Help! - pls solve these puzzles - esp. escalator oriented probs how 2 handle?

[koolfriend4u]

1. There is a escalator and 2 persons move down it.A takes 50 steps and B takes 75 steps while the escalator is moving down.Given that the time taken by A to take 1 step is equal to time taken by B to take 3 steps.Find the no. of steps in the escalator while it is staionary.

2. In a farm, there is some stock of grass is there, in which 40 cows can comeplete the grass in 40 days. in case if there is 30 cows, then the grass will be completed in 60 days. No the question is, if there is 20 cows are there, in how many days the grass will be completed ?

3. The length of a river trench is 4100 inches. a bridge is there above that river. one seventh of the length of that bridge falls left to that river. and one eighth of the bridge falls right to that river . then wats the length of that bridge?

4. In a party, 37 people were attending. there was no children. and there was 20 women. and 4 men were single. then wats the number of married men present at that party ?

[zango]

Originally Posted by koolfriend4u

1. There is a escalator and 2 persons move down it.A takes 50 steps and B takes 75 steps while the escalator is moving down.Given that the time taken by A to take 1 step is equal to time taken by B to take 3 steps.Find the no. of steps in the escalator while it is staionary.

Assume A takes 1 step per unit time. Then B will take 3 steps per same unit time. Also, assume the the escalator is moving at E steps per unit time.
Let T be the total number of steps.
Let ta be time taken by A on the escalator, tb = time taken by B on the escalator.
Since A takes 50 steps - therefore we have:
50 = T/(1+E) units of time.
similarly,
75 = T/(3+E) units of time.
Solving for T, E we get E = 1 step per unit time; T = 100 steps

Originally Posted by koolfriend4u

2. In a farm, there is some stock of grass is there, in which 40 cows can comeplete the grass in 40 days. in case if there is 30 cows, then the grass will be completed in 60 days. No the question is, if there is 20 cows are there, in how many days the grass will be completed ?

I am not sure of my solution - but this is how i did it:
assume that the rate at which the grass is eaten is partly dependent on the number of cows.
Then,
nDays = k1 * nCows + k2
thus,
40 = 40k1 + k2
60 = 30k1 + k2
Solving for k1, k2;
k1 = -2, k2 = 120
Therefore,
in case of 20 cows:
nDays = 20*-2 + 120 = 80 days I hope that is correct

Originally Posted by koolfriend4u

3. The length of a river trench is 4100 inches. a bridge is there above that river. one seventh of the length of that bridge falls left to that river. and one eighth of the bridge falls right to that river . then wats the length of that bridge?

4100 = (1 - 1/7 - 1/total length
total length = 56/41*4100 = 5600m

Originally Posted by koolfriend4u

4. In a party, 37 people were attending. there was no children. and there was 20 women. and 4 men were single. then wats the number of married men present at that party ?

This one was perhaps the simplest.
37 people - 20 women = 17 men.
4 single men = 17-4 married men = 13

Enjoy!

[koolfriend4u]

check with escalator problem. B speed 3 times of A.

75 = T/(3+E) units of time;

with T = 100 & E =1 not tallying boss.

help me out.

[zango]

Originally Posted by koolfriend4u

check with escalator problem. B speed 3 times of A.

75 = T/(3+E) units of time;

with T = 100 & E =1 not tallying boss.

help me out.

Sorry there's a typo
it should have read
75/3 = T/(3+E) units of time.

It will tally now i figured out i had made the typo y'day but didn't bother to update. Sorry :P

Take care!

[zango]

Originally Posted by zango

Sorry there's a typo
it should have read
75/3 = T/(3+E) units of time.

It will tally now i figured out i had made the typo y'day but didn't bother to update. Sorry :P

Take care!

Btw, are the answers correct?

Thanks.

[koolfriend4u]

thanks baiyaa

[koolfriend4u]

thanks a lot.

some more puzzles here.

1.An escalator is descending at constant speed. A walks down and takes 50 steps to reach the bottom. B runs down and takes 90 steps in the same time as A takes 10 steps.
How many steps are visible when the escalator is not operating?

2.If 5/2 artists make 5/2 paintings using 5/2 canvases in 5/2 days then how many artists r required to make 25 paintings using 25 canvases in 25 days?

3. There are 6561 balls out of them 1 is heavy.Find the min. no. of times the balls have to be weighed for finding out the haevy ball.


