after 14 steps he will reach of the top of the building
Answer:
To solve this problem, let's break down the climbing process and account for the slips.
1. **Net Distance Per Cycle**:
- The person climbs up 5 meters.
- Then he slips down 1 meter.
- So, the net gain in height after each cycle of climbing 5 meters and slipping 1 meter is:
\[
5 \, \text{m} - 1 \, \text{m} = 4 \, \text{m}
\]
2. **Total Height to be Climbed**:
- The building is 53 meters high.
3. **Climbing in Cycles**:
- In each complete cycle (climbing 5 meters and slipping 1 meter), the person effectively climbs 4 meters.
- We need to find out how many full cycles (each resulting in a net gain of 4 meters) are required to approach the top without exceeding the height of the building.
4. **Calculate the Effective Climbing Steps**:
- First, determine how many full cycles of 4 meters it takes to get close to the top but not exceed it:
\[
\left\lfloor \frac{53 \, \text{m}}{4 \, \text{m}} \right\rfloor = \left\lfloor 13.25 \right\rfloor = 13 \, \text{cycles}
\]
- Each of these 13 cycles gains the person 4 meters:
\[
13 \times 4 \, \text{m} = 52 \, \text{m}
\]
- After 13 cycles, the person is 52 meters high.
5. **Final Step to Reach the Top**:
- The person is 1 meter away from the top (53 meters - 52 meters = 1 meter).
- The person can climb the final meter without slipping back because the next slip happens after he climbs 5 meters.
6. **Total Steps**:
- Each cycle consists of climbing 5 meters, so 13 cycles involves:
\[
13 \times 5 \, \text{steps} = 65 \, \text{steps}
\]
- Then he climbs the last 1 meter directly (1 step):
\[
65 \, \text{steps} + 1 \, \text{step} = 66 \, \text{steps}
\]
Therefore, the person needs to take a total of \(66\) steps to reach the top of the 53-meter-high building.
