Alka, Neelam, Anju and Chander live in houses in a lane where the houses are numbered as on a number line . The house numbers are as follows :
Alka : - 9, Neelam : 6, Anju : -12, Chander : -5.
If there is a house numbered '0' also, find :
a. How many houses are there between Alka's house and Neelam's house ?
b. How many houses are there between Anju's and Chander's house ?

Answer

To solve the problem step by step, we will analyze the positions of the houses on a number line and count the houses between the specified locations.

### Step-by-Step Solution:

**Step 1: Identify the positions of the houses on a number line.**

- Alka's house is at -9.
- Neelam's house is at 6.
- Anju's house is at -12.
- Chander's house is at -5.

**Step 2: Draw a number line.**

We can visualize the number line as follows:

```
... -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 ...
```

**Step 3: Locate Alka's and Neelam's houses.**

- Alka's house at -9.
- Neelam's house at 6.

**Step 4: Count the houses between Alka's and Neelam's houses.**

To find the number of houses between Alka's house (-9) and Neelam's house (6), we need to count all the integers from -8 to 5 (inclusive):

- The houses are: -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5.

Counting these gives us a total of 14 houses.

**Answer for Part A:** There are 14 houses between Alka's house and Neelam's house.

---

**Step 5: Locate Anju's and Chander's houses.**

- Anju's house at -12.
- Chander's house at -5.

**Step 6: Count the houses between Anju's and Chander's houses.**

To find the number of houses between Anju's house (-12) and Chander's house (-5), we count all the integers from -11 to -6 (inclusive):

- The houses are: -11, -10, -9, -8, -7, -6.

Counting these gives us a total of 6 houses.

**Answer for Part B:** There are 6 houses between Anju's house and Chander's house.

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