4. There are some bulbs,which are numbered from 1 to 100.all the bulbs are in on conditions. The following operations are performed.
1.those bulbs number which are divisible by 2 are switched OFF.
2.those bulbs numbered which are divisible by 3 are switched ON (which are already OFF) and OFF bulbs are switched ON.
3.similarly bulbs numbers divisible by 4 are either switched ON or OFF depending upon there previous condition.
4.this procedure is adopted till 100th bulb. At the end there were how many bulbs which were in ON condition.

[zango]

Originally Posted by koolfriend4u

thanks a lot.

You are welcome

Originally Posted by koolfriend4u

some more puzzles here.

1.An escalator is descending at constant speed. A walks down and takes 50 steps to reach the bottom. B runs down and takes 90 steps in the same time as A takes 10 steps.
How many steps are visible when the escalator is not operating?

Some information is missing here? If not - then I don't know how to answer this one

Originally Posted by koolfriend4u

2.If 5/2 artists make 5/2 paintings using 5/2 canvases in 5/2 days then how many artists r required to make 25 paintings using 25 canvases in 25 days?

Answer: 5/2.
5/2 artists take 5/2 days for 5/2 paintings (the canvases info is useless, i think).
So, 5/2 artists will take 1 day for 1 painting.
Similarly, 5/2 artists will take 25 days for 25 paintings.

Originally Posted by koolfriend4u

3. There are 6561 balls out of them 1 is heavy.Find the min. no. of times the balls have to be weighed for finding out the haevy ball.

Divide the balls into 3 groups - each of size 6561/3 = 2187 - weigh them individually = 3 weighings.
Now take the heaviest - and sub-divide into 3 more groups 2187/3 = 729 - weigh them individually = 3 more weighings.
Take the heaviest - divide into 3 - 729/3 = 243 - weigh them individually = 3 more weighings.
Take the heaviest - divide into 3 - 243/3 = 81 - weigh them individually = 3 more weighings.
Take the heaviest - divide into 3 - 81/3 = 27 - weigh them individually = 3 more weighings.
Take the heaviest - divide into 3 - 27/3 = 9 - weigh them individually = 3 more weighings.
Take the heaviest - divide into 3 - 9/3 = 3 - weigh them individually = 3 more weighings.
Take the heaviest - divide into 3 - 3/3 = 1 - weigh them individually = 3 more weighings.
The heaviest now is your required ball. The total number of weighings required was: 3+3+3+3+3+3+3+3 = 24
(PS: I would have thought the answer was 1 - because - if you take a wild wild guess - and just pick one ball - and weigh it - chances are that this may be the heaviest ball and you hit jackpot on your first attempt - however, using this logic, i attempted a question in Careerlauncher mock test 1 - question number 100 - i answered 1 - and got it wrong :P - i still wonder why 1 doesn't work, but wth, if it is supposed to be solved this way, i will use this method to solve, and not use probabilities ).)

Originally Posted by koolfriend4u

4. There are some bulbs,which are numbered from 1 to 100.all the bulbs are in on conditions. The following operations are performed.
1.those bulbs number which are divisible by 2 are switched OFF.
2.those bulbs numbered which are divisible by 3 are switched ON (which are already OFF) and OFF bulbs are switched ON.
3.similarly bulbs numbers divisible by 4 are either switched ON or OFF depending upon there previous condition.
4.this procedure is adopted till 100th bulb. At the end there were how many bulbs which were in ON condition.

Will work on this later busy right now :P

[quest4cat]

hi,
was working with a friend on the paintings wala sum........he is sure that the answer is 25..........cud u plz explain the funda again.

also for the 6561 balls wala sum........i got the answer as 13........here's how i got it
6561/2=3280+3281
similarly 3281=1640+1641.........likewise go on.........the total no of weighings comes out as 13.........which is lesser than 24. do u agree? if u find it wrong plz let me know where i'm going wrong
cheers

[mar2782]

Soln to 4 Quest..
the funda here is that all the bulb no. which have odd no are factors would have changed states ..and all those having even no.. of factors wld be in same state at the end..only PERFECT squares have odd no. of factors...so from 1-100 we have 10 no's which have odd factors....so only 10 bulbs i.e 1,4,9...would have difff state from there initial state..
so 10 off..
90 on..