a = – 10, evaluate :

(i) 5a

(ii) a^{2}

(iii) a^{3}

**Solution:**

(i)5a

= 5 x (-10) = -50

**Question 10.**

If x = – 6, evaluate :

(i) 11x

(ii) 4x^{2}

(iii) 2x^{3}

**Solution:**

**Question 11.**

If m = – 7, evaluate :

(i) 12m

(ii) 2m^{2}

(iii) 2m^{3}

**Solution:**

**Question 12.**

Find the average (A) of four quantities p, q, r and s. If A = 6, p = 3, q = 5 and r = 7 ; find the value of s.

**Solution:**

Given, average of four quantities (A) = 6

and p = 3,q = 5, r = 7 and s = ?

**Question 13.**

If a = 5 and b = 6, evaluate :

(i) 3ab

(ii) 6a^{2}b

(iii) 2b^{2}

**Solution:**

**Question 14.**

If x = 8 and y = 2, evaluate :

(i) 9xy

(ii) 5x^{2}y

(iii) (4y)^{2}

**Solution:**

**Question 15.**

If x = 5 and y = 4, evaluate :

(i) 8xy

(ii) 3x^{2}y

(iii) 3y^{2}

**Solution:**

**Question 16.**

If y = 5 and z = 2, evaluate :

(i) 100yz

(ii) 9y^{2}z

(iii) 5y^{2}

(iv) (5z)^{3}

**Solution:**

**Question 17.**

If x = 2 and y = 10, evaluate :

(i) 30xy

(ii) 50xy^{2}

(iii) (10x)^{2}

(iv) 5y^{2}

**Solution:**

**Question 18.**

If m = 3 and n = 7, evaluate :

(i) 12mn

(ii) 5mn^{2}

(iii) (10m)^{2}

(iv) 4n^{2}

**Solution:**

**Question 19.**

If a = -10, evaluate :

(i) 3a – 2

(ii) a^{2} + 8a

(iii) x a2

**Solution:**

**Question 20.**

If x = -6, evaluate :

(i) 4x – 9

(ii) 3x^{2} + 8x

(iii)

**Solution:**

**Question 21.**

If m = -8, evaluate :

(i) 2m + 21

(ii) m^{2} + 9m

(iii)

**Solution:**

**Question 22.**

If p = -10, evaluate :

(i) 6p + 50

(ii) 3p^{2} – 20p

(iii)

**Solution:**

(i) 6p + 50

= (6 x p) + 50

**Question 23.**

If y = -8, evaluate :

(i) 6y + 53

(ii) y^{2 }+ 12y

(iii)

**Solution:**

**Question 24.**

If x = 2 and 7 = -4, evaluate :

(i) 11xy

(ii) 5x^{2}y

(iii) (5y)^{2}

(iv) 8x^{2}

**Solution:**

**Question 25.**

If m = 9 and n = -2, evaluate

(i) 4mn

(ii) 2m^{2}n

(iii) (2n)^{3}

**Solution:**

**Question 26.**

If m = -8 and n = -2, evaluate :

(i) 12mn

(ii) 3m^{2}n

(iii) (4n)^{2}

**Solution:**

**Question 27.**

If x = -5 and y = -8, evaluate :

(i) 4xy

(ii) 2xy^{2}

(iii) 4x^{2}

(iv) 3y^{2}

**Solution:**

**Question 28.**

Find T, if T = 2a – b, a = 7 and b = 3.

**Solution:**

T = 2a – b, a = 1 and b = 3

Put the value of a = 1, and b = 3 in above equation

T = (2 x 7) -3

T = 14 – 3 = 11

T = 11

**Question 29.**

From the formula B = 2a^{2} – b^{2}, calculate the value of B when a = 3 and b = -1.

**Solution:**

B = 2a^{2} – b^{2}

Put the values of a = 3 and b = -1 in above equation

B = 2 x (3)^{2} – (-1)^{2}

B = 18 – 1

B = 17

Value of B is = 17

**Question 30.**

The wages ₹ W of a man earning ₹ x per hour for t hours are given by the formula W = xt. Find his wages for working 40 hours at a rate of ₹ 39.45 per hour.

**Solution:**

T = 40 hours

x = ₹ 39.45

W = xt = 40 x 39.45

W = ₹ 1578

**Question 31.**

The temperature in Fahrenhiet scale is represented by F and the tempera¬ture in Celsius scale is represented by C. If F = x C + 32, find F when C = 40.

**Solution:**

F = x C + 32

Given, C = 40

F = x 40 + 32 = 9 x 8 + 32

F = 104°

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