Interesting Question :
A man is climbing up a mountain which is inclined. He has to travel 100 km to reach the top of the mountain. Every day He climbs up 2 km forward in the day time. Exhausted, he then takes rest there at night time. At night, while he is asleep, he slips down 1 km backwards because the mountain is inclined. Then how many days does it take him to reach the mountain top?
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Answers
Given:
✰ A man has to travel 100 km to reach the top of the mountain.
✰ Every day, he climbs up 2 km forward in the day time.
✰ At night, while he is asleep, he slips down 1 km backwards because the mountain is inclined.
To find:
✠ How many days does it take him to reach the mountain top?
Solution:
Let's understand the concept first! We know that a man has to travel 100 km to reach the top of the mountain i.e, the distance travelled by a man to reach the top of the mountain is 100 km. Every day, he climbs up 2 km forward in the day time that means he covers 2 km distance everyday. At night, while he is asleep, he slips down 1 km backwards because the mountain is inclined that means because of inclination of the mountain he slips back 1 km. So, we need to find how many days will it take for him to climb 100 km because the distance travelled by him to reach the top of the mountain is 100 km.
Let's find out...!
➛ Height achieved on 1st day = 2 km
At night, while he is asleep, he slips down 1 km backwards because the mountain is inclined.
∴ Each day progress = 2 - 1 = 1 km
∴ Effective height achieved by him on the beginning of 2nd day = 1 km
➛ Height achieved on 2nd day = 2 + 1
➛ Height achieved on 2nd day = 3 km
At night, while he is asleep, he slips down 1 km backwards because the mountain is inclined.
∴ Effective height achieved by him on the beginning of 3rd day = 3 - 1 km
Effective height achieved by him on the beginning of 3rd day = 2 km
➛ Height achieved on 3rd day = 3 + 1
➛ Height achieved on 3rd day = 4 km
At night, while he is asleep, he slips down 1 km backwards because the mountain is inclined.
∴ Effective height achieved by him on the beginning of 4th day = 4 - 1 km
Effective height achieved by him on the beginning of 4th day = 3 km
➛ Height achieved on 4th day = 4 + 1
➛ Height achieved on 4th day = 5 km
At night, while he is asleep, he slips down 1 km backwards because the mountain is inclined.
∴ Effective height achieved by him on the beginning of 5th day = 5 - 1 km
Effective height achieved by him on the beginning of 5th day = 4 km
So on... [ upto 97th day ]
then,
Effective height achieved by him on the beginning of 98th day = 97 km
➛ Height achieved on 98th day = 98 + 1
➛ Height achieved on 98th day = 99 km
At night, while he is asleep, he slips down 1 km backwards because the mountain is inclined.
∴ Effective height achieved by him on the beginning of 5th day = 99 - 1 km
Effective height achieved by him on the beginning of 5th day = 98 km
Now,
∵ He climbs a distance of 2 km everyday.
∴ On 99th day he can reach top of the mountain by travelling 2 km forward in the day time.
So,
➤ Height achieved on 99th day = 98 + 2
➤ Height achieved on 99th day = 100 km
∴ It will take 99 days to reach the mountain top.
_______________________________
1st day height achieved 2km
1st night -1km
effective climb on beginning of day 2 is 1km
2nd day height achieved 3km
2nd night -1km
effective climb on beginning of day 3 is 2km
so on….
.
.
.
effective climb on beginning of day 98 is 97km
98th day height achieved 99km
98th night -1km
effective climb on beginning of day 99 is 98km
99th day height achieved is 100km