Integers (Word Problems) interactive worksheet - Free Printable

Let's solve the problems step by step.

---

Problem 1:

Merchant sells 1800 bags of orange and 2500 bags of grapes. What is the profit or loss?

- Profit per bag of orange = Rs. 6
- Loss per bag of grapes = Rs. 4

#### Step 1: Calculate the total profit from oranges.
\[
\text{Total profit from oranges} = 1800 \times 6 = 10800 \, \text{Rs.}
\]

#### Step 2: Calculate the total loss from grapes.
\[
\text{Total loss from grapes} = 2500 \times 4 = 10000 \, \text{Rs.}
\]

#### Step 3: Determine the net profit or loss.
\[
\text{Net result} = \text{Total profit from oranges} - \text{Total loss from grapes}
\]
\[
\text{Net result} = 10800 - 10000 = 800 \, \text{Rs.}
\]

Since the result is positive, it is a profit.

Answer:
\[
\boxed{800}
\]

---

Problem 2:

What is the number of bags of oranges to be sold to have neither profit nor loss if the number of grape bags sold is 900 bags?

- Profit per bag of orange = Rs. 6
- Loss per bag of grapes = Rs. 4
- Number of grape bags sold = 900

#### Step 1: Calculate the total loss from grapes.
\[
\text{Total loss from grapes} = 900 \times 4 = 3600 \, \text{Rs.}
\]

#### Step 2: Determine the number of orange bags needed to offset this loss.
To have neither profit nor loss, the total profit from oranges must equal the total loss from grapes.
\[
\text{Profit per bag of orange} \times \text{Number of orange bags} = \text{Total loss from grapes}
\]
\[
6 \times \text{Number of orange bags} = 3600
\]

#### Step 3: Solve for the number of orange bags.
\[
\text{Number of orange bags} = \frac{3600}{6} = 600
\]

Answer:
\[
\boxed{600}
\]

---

Problem 3:

The sum of two integers is 116. If one of them is -79, find the other integer.

- Sum of two integers = 116
- One integer = -79

#### Step 1: Let the other integer be \( x \).
\[
-79 + x = 116
\]

#### Step 2: Solve for \( x \).
\[
x = 116 - (-79)
\]
\[
x = 116 + 79 = 195
\]

Answer:
\[
\boxed{195}
\]

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Problem 4:

Taking today as zero on the number line, if the day before yesterday is 17 January, what is the date on 3 days after tomorrow?

- Today = 0
- Day before yesterday = -2
- Day before yesterday is 17 January.

#### Step 1: Determine today's date.
If the day before yesterday is 17 January, then:
- Yesterday = 18 January
- Today = 19 January

#### Step 2: Determine the date 3 days after tomorrow.
- Tomorrow = 20 January
- 3 days after tomorrow = 20 + 3 = 23 January

Answer:
\[
\boxed{23}
\]

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True/False Questions:

#### Question 5:
5 - (-8) is the same as 5 + 8.

- Simplify \( 5 - (-8) \):
\[
5 - (-8) = 5 + 8 = 13
\]

- Simplify \( 5 + 8 \):
\[
5 + 8 = 13
\]

Both expressions are equal.

Answer:
\[
\boxed{\text{True}}
\]

#### Question 6:
(-9) + (-11) is greater than (-9) - (-11).

- Simplify \( (-9) + (-11) \):
\[
(-9) + (-11) = -20
\]

- Simplify \( (-9) - (-11) \):
\[
(-9) - (-11) = -9 + 11 = 2
\]

Compare:
\[
-20 \not> 2
\]

Answer:
\[
\boxed{\text{False}}
\]

#### Question 7:
When we change the order of integers, their sum remains the same.

This is the commutative property of addition, which states:
\[
a + b = b + a
\]

Answer:
\[
\boxed{\text{True}}
\]

#### Question 8:
Sum of two negative integers always gives a number smaller than both the integers.

Let the two negative integers be \( -a \) and \( -b \), where \( a \) and \( b \) are positive.
\[
(-a) + (-b) = -(a + b)
\]
Since \( a + b \) is positive, \( -(a + b) \) is negative and smaller than both \( -a \) and \( -b \).

Answer:
\[
\boxed{\text{True}}
\]

#### Question 9:
Difference of two negative integers cannot be a positive integer.

Consider two negative integers \( -a \) and \( -b \), where \( a \) and \( b \) are positive.
\[
(-a) - (-b) = -a + b = b - a
\]
If \( b > a \), then \( b - a \) is positive.

For example:
\[
(-3) - (-5) = -3 + 5 = 2
\]

Thus, the difference can be positive.

Answer:
\[
\boxed{\text{False}}
\]

#### Question 10:
We can write a pair of integers, whose sum is not an integer.

The sum of two integers is always an integer. There are no exceptions.

Answer:
\[
\boxed{\text{False}}
\]

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Final Answers:

1. \(\boxed{800}\)
2. \(\boxed{600}\)
3. \(\boxed{195}\)
4. \(\boxed{23}\)
5. \(\boxed{\text{True}}\)
6. \(\boxed{\text{False}}\)
7. \(\boxed{\text{True}}\)
8. \(\boxed{\text{True}}\)
9. \(\boxed{\text{False}}\)
10. \(\boxed{\text{False}}\)