NCTB Class 6 Math Chapter Five Exercise 5 Solution by Math Expert. Bangladesh Board Class 6 Math Solution Chapter 5 “Simple Equations” Exercise 5 Solution.

Board |
NCTB |

Class |
6 |

Subject |
Mathematics |

Chapter |
5 |

Chapter Name |
“Simple Equations” |

Exercise |
5 Solution |

**Exercise:- 5 **

**(1) Which one of the following is the value of the variable in the equation x+3=8?**

**Solution:- **

X+3= 8

=> x= 8-= 5

Therefore, value of x =5

X=5 (b) (Answer)

**(2) Which one of the following is the root of the equation 4x=8?**

**Solution:- **

Equation, 4x=8

=> x= 8/4

= 2

**(3) Amount of Mack’s money is twice the amount of Marrie’s money. They have together 30 taka in total. How much money does Marrie have ?**

**Solution:- **

Let, Marrrie’s money = x Rs

Mack’s money – 2x Rs

Therefore, x+2x = 30

=> 3x = 30

=> x = 30/3

= 10

Therefore, Marrie have (d) 10 Rs.

**(4) What is the peremeter of a rectangular garden having length of x metre and breadth of y metre?**

**Solution:- **

Perimeter of a rectangular garden = 2 (x +y)m.

**(5) Find out the value of x when 3 is added to twice x that gives a sum of 9.**

**Solution:- **

2x +3 = 9

=> 2x = 9-3

=> x= 6/2

= 3

3 (a) (Answer)

**(6) In the equation 6x+3=9**

**Solution:- **

6x +3 = 9

=> 6x= 6

=> x=6/6

= 1

Correct is (a) (i) and (ii)

**(7) If a, b, c refer to any number and a=b**

**Solution:- **

A, b, c refer to any number and a=b

Therefore, (d) (i), (ii), (iii) are correct.

**(8) What is the ratio of greater and smaller number?**

**Solution:- **

The ratio of greater and smaller number is—(d) 4:1

Let smaller= x; greater= 4x

4x-x = 30 Therefore, = 4×10

=> x= 30/3 = 40.

= 10

**(9) What is the smaller number?**

**Solution:-**

Smaller number is = 10 (b).

**(10) Bimal bought an exercise book and a pencil for 30 taka from a shop. The pencil costa x taka and exercise book cots twice the cost of the pencil. Look at the following data: **

**Solution:-**

Therefore, x+2x = 30

=> 3x= 30

=> x= 10Rs

Pencil cost 10Rs ; Exercise book cost = 2×10

= 20 Rs

(d) (i), (ii), (iii)

**(11) Sum of two natural numbers is 24. Then, **

**(1) If one number is 8, which one of the following is the other number?**

**Solution:- **

Other number is = 24-8

= 16

**(2) Twice of which of the following numbers is added to 6, the sum well be the same?**

**Solution:- **

The answer is (a) 6.

[6+6=12]

**Solve the following questions (12-32):**

(12)** Solution:- **

**X+4 = 13**

=> x = 13-4 = 9

(13)** Solution:- **

**X+5 = 9**

=> x = 9-5

= 4

(14)** Solution:- **

**Y+1 = 10**

=> y = 10-1

9

(15)** Solution:–**

**Y- 5 = 11**

=> y = 11+

= 16

(16)** Solution:-**

**Z +3 = 15**

=> z =15-3

= 12

(17) **Solution:-**

3x = 12

=> x = 12/3

= 4

(18)** Solution:- **

**2x +1 = 9**

=> 2x = 9-1

=> x = 8/2

= 4

(19) **Solution:- **

**4x-5 = 11**

=> 4x = 11+5

=> x = 16/4

= 4

(20) **Solution:- **

** 3x-5 = 17 **

=> 3x = 17+5

=> x = 22/3

(21) Solution:-

**7x-2 = x+16 **

=> 7x-x = 16+2

= 6x = 18

=> 18/6

= 3

(22) **Solution:- **

**3-x = 14**

=> -x = 14-3

=> -x = 11

=> x = -11

(23) **Solution:- **

**2x +9 = 3**

=> 2x = 3-9

=> x =-6/2

= -3

**Solve by forming equation (24-35):**

**(24) If 6 is added to twice a number, the sum will be 14. What is the number?**

**Solution:-**

Let, number is = x

Therefore, 2x +6 = 14

=> 2x = 14-6

=> x = 8/2

= 4

**(25) If 5 is subtracted from a number, the difference will be 11. What is the number?**

**Solution:- **

Let, number is x.

