There are 20 steps to go to the first floor of a building from the ground floor .
A child starts climbing up from the first step of the ground level . Mother starts coming down from the fourth step from the floor level of the first floor .
If both have started at the same time with same speed, at which step would they meet counting from the first steps from the floor level of the first floor ?

Options

A. 9
B. 10
C. 11
D. 12

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Understand the positions of the child and the mother
- The child starts at the 1st step of the ground level.
- The mother starts at the 4th step from the top (which is the 20th step - 4 = 17th step from the ground).

### Step 2: Define the meeting point
- Let’s assume they meet at the x-th step from the ground level.
- Therefore, the child will have climbed to the (1 + x) step, while the mother will have descended to the (20 - (x - 1)) step.

### Step 3: Set up the equation
- Since both are moving at the same speed and started at the same time, the distance they cover must be equal when they meet.
- The child climbs from step 1 to step (1 + x), which means he climbs x steps.
- The mother descends from step 17 to step (20 - x), which means she descends (17 - (20 - x)) = (x - 3) steps.
- Set the distances equal:
\[ x = x - 3 \]

### Step 4: Solve the equation
- Rearranging the equation gives:
\[ 2x = 16 \]
- Therefore,
\[ x = 8 \]

### Step 5: Determine the steps they meet at
- The child will be at step (1 + x) = (1 + 8) = 9th step from the ground.
- The mother will also be at step 9 from the ground when they meet.

### Step 6: Find the step counting from the first floor
- To find the step counting from the first floor, we need to calculate:
\[ 20 - 9 + 1 = 12 \]
- Thus, they meet at the 12th step counting from the first floor.

### Final Answer
The child and the mother meet at the 12th step counting from the first floor.

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