Q. Amar, Akbar and Anthony are playing a game. Amar climbs 5 stairs and gets down 2 stairs in one turn. Akbar goes up by 7 stairs and comes down by 2 stairs every time. Anthony goes 10 stairs up and 3 stairs down each time. Doing this they have to reach to the nearest point of 100th stairs and they will stop once they find it impossible to go forward. They can not cross 100th stair in anyway. (i) Who reaches the nearest point? (a) Amar (b) Akbar (c) Anthony (d) All together reach to the nearest point. (ii) How many times can they meet in between on same stair ? (a) 3 (b) 4 (c) 5 (d) No, they cannot meet in between on same stair. (iii) Who takes least number of steps to reach near hundred? (a) Amar (b) Akbar (c) Anthony (d) All of them take equal number of steps. (iv) What is the first stair where any two out of three will meet together? (a) Amar and Akbar will meet for the first time on 15th stair. (b) Akbar and Anthony will meet for the first time on 35th stair. (b) Amar and Anthony will meet for the first time on 21th stair. (d) Amar and Akbar will meet for the first time on 21th stair. (v) What is the second stair where any two out of three will meet together? (a) Amar and Akbar will meet on 21th stair. (b) Akbar and Anthony will meet on 35th stair. (c) Amar and Anthony will meet on 21th stair. (d) Amar and Anthony will meet on 35th stair.
Answers & Comments
Let's analyze the movements of Amar, Akbar, and Anthony:
Amar:
- Climbs 5 stairs.
- Gets down 2 stairs.
Akbar:
- Climbs 7 stairs.
- Gets down 2 stairs.
Anthony:
- Climbs 10 stairs.
- Gets down 3 stairs.
Now, let's calculate their movements and see who reaches the nearest point to the 100th stair:
Amar:
- First turn: 5 - 2 = 3 stairs climbed.
- Second turn: 3 + 5 - 2 = 6 stairs climbed.
- Third turn: 6 + 5 - 2 = 9 stairs climbed.
- Fourth turn: 9 + 5 - 2 = 12 stairs climbed.
- Fifth turn: 12 + 5 - 2 = 15 stairs climbed.
Akbar:
- First turn: 7 - 2 = 5 stairs climbed.
- Second turn: 5 + 7 - 2 = 10 stairs climbed.
- Third turn: 10 + 7 - 2 = 15 stairs climbed.
Anthony:
- First turn: 10 - 3 = 7 stairs climbed.
- Second turn: 7 + 10 - 3 = 14 stairs climbed.
Now, let's see who reaches the nearest point to the 100th stair:
- Amar reaches the 15th stair.
- Akbar reaches the 15th stair.
- Anthony reaches the 14th stair.
So, Amar and Akbar both reach the nearest point to the 100th stair. (ii) They meet on the same stair when both Amar and Akbar reach the 15th stair. So, they can meet twice in between on the same stair. (iii) Among Amar, Akbar, and Anthony, Akbar takes the least number of steps (10 steps) to reach near the hundred (15th stair). (iv) Amar and Akbar will meet for the first time on the 15th stair. So, the answer is (a) Amar and Akbar will meet for the first time on the 15th stair. (v) Amar and Akbar will meet on the 15th stair. So, the answer is (a) Amar and Akbar will meet on the 15th stair.