A man always keeps a spare tyre in his car. To make full use of all the five tyres, he changes the tyres in a manner that for a distance of 1, 00,000 km, each of them runs the same distance.
Can you calculate the distance traveled by each tyre in that journey ?
80,000.
We need to calculate the 4/5th of the total distance to solve the problem.
4/5 * 1, 00,000 km = 80, 000 km
Thus, each tyre traveled 80, 000 km.
There are two candles. Both will only burn exactly for an hour. How will you use these two candles to measure forty-five minutes?
Burn one candle from both the ends and simultaneously burn the other candle from just one end. In half an hour, the first candle would have been burnt fully and the second one would have been burnt half. Now light the other end of the second candle as well. In this way, the second candle will take only half the time (30/2 = 15) to burn fully.
Thus, you will have measured forty five minutes.
A costume party is going on in a class of a few students. The average of the boys (b) is g and the average age of the girls (g) is b. If the average age of all of them including their class teacher who is 42 years old is b+g.
Can you find the value of b+g?
8
for b in range(1,99):
for g in range(1,99):
sum1=2*b*g+42
sum2=(b+g)*(b+g+1)
if(sum1==sum2):
print(b,g,sum1)
(b,g)=(3,5) => b + g=8
A family is trapped in a jungle. There is a bridge which can lead them to safety. But at one time, the bridge can only allow two people to pass through. Also, all of them are afraid of the dark and thus, they can’t go alone.
Father takes 1 minute to cross, mother takes 2 minutes, son takes 4 and the daughter takes 5 minutes. While crossing the time taken will be according to the slower one. How can they all reach at the other side in the minimum possible time ?
12 minutes
Father and Mother goes first: 2 minutes.
Father comes back: 2+1 = 3 minutes.
Both children go to mother: 3 + 5 = 8 minutes.
Mother comes back to Father: 8 + 2 = 10 minutes.
Mother and Father go: 10 + 2 = 12 minutes.
Thus, all of them reach the other sides in 12 minutes.
You are frying fishes on a pan which can accommodate only 2 fishes at one time. It takes 5 minutes to fry one side of the fish.
What is the shortest time in which you can fry 3 fishes in the same pan ?
15 minutes.
Put 2 fishes in the pan. Fry for 5 minutes and then take out one and turn the other one. Also put in the third fish. Now fry for 5 minutes. The fish that you turned must be ready now so take it off while turning the other one. Also put in the fish which was fried from one side only in the pan. Fry them for 5 minutes and all the three fishes are fried now.
There are two insects on a tile. Insect X is sitting on one side of the tile (point A) and Insect Y is sitting opposite on the other side of the tile (point B). Now both of them decide to change their position and thus X starts crawling to point B and Y starts crawling to point A. When they meet and pass each other in between, X takes 20 seconds to reach to B and Y takes just 5 seconds to reach A.
Can you calculate the total time each of the insects took to change their positions?
Assume that P is the speed of Insect X and Q is the speed of Insect Y.
Let T be the number of seconds it takes them to cross paths.
Now Distance = Speed * Time
Thus for Insect X
Distance = P * T before meeting
And Distance = P *20 after meeting
For Insect Y
Distance = Q * T before meeting
And Distance = Q * 5 after meeting
Now the distance travelled by X before meeting is equal to the distance travelled by Y after meeting and vice versa
Thus
P * T = Q * 5
And Q * T = P * 20
Solving both equations, we get T = 10
Thus Insect X requires 10 + 20 = 30 seconds,
Whereas Insect Y requires 10 + 5 = 15 seconds to change the position.
Emily learnt how to ride a horse recently. Just to test her skills, she rode the horse from her home till a mine which she covered in three minutes and returned back home from the same path only this time she took four minutes. The reason was that while riding away from home, she was supported by wind however while riding back, she was riding against the wind.
How fast do you think she could have rode a mile if there was no wind ?
3 minutes and 25 5/7 seconds.
The most common way how most of people see this problem is adding 3 and four to obtain 7 and they believe it should give a correct average and thus her time should be taken to 3 and half minutes. But if you do like that, you will get to a wrong answer. This is because, the wind has only helped her for three minutes while it has worked against her for four minutes.
If she could ride a mile in three minutes with the wind, it is evident that she could go a mile and 1/3 of a mile in four minutes. Thus two and 1/3 miles in eight minutes will give her actual speed as the wind has helped her as much as it has worked against her.
Thus her actual time for a single mile without wind will be 3 minutes and 25 5/7 seconds.
I possess two wires. Both of them have an inconstant thickness but both of them burns completely in sixty minutes. The problem is that I want to measure forty-five minutes while using these two wires.
How can I measure if cutting the wire in half is not possible due to non-homogeneous construction ?
45minutes
It is not as hard as it seems. I will burn one wire on both ends and the other wire at one end only. The first wire will burn completely in thirty minutes and at that very moment, I will burn the other end of the second wire and it will burn in fifteen minutes. Thus both of the wires will be burnt in 30 + 15 = 45 minutes.
Accidentally, two trains are running in the opposite direction and enter a tunnel that is 200 miles long. A supersonic bird that has fled the lab and taken shelter in the tunnel starts flying from one train towards the other at a speed of 1000 mph. As soon as it reaches the second train, he starts flying back to avoid collision and meets the first train again at the other end. The bird keeps flying to and fro till the trains collide with each other.
What is the total distance that the supersonic bird has traveled till the trains collided?
Let us consider the length of the tunnel first; which is 200 miles. Now, the trains are running on the same speed which means that they will collide at the center of the tunnel and will take an hour to reach the center. Now the bird is travelling at a speed of 1000 mph and it is flying for an hour (since the trains will take an hour to collide). Thus the bird will travel 1000 miles in the process.
John was gifted a new Hayabusa. He drove x miles at 55mph. Then he drove x+20 miles at 40mps. He drove his bike for 100 minutes. How much distance did he travel?
t1 + t2 = 100 minutes = 100/60 hours
t1 = x/55
t2 = (x+20)/40
x/55 + (x+20)/40 = 100/60
x = 1540/57
Thus, Total distance = x + (x+20) = 4220/57 miles = 74 2/57 miles