Question

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 have less number of stairs than required forward stairs).(iii) Who takes least number of steps to reach near hundred?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 have less number of stairs than required forward stairs).(iii) Who takes least number of steps to reach near hundred?​

Answer 1

Answer:

Step-by-step explanation:

(i) Who reaches the nearest point?

(a) Amar

(b) Akbar

(c) Anthony

(d) All together reach to the nearest point.

Ans :

Amar will reach up to 93 steps then he will go for 5 steps up and 2 steps down hence covering

96 steps. Since 100 th step is final, so he will not cover more steps. Akbar will reach up to

95 steps, since 100 th step is final, so he will not cover more steps. Anthony will reach up to

91 steps, since 100 th step is final, so she will not cover more steps. Thus akbar reaches the

nearest point.

Thus (b) is correct option.

(ii) How many times can they meet in between on same step?

(a) 3

(b) 4

(c) 5

(d) No, they cannot meet in between on same step.

Ans :

LCM (3, 5, 7) =105 step.

Since, total steps are 100 steps, they cannot meet in between on same step.

Thus (d) is correct option.

(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.

Ans :

Amar will take 32 steps, Akbar will take 19 steps and Anthony will take 13 steps to reach to

96 steps, 95 steps and 91 steps respectively.

Thus (c) is correct option.

(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 after 15 steps.

(b) Akbar and Anthony will meet for the first time after 35 steps.

(b) Amar and Anthony will meet for the first time after 21 steps.

(d) Amar and Akbar will meet for the first time after 21 steps.

Ans :

Since LCM(3, 5)=15 ; LCM(5, 7)=35 ; LCM(3, 7)=21. Since, 15 is the smallest so Amar and

Akbar will meet for the first time after 15 steps.Thus (a) is correct option.

(v) What is the second stair where any two out of three will meet together?

(a) Amar and Akbar will meet after 21 steps.

(b) Akbar and Anthony will meet after 35 steps.

(b) Amar and Anthony will after 21 steps.

(b) Amar and Anthony will after 35 steps.

Ans :

As already calculated in (iii), LCM(3, 7) =21

Thus (b) is correct option.

Answer 2

The answer is Anthony.

Given:

Amar climbs 5 stairs and gets down 2 stairs in one turn.

Akbar goes up 7 stairs and comes down 2 stairs every time.

Anthony goes 10 stairs up and 3 stairs down each time.

To Find:

Who takes the least number of steps to reach near hundred

Solution:

As Amar climbs 5 stairs and gets down 2 stairs, the net change in stairs is 3 in one turn.

As Amar climbs in multiples of 3, he will reach the 96th step at one point. But beyond this point, he won't be able to move as he can't take 5 stairs because that will cross 100 steps.

Therefore the number of turns taken by Amar is

$\frac{96}{3}=22$

As Akbar climbs 7 stairs and gets down 2 stairs, the net change in stairs is 5 in one turn.

So as Akbar climbs in multiples of 5, he will reach the 95th stair at one point. But after this he won't be able to climb as that will cross 100 stairs.

Hence the number of turns taken by Akbar is

$\frac{95}{5}=19$

As Anthony climbs 10 stairs and gets down 3 stairs, the net change in stairs is 7 in one turn.

So as Anthony climbs in multiples of 7, he will reach the 91st stair at one point. But after this he won't be able to climb as that will cross 100 stairs.

Hence the number of turns taken by Anthony is

$\frac{91}{7}=13$

Therefore Anthony takes the least number of turns to reach near hundred.

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