## NCERT Solutions For Class 6 Maths Chapter 11 Algebra Ex 11.5

**Ex 11.5 Class 6 Maths Question 1.**

**State which of the following are equations (with a variable). Give reason for your answer. Identify the variable from the equations with a variable.**

**(a) 17 = x + 7**

**(b) (t – 7) > 5**

**(c) 4/2 = 2**

**(d) (7 x 3) – 19 = 8**

**(e) 5 x 4 – 8 = 2x**

**(f) x -2 = 0**

**(g) 2m < 30**

**(h) 2n + 1 = 11**

**(i) 7 = (11 x 5) – (12 x 4)**

**(j) 7 = (11 x 2) + p**

**(k) 20 = 5y**

**(l) 3q/2 < 5 (m) z + 12 > 24**

**(n) 20 – (10 – 5) = 3 x 5**

**(o) 7 – x = 5**

**Solution:**

(a) 17 = x + 7 is an equation with a variable x.

(b) (t – 7) > 5 is not an equation because it does not have ‘=’ sign.

(c) 4/2 = 2 is not an equation because it has no variable.

(d) (7 x 3) – 19 = 8 is not an equation because it has no variable.

(e) 5 x 4 – 8 = 2x is an equation with a variable x.

(f) x – 2 = 0 is an equation with a variable x.

(g) 2m < 30 is not an equation because it does not have ‘=’ sign.

(h) 2n + 1 = 11 is an equation with a variable n.

(i) 7 = (11 x 5) – (12 x 4) is not an equation because it does not have a variable.

(j) 7 = (11 x 2) + p is an equation with a variable p.

(k) 20 = 5y is an equation with a variable y.

(l) 3q/2 < 5 is not an equation because it does not have ‘=’ sign. (m) z + 12 > 24 is not an equation because it does not have ‘=’ sign.

(n) 20 – (10 – 5) = 3 x 5 is not an equation because it has no variable.

(o) 7 – x = 5 is an equation with a variable x.

**Ex 11.5 Class 6 Maths Question 2.**

**Complete the entries in the third column of the table.**

S. No. | Equation | Value of variable | Equations satisfied Yes /No |

(a) | 10y = 80 | y = 10 | |

(b) | 10y = 80 | y = 8 | |

(c) | 10y = 80 | y = 5 | |

(d) | 4l = 20 | l = 20 | |

(e) | 4l = 20 | l = 80 | |

(f) | 4l = 20 | l = 5 | |

(g) | b + 5 = 9 | b = 5 | |

(h) | b + 5 = 9 | b = 9 | |

(i) | b + 5 = 9 | b = 4 | |

(J) | h – 8 = 5 | h = 13 | |

(k) | h – 8 = 5 | h = 8 | |

(l) | h – 8 = 5 | h = 0 | |

(m) | P + 3 = 1 | p = 3 | |

(n) | p + 3 = 1 | p = 1 | |

(o) | p + 3 = 1 | p = 0 | |

(P) | p + 3 = 1 | p = -1 | |

(q) | p + 3 = 1 | p = -2 |

**Solution:**

S. No. | Equation | Value of variable | Equations satisfied Yes /No |

(a) | 10y = 80 | y = 10 | No |

(b) | 10y = 80 | y = 8 | Yes |

(c) | 10y = 80 | y = 5 | No |

(d) | 4l = 20 | l = 20 | No |

(e) | 4l = 20 | l = 80 | No |

(f) | 4l = 20 | l = 5 | Yes |

(g) | b + 5 = 9 | b = 5 | No |

(h) | b + 5 = 9 | b = 9 | No |

(i) | b + 5 = 9 | b = 4 | Yes |

(J) | h – 8 = 5 | h = 13 | Yes |

(k) | h – 8 = 5 | h = 8 | No |

(l) | h – 8 = 5 | h = 0 | No |

(m) | P + 3 = 1 | p = 3 | No |

(n) | p + 3 = 1 | p = 1 | No |

(o) | p + 3 = 1 | p = 0 | No |

(P) | p + 3 = 1 | p = -1 | No |

(q) | p + 3 = 1 | p = -2 | Yes |

**Ex 11.5 Class 6 Maths Question 3.**

**Pick out the solution from the values given in the brackets next to each equation. Show that the other values do not satisfy the equation.**

**(а) 5m = 60 (10, 5, 12, 15)**

**(b) n + 12 = 20 (12, 8, 20, 0)**

**(c) p – 5 = 5 (0, 10, 5, -5)**

**(d) q/2 = 7 (7, 2, 10, 14)**

**(e) r – 4 = 0 (4, -4, 8, 0)**

**(f) x + 4 = 2 (-2, 0, 2, 4)**

**Solution:**

(a) For m = 10, LHS = 5 x 10 = 50, RHS = 60

Here, LHS ≠ RHS

∴ m = 10 is not the solution of the equation

For m = 5, LHS = 5×5 = 25, RHS = 60

Here, LHS ≠ RHS

∴ m = 5 is not the solution of the equation

For m = 12, LHS = 5 x 12 = 60, RHS = 60

Here, LHS = RHS

∴ m = 12 is the solution of the equation

For m = 15 LHS = 5 x 15 = 75, RHS = 60

Here, LHS ≠ RHS

∴ m = 15 is not the solution of the equation

(b) n + 12 = 20 (12, 8, 20, 0)