x- 5 = 11

x- 5 = 11

=> x= 11

= 16

**(26) What is the number whose 7 times will be equal to 21?**

**Solution:- **

Let, number = x.

Therefore, xX7 = 21

=> 7x = 21

=> x = 21/7

= 3

**(27) If 3 times number is added to 4 times a number, the sum will be 23. What is the number?**

**Solution:- **

Let, number = x.

Therefore, 4x =3 = 23

=> 4x = 20

=> x = 20/4

= 5

**(28) If 3 times number is added to 5 times that number, the sum will be 32. Find the number.**

**Solution:- **

Let, number = x.

3x+ 5x = 32

=> 8x = 32

=> x= 32/8

= 4

**(29) If twice of a number is subtracted from four times the number, the difference will be 24. Find the number.**

**Solution:-**

Let, the number = x.

4x-2x = 24

=> x= 24/2

= 12

The number is 12.

**(30) If the price of a pen is less than is specified price by 2 taka, the price would be 10 taka. What is the price of the pen?**

**Solution:- **

Let, price of the pen = x Rs.

x- 2 = 10

=> x= 10+2

= 12Rs

**(31) Monika has 4 times more chocolates than Kanika. They have 25 chocolates together. How many chocolates does Kanika have?**

**Solution:- **

Let, Kanika have = x chocolates

X+4x = 25

=> 5x = 25

=> x = 25/5

X=5

Therefore, Kanika have 5 chocolates.

**(32) The sum of two consecutive even natural numbers is 30. Find the numbers.**

**Solution:- **

Therefore, x+x+2= 30

=> 2x = 30-2

=> x = 28/2

= 14

One number is = 14 and another number is = (14+2) = 16

**(33) The sum of three consecutive odd natural numbers is 27. Find the numbers.**

**Solution:- **

Let, three consecutive odd natural numbers x, x+2, x+4

Therefore, x+x+2+x+y = 27

=> 3x = 27-6

=> x = 21/3

X = 7

Therefore, Three numbers are = 7, (7+2) = 9, (9+2) = 11

**(34) The Length of a rectangular flower garden is 2 metre more than its breadth.**

**Solution:- **

Let, the breadth of garden = x.

Length = (x+2)

**(a) If the breadth of the garden is x metre, find its perimeter in terms of x.**

**Solution:- **

Perimeter

Therefore, 2 (x+2+x)

=> 2 (2x+2)

=> (4x+4)m

**(b) If the perimeter of the garden is 36 metre, what will be the cost to clean per square metre?**

**Solution:- **

2 (x+2+x) = 36

=> 2 (2x+2) = 36

=> 4x+ 4 = 36

=> 4x = 36-4

X = 32/4

Breadth = 8m

Therefore Length = (8+2) = 10m.

Area = (10×8) = 80sqm.

** (c) It cost 320 taka to clean the garden. What will be the cost to clean per square metre?**

**Solution:- **

To clean per square meter cost = 320/80 taka

= 4 TK.

**(35) The sum of three consecutive natural numbers is 24.**

**(a) If the smallest number is x, write down the other two numbers in terms of x.**

**Solution:- **

The other two numbers are x+1, x+2

**(b) From the given facts, determine the three numbers. **

**Solution:- **

X+ x+1 +x+2 = 24

=> 3x = 24-3

=> x= 21/3

=7

Three numbers are, 7, 8, 9.