Simple Equations Test

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Simple Equations Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

Some children are sitting in a park. They have a certain number of chocolates. If each child eats 2 chocolates, then 2 extra chocolates will be left. If eat child eats 3 chocolates, then they will be short by 2 chocolates. Find the number of children and the number of chocolates, respectively.

A
3, 10

B
4, 10

C
5, 12

D
None of the above

Solution

Let number of children = x
and number of chocolate = y

So, y = 2x + 2 ... (1)
Also, y = 3x - 2 ... (2)

From (1) and (2), we get
2x + 2 = 3x - 2

⇒ x = 4
Thus, y = 3(4) - 2 = 12 - 2 = 10

So, there are 4 children and they have 10 chocolates.
Question 2
1 / -0

Sum of two digits of a number is 7. When 27 is subtracted from this number, its digits get interchanged. Which of the following are correct steps to find the number?

I. Let tens digit be m.

II. Then, ones digit = (7 - m)
Number = 10 × m + (7 - m) = 9m + 7

III. Subtracting 27 from the number, we get 9m - 20.

IV. Number with its digits interchanged = 10 × (7 - m) + m

V. 9m – 20 = 70 – 9m

VI. Hence, the number = 52

A
Steps II and VI

B
Steps I and III

C
Steps IV and V

D
All of the given steps

Solution

Lets take all the steps.
I. Let tens digit be m. - Correct.

II. Then, ones digit = (7 - m)
Number = 10 × m + (7 - m) = 9m + 7 - Correct.

III. Subtracting 27 from the number, we get 9m - 20.
i.e 9m + 7 - 27 = 9m - 20 - Correct.

IV. Number with its digits interchanged = 10 × (7 - m) + m - Correct.

V. 9m – 20 = 70 – 9m
i.e. 18m = 90, m = 5 - Correct.

VI. Hence, the number = 52
i.e m = 5 (tens digit) and 7 - 5 = 2 (ones digit)
Question 3
1 / -0

Select the incorrect statement:

a. In an equation, whatever operation happens on the right side of equals sign also happens on the left side.
b. If a number is subtracted from one side of the equation, the same number is subtracted from the other side as well.
c. If one side of the equation is multiplied by a number, then the other side of the equation is multiplied by any other number.
d. If a number is added to one side of the equation, then the same number is added to the other side as well.

A
(a)

B
(b)

C
(c)

D
(d)

Solution

a) In an equation, whatever operation happens on the right side of equals sign also happens on the left side.
This means if one side is halved, then the other side will be halved as well, which is true.

b) If a number is subtracted from one side of the equation, the same number is subtracted from the other side as well.
This means that if 3 is subtracted from one side, it is also subtracted from the other side, which is true.

c) If one side of the equation is multiplied by a number, then the other side of the equation is multiplied by any other number.
This means that if one side is multiplied by 2, then the other side can be multiplied by any number other than 2, which is incorrect.

d) If a number is added to one side of the equation, then the same number is added to the other side as well.
This means that if 5 is added to one side, then 5 is added to the other side too, which is true.

So, statement (c) is incorrect.
Question 4
1 / -0

A shoe store has 48 pairs of shoes in black and brown colours only. Each black pair costs Rs. 1500 and each brown pair costs Rs. 1900. If the total earnings from the sale of all the pairs are Rs. 79,200, then

I. form an equation representing the case
II. find the number of pairs of black shoes
III. find the number of pairs of brown shoes

A
I. 1500 × m + 1900 × (48 - m) = 79,200
II. 30
III. 18

B
I. 15 × m + 19 × m = 48
II. 30
III. 18

C
I. 1900 × m + 1500 × (48 - m) = 79,200
II. 38
III. 10

D
None of these.

Solution

Let the number of black shoe pairs be m and the number of brown shoe pairs be 48 - m.

1. According to question statement:
1500 × m + 1900 × (48 - m) = 79,200

2. Number of black shoe pairs:
1500 × m + 1900 × (48 - m) = 79,200
1500m + 91200 - 1900m = 79,200
- 400m = - 12000
400m = 12000
m = 30

3. Number of brown shoe pairs = 48 - m = 48 - 30 = 18
Question 5
1 / -0

The solution of the equation 20 – 3p = 2 is

A
3

B
4

C
6

D
8

Solution

20 – 3p = 2
18 = 3p
p = 6

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Simple Equations Test - 5

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Simple Equations Test - 5

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Question 1

3, 10

4, 10

5, 12

None of the above

Solution

Question 2

Steps II and VI

Steps I and III

Steps IV and V

All of the given steps

Solution

Question 3

(a)

(b)

(c)

(d)

Solution

Question 4

I. 1500 × m + 1900 × (48 - m) = 79,200 II. 30 III. 18

I. 15 × m + 19 × m = 48 II. 30 III. 18

I. 1900 × m + 1500 × (48 - m) = 79,200 II. 38 III. 10

None of these.

Solution

Question 5

3

4

6

8

Solution

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I. 1500 × m + 1900 × (48 - m) = 79,200
II. 30
III. 18

I. 15 × m + 19 × m = 48
II. 30
III. 18

I. 1900 × m + 1500 × (48 - m) = 79,200
II. 38
III. 10