# Free Simple Equations 01 Practice Test - 7th grade

If 50 is subtracted from a number , the result is 4. Find the number.

A.

54

B.

46

C.

25

D.

45

#### SOLUTION

Solution : A

Let us say 'x' is the number . Given that  50 is subtracted from it and the result obtained is 4.

So mathematically, x50=4 is the equation.

Thus, x=50+4=54

54 is the number.

Krishna and Karan are on the see-saw.  Krishna's weight is 60 kg and Karan's is 80 kg. Who among the following kids can help Krishna balance the see-saw. (All of them can sit at extreme ends only).

A. Peter who has weight of  21 kg
B. Alison who has weight of  23 kg
C.

Pandu who has weight of 20 kg

D.

Mahi who has weight of  10 kg

#### SOLUTION

Solution : C

It is given that Krishna's weight is 60 kg and Karan's weight is 80 kg. To balance the see-saw Krishna needs another person.

Let the required weight needed to balance the see-saw be x kg
Then, 60+x=80         x=8060=20

So, Krishna should take help of a kid who weighs exactly 20 kg. Thus, Pandu would be the correct selection.

In a quiz program,the correct answer gets you 2 marks. For each wrong answer, one mark is deducted from the total score. There are 50 questions to be answered. If Preeti scored 76 marks for the quiz, how many of her questions were right?

A. 26
B. 13
C. 42
D. 38

#### SOLUTION

Solution : C

As the number of questions answered is unknown, let us assume that unknown variable as 'x'.
If the number of questions answered correctly are x, then the number of questions answered incorrectly will be (50x).
For each correct answer, she gets 2 marks. So the marks scored for x correctly answered questions are 2x. Similarly, the marks deducted  for (50-x) incorrectly answered questions are (50x)×1=50x
Now, the total marks scored by Preeti will be
2x- (50 -x) = 2x -50 +x = 3x -50 (For each wrong answer, one mark is deducted from the total score)

The final equation is, 3x -50 = 76
3x = 50 +76 = 126
x=1263=42
So, the total number of questions answered correctly by Preeti are 42.

Step 1: 3x+2=17
Step 2: 3x=172
This process of shifting the number from one side of the equation to the other side is called as ___.

A.

translation

B.

root of equation

C.

transposition

D.

correlation

#### SOLUTION

Solution : 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+22=172 i.e., 3x=172.
Instead of following the above process, 2 is shifted to the other side of the equation.
Therefore, we get 3x=172
This process is known as transposition.

Karan and Kundan are two brothers. Presently Karan's age is four times the age of Kundan. After 6 years Karan's age will be twice as that of Kundan. What is the present age of Kundan?

__

#### SOLUTION

Solution :

Let the present age of Kundan be x.

So, Karan's present age is 4x.

After 6 years,
Kundan's age = (x+6)
Karan's age = (4x+6)

Also, Karan's age would be twice of Kundan.

So, (4x +6) = 2 (x +6)

4x +6 = 2x +12

x = 3

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'?

A. 8,8
B. 8,4
C. 4,4
D. 8,10

#### SOLUTION

Solution : 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
aa2=4
a2=4
a=8

Since a = b b = 8

Bittu tells Kitty " I have 5 chocolates more than  seven times the number of chocolates you have”, if Kitty has 5 chocolates, how many chocolates does Bittu have ?

___

#### SOLUTION

Solution :

The number of chocolates Bittu has
= 5+(7×number of chocolates Kitty has)=5+(7×5)
=40

My granddaughter is 10 years old in 2015. I am 8 more than 6 times her age. I was born in the year

#### SOLUTION

Solution :

Grand daughter's age is 10 years now. So her grandpa's age is
8+6×10=8+60=68
Grandpa is  68 years old by 2015. So he was born in 1947.

There is always an equality sign in an equation.

A.

True

B.

False

#### SOLUTION

Solution : A

An expression having equality sign is called an equation.

2a15=10 and 10=15+2a are not the same equations.

A.

True

B.

False

#### SOLUTION

Solution : B

An equation remains same even if the LHS and RHS are interchanged.