For n = 12, LHS = 12 + 12 = 24, RHS = 20

Here, LHS ≠ RHS

∴ n = 12 is not the solution of the equation

For n = 8, LHS = 8 + 12 = 20, RHS = 20

Here, LHS = RHS

∴ n = 8 is the solution of the equation

For n = 20, LHS = 20 + 12 = 32, RHS = 20

Here, LHS ≠ RHS

∴ n = 20 is not the solution of the equation

For n = 0, LHS = 0 + 12 – 12, RHS = 20

Here, LHS ≠ RHS

∴ n= 0 is not the solution of the equation

(c) p – 5 = 5 (0, 10, 5, -5)

For p = 0, LHS = 0 – 5 = -5, RHS = 5

Here, LHS ≠ RHS

∴ p = 0 is not the solution of the equation

For p = 10, LHS = 10 – 5 = 5, RHS = 5

Here, LHS = RHS

∴ p = 10 is the solution of the equation

For p = 5, LHS = 5-5-0, RHS = 5

Here LHS ≠ RHS

∴ p = 5 is not the solution of the equation

For p = 5, LHS = 5 – 5 = 0, RHS = 5

Here, LHS ≠ RHS

∴ p = -5 is not the solution of the equation

(d) q/2 = 7 (7, 2, 10, 14)

For q = 7, LHS = 7/2 , RHS = 7

Here LHS ≠ RHS

∴ q = 7 is not the solution of the equation

For q = 2, LHS = 2/2 = 1, RHS = 7

Here, LHS ≠ RHS

∴ q = 2 is not the solution of the equation

For q = 10, LHS = 10/2 = 5, RHS = 7

Here, LHS ≠ RHS

For q = 14, LHS = 14/2 = 7, RHS = 7

Here, LHS = RHS

∴ q = 14 is the solution of the equation

(e) r – 4 = 0 (4, -4, 8, 0)

For r = 4, LHS = 4 – 4 = 0, RHS = 0

Here, LHS = RHS

∴ r = 4 is the solution of the equation

For r = -4, LHS = -4 – 4 = -8, RHS = 0

Here, LHS ≠ RHS

∴ r = -4 is not the solution of the equation

For r = 8, LHS = 8 – 4 = 4, RHS = 0

Here, LHS ≠ RHS

For r = 8 is not the solution of the equation

For r = 0, LHS = 0 – 4 = – 4, RHS = 0

Here, LHS ≠ RHS

∴ r = 0 is not the solution of the equation

(f) x + 4 = 2 (-2, 0, 2, 4)

For x = -2, LHS = -2 + 4 = 2, RHS = 2

Here, LHS – RHS

∴ x = -2 is the solution of the equation

For x = 0, LHS = 0 + 4 – 4, RHS = 2

Here, LHS ≠ RHS

∴ x = 0 is not the solution of the equation

For x = – 2, LHS = -2 + 4 – 6, RHS = 2

Here, LHS ≠ RHS

∴ x = 2 is not the solution of the equation

For r = 4, LHS = 4 + 4 = 8, RHS = 2

Here, LHS ≠ RHS

∴ x = 4 is not the solution of the equation

**Ex 11.5 Class 6 Maths Question 4.**

**(a) Complete the table and by inspection of the table find the solution to the equation m + 10 = 6**

**(b) Complete the table and by inspection of the table find the solution to the equation 51 – 35**

**(c) Complete the table and find the solution of the equation g = 4 using the table.**

**(d) Complete the table and find the solution to the equation m – 7 = 3**

**Solution:**

(a) By inspections, we have

So, m – 6 is the solution of the equation.

(b) Given that 5t = 35

So, t = 7 is the solution of the equation.

(c) Given that z/3 = 35

So, z = 12 is the solution of the equation.

(d) Given that m – 7 = 3

So, m = 10 is the solution of the equation.

**Ex 11.5 Class 6 Maths Question 5.**

**Solve the following riddles, you may yourself construct such riddles. Who am I?**

**(i) Go round a square**

**Counting every corner**

**Thrice and no more!**

**Add the count to me**

**To get exactly thirty four!**

**(ii) For each day of the week**

**Make an upcount from me**

**If you make no mistake**

**you will get twenty three!**

**(iii) I am a special number**

**Take away from me a six!**

**A whole cricket team**

**You will still be able to fix!**

**(iv) Tell me who I am**

**I shall give you a pretty clue!**

**you will get me back**

**If you take me out of twenty two!**

**Solution:**

(i) According to the condition,

I + 12 = 34 or x + 12 = 34

∴ By inspection, we have

22 + 12 = 34

So, I am 22.

(ii) Let I am ‘x’.

We know that there are 7 days in a week.

∴ upcounting from x for 7, the sum = 23

By inspections, we have

16 + 7 = 23

∴ x = 16

Thus I am 16.

(iii) Let the special number be x and there are 11 players in cricket team.

∴ Special Number -6 = 11

∴ x – 6 = 11

By inspection, we get

17 – 6 = 11

∴ x = 17

Thus I am 17.

(iv) Suppose I am ‘x’.

∴ 22 – I = I

or 22 – x = x

By inspection, we have

22 – 11 = 11

∴ x = 11

Thus I am 11.