Ncert -Class 7- Maths -worksheet – Simple Equations
Single choice correct answer
1.The equation form of the given statement ‘one fourth of p is more than 7 by 3’ is
(a) p – 7 = 4.
(b) 1/4(p-7)=3
(c) (p/4 )-7 =3
(d) p – 4 = 3.
Ans: (c)
Explanation:
One fourth of p = p/4,
It is greater than 7 by 3, i.e., .
2. The equation form of the given statement ‘6 less than a number is 13’ will be
(a) x – 6 = 13.
(b) 6x = 13.
(c) x – 13 = 6.
(d) x= 13 – 6.
Ans: (a)
Explanation:
Let the number is x, then
x – 6 = 13.
3. The statement form of the given equation ‘2x +6 = 24’ is
(a) Twice a number is 24 increased by 6.
(b) Twice a number increased by 6 is 24.
(c) Twice a number is 24 and increased by 6.
(d) Twice a number increased by 24 is 6.
Ans: (b)
Explanation:
2x = Twice a number of x
And, 2x + 6 = twice a number increase by 6
( 1 p – 7) = 3 4
p -7=3 4
p -7=3
4.The statement form of the given equation ‘x – 4 = 5’ is
(a) Taking away 5 from x gives 4.
(b) Taking away 4 from 5 gives x.
(c) Taking away 4 from x gives 5.
(d) Taking away 5 from 4 gives x.
Ans: (c)
Explanation:
x – 4 = Taking away 4 from x
x – 4 = 24 means taking away 4 from x gives 5.
5. If L.H.S. = R.H.S. of an equation, then the equation will be
(a) balanced.
(b) unbalanced.
(c) constant.
(d) wrong.
Ans: (a)
Explanation:
If L.H.S. = R.H.S. of an equation, then the equation is said to be balanced because the value of the left hand side is equal to the value of the right hand side of an equation.
6. Subtract 7 from thrice a number the result is 8 The equation form of the above statement is
(a) 7x – 2 = 8.
(b) 8x – 2 = 7.
(c) 3x – 7 = 8.
(d) 2x – 8 = 7.
Ans: (c)
7. For the equation 6p – 4 = 8, the solution will be
(a) p = 1.
(b) p = 2.
(c) p = 3.
(d) p = 4.
Ans: (b)
Explanation:
Given 6p – 4 = 8
For p = 2,
L.H.S. = 6 x 2 – 4 = 12 – 4 = 8 = R.H.S.
Thus, L.H.S. = R.H.S.
Therefore, p = 2 is a solution for the given equation 6p – 4 = 8.
8.Karan says that he has 6 balls more than five times the number of balls Sumit has. If Karan has 36 balls and Sumit has x number of balls, then the equation form for this statement is
(a) 5x + 6 = 36.
(b) 5x + 36 = 6.
(c) 5x – 6 = 36.
(d) 5x – 36 = 6.
Ans: (a)
9.If the sum of three consecutive even numbers is 78 then the numbers will be
(a) 10, 12 an 14.
(b) 16, 18 and 20.
(c) 22, 24 and 26.
(d) 24, 26 and 28.
Ans: (d)
Explanation:
Let us assume three consecutive even numbers
are x, x + 2 and x + 4.
Therefore, according to question
x + (x + 2) + (x + 4) = 78
3x + 6 = 78
3x = 78 – 6 = 72
x = 24 (Divide both side by 3)
Thus, the numbers are
x = 24, x + 2 = 26 and x + 4 = 28.
10. If the sum of four consecutive numbers is 50 then the smallest among them will be
(a) 11.
(b) 12.
(c) 13.
(d) 14.
Ans: (a)
Explanation:
Let us assume four consecutive odd numbers are x, x +1, x + 2 and x + 3.
Therefore, according to question
x + (x + 1) + (x + 2) + (x + 3) = 50
4x + 6 = 50
4x = 50 – 6 = 44
x = 11 (Divide both side by 4)
Thus, the numbers are x = 11, x + 1 = 12, x+ 2 = 13 and x + 3 = 14.
And the smallest number = 11
11. If 4 + 3(a + 5) = 28 then the value of a will be
(a) 0.
(b) 1.
(c) 2.
(d) 3.
Ans: (d)
Explanation:
4 + 3(a + 5) = 28 (Given)
3(a + 5) = 28 – 4 (Transposing 4 from L.H.S. to R.H.S.)
3(a + 5) = 24
a + 5 = 8 (Divide 3 from both sides)
a = 8 – 5 (Transposing 5 from L.H.S. to R.H.S.) a=3
12. If 16 + 4(p – 6) = 0 then the value of p will be
(a) 0.
(b) 1.
(c) 2.
(d) 3.
Ans: (c)
13. Start with x = 3, we can construct the following equations
(a) 4x – 5 = 7 and 2x + 3 = 9.
(b) 2x + 8 = 12 and 3x + 11 = 32.
(c) 3x + 4 = 19 and 4x + 7 = 10.
(d) 4x + 6 = 15 and 3x + 4 = 5.
Ans: (a)
Explanation:
(i) Start with x = 3
Multiply both sides by 4
4x = 12
Subtract 5 from both sides, we get
4x – 5 = 7 ……(1)
(ii) Start with x = 3
Multiply both sides by 2
2x = 6
Add 3 to both sides
2x + 3 = 9 …………(2)
14. The length of a rectangular field is twice its breadth. If the perimeter of the field is 120m then the length and breadth will be
(a) 20 and 40.
(b) 30 and 20.
(c) 40 and 20.
(d) 25 and 35.
Ans: (c)
15. If then the value of x will be
(a) 5.
(b) 7.
(c) 10.
(d) 12.
Ans: (a)
Explanation:
Let breadth = x
lenght = 2x (Given)
Now, according to the given question
2(l+b)=120
2(2x+ x)=120
2 3x =120
6x =120
120
x = 6
x =20 i.e. breadth=20m
ength=2×20= 40m
Check for L.H.S
2(2x+ x)
2(40+20)
=2×60
=120m=R.H.S.
16. If sum of two numbers is 12 and their difference is 4 then the value of two numbers will be
(a) 8 and 4.
(b) 4 and 4.
(c) 6 and 2.
(d) 7 and 5.
Ans: (a)
DESCRIPTIVE
Question
Solve the following equations by trial and error method:
(i) 5p + 2 = 17 (ii) 3m − 14 = 4
Question
Write equations for the following statements:
(i) The sum of numbers x and 4 is 9.
(ii) 2 subtracted from y is 8.
(iii) Ten times a is 70.
(iv) The number b divided by 5 gives 6.
(v) Three-fourth of t is 15.
(vi) Seven times m plus 7 gets you 77.
(vii) One-fourth of a number x minus 4 gives 4.
(viii) If you take away 6 from 6 times y, you get 60.
(ix) If you add 3 to one-third of z, you get 30.
Question
Set up an equation in the following cases:
(i) Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. (Take m to be the number of Parmit’s marbles.)
(ii) Laxmi’s father is 49 years old. He is 4 years older than three times Laxmi’s age. (Take Laxmi’s age to be y years.)
(iii) The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. (Take the lowest score to be l.)
(iv) In an isosceles triangle, the vertex angle is twice either base angle. (Let the base angle be b in degrees. Remember that the sum of angles of a triangle is 180 degrees.)