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.
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Board |
NCTB |
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Class |
6 |
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Subject |
Mathematics |
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Chapter |
5 |
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Chapter Name |
“Simple Equations” |
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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.
