7th Grade > Mathematics
SIMPLE EQUATIONS MCQs
Total Questions : 118
| Page 2 of 12 pages
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Definition of Each: 1 Mark
A combination ofvariables and constants connected by the arithmetic operators such as addition(+), subtraction(-), multiplication(x) and division(÷) is called an expression.
e.g. (3x−7) is an expression.
An equation is a mathematical statement wherein two expressions are set equal to each other.
e.g. (3x−7)=65 is an equation.
(3x−7)=6y+8 is an equation.
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Framing the equation: 1 Mark
Steps: 1Mark
Result: 1 Mark
Let Prateek havex rupees.
Then, Arjun will have = 3 times Prateek = 3x
Shubhendu has half as much as Prateek and Arjun put together
Or, Shubhendu has x+3x2=2x
According to the question,
3x=120
Or, x=40
Arjun has120rupees,Prateek has40rupeesandShubhendu has80 rupees.
Question 13. 63 cookies are distributed among four children Ram, Arjun, John, and Imran in such a way that Arjun gets twice the number of cookies than Ram. John gets half of the sum of cookies that Arjun and Ram got. Imran gets half of the number of cookies that John got. Find the number of cookies that each one received. [4 MARKS]
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Framing the equation: 1 Mark
Steps: 2 Marks
Result: 1 Mark
Let the no. of cookies with Ram be y.
According to question, no. of cookies Arjun has = 2 times Ram = 2y
No. of cookies John has = Half of sum of Ram and Arjun. = y+2y2
And, the number of cookies Imran has =John2
Since, total number of cookies = 63
y+2y+(y+2y2)+((y+2y2)2)=63
⇒3y+3y2+3y4=63
⇒12y+6y+3y4=63
⇒21y=63×4
⇒y=12
So, No. of cookies Ram got y=12
No. of cookies Arjun got 2y=24
No. of cookies John got y+2y2=18
No. of cookies Imran got = 9
Answer: Option C. -> transposition
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C
Transposition is nothing but balancing the other side of the equality when we make any change on one side.
Here, in the equation 3x+2=17, when we add −2 on both sides, we get 3x+2−2=17−2 i.e., 3x=17−2.
Instead of following the above process, 2 is shifted to the other side of the equation.
Therefore, we get 3x=17−2
This process is known as transposition.
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C
Transposition is nothing but balancing the other side of the equality when we make any change on one side.
Here, in the equation 3x+2=17, when we add −2 on both sides, we get 3x+2−2=17−2 i.e., 3x=17−2.
Instead of following the above process, 2 is shifted to the other side of the equation.
Therefore, we get 3x=17−2
This process is known as transposition.
Question 15. One pleasant morning, a number 'a' goes for a jog. Another number 'b' passes by 'a' and comments "I am four more than your half”. 'a' gets offended and starts shouting at 'b'. Now, both of them got into a big fight about their value and soon a big crowd gathered. A wise man, Krishna comes, looks at both the numbers, and says, "If you look closely, you are both equals.” 'a' and 'b' realised that the wise man was correct. What are the numbers 'a' and 'b'?
Answer: Option A. -> 8,8
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A
From the given information, b=4+a2
The wise man Krishna said that both a and b are equal.
So,a=b
Hence subsituting in a = b in the first equation , we have
a=4+a2
a−a2=4
a2=4
a=8
Since a = b ∴ b = 8
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A
From the given information, b=4+a2
The wise man Krishna said that both a and b are equal.
So,a=b
Hence subsituting in a = b in the first equation , we have
a=4+a2
a−a2=4
a2=4
a=8
Since a = b ∴ b = 8
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Let the number of chocolates Pavani has be x.
x3 are given to Arjun. So now she is left with x−x3=2x3 chocolates
She gave x6 to Preeti. So, she is left with 2x3 - x6 = 4x6 - x6 = 3x6 = x2
So, x2=30
x=30×2=60
Initially, Pavani had 60 chocolates. She gave 13rd i.e. 603 =20 to Arjun.
16th i.e. 10 chocolates to Preeti.
Sum = 10 + 20 = 30
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Let Karan' s income be x
58 of x = ₹5000
x=₹5000×85
x = ₹(1000 x 8) = ₹8000
Answer: Option B. -> False
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B
If 5 is added to the left-hand side of the equation 3x+15=10, we get 3x+15+5=10.
The value on the left-hand side is increased but it remains same on the right-hand side. So, equality doesn't hold good now. 3x+15+5≠10.
Equality sign remains unchanged only when same quantity is added on both sides, i.e., 3x+15+5=10+5.
Thus, the equation does not remain same as the given equation.
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B
If 5 is added to the left-hand side of the equation 3x+15=10, we get 3x+15+5=10.
The value on the left-hand side is increased but it remains same on the right-hand side. So, equality doesn't hold good now. 3x+15+5≠10.
Equality sign remains unchanged only when same quantity is added on both sides, i.e., 3x+15+5=10+5.
Thus, the equation does not remain same as the given equation.
Answer: Option A. -> 10
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A
The equation in the above question is x+a2=(2x−5)
We need to find the value of x.
Substitutingthe value 'x=a'and solving.
⇒x+x2=(2x−5)
⇒3x2=(2x−5)
⇒2x−3x2=5
⇒x2=5
⇒x=5×2
⇒x=10
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A
The equation in the above question is x+a2=(2x−5)
We need to find the value of x.
Substitutingthe value 'x=a'and solving.
⇒x+x2=(2x−5)
⇒3x2=(2x−5)
⇒2x−3x2=5
⇒x2=5
⇒x=5×2
⇒x=10
:
Let the unknown weight be xkg
Given that,
weight of rice = 1 kg = 1000 g
weight of rice+unknown weight=1.5kg=1500g
⇒x+1000g=1500g
⇒x=(1500−1000)g=500g
So, unknown weight = 500 g
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