A hiker comes across an intersection where three roads cross. He looks
for the sign indicating the direction to his destination city. He finds
that the pole carrying three city names and arrows pointing to them has
fallen. He picks it up, considers it, and pops it back into place,
pointing out the correct direction for his destination. How did he do
it?
Since he knew very well from which city he came; he just oriented that arrow in right direction. And obviously hence rest of all arrows are pointed in the right directions as well. This is how he found his right way!
Let's first recall the formula for the calculation of area of a triangle.
Area of triangle = 1/2 x Base x Height
Let's assume the side of the square is 1.
Now the triangle with the pink shade & triangle opposite to it are similar triangles. Similar triangles are triangle whose sides are in proportion with each other.
Since here base of pink triangle is double of un shaded opposite triangle, the height of pink triangle must be double of that smaller triangle.
But together, heights of both triangles must be equal to side of the square i.e. 1.
And hence, height of smaller triangle must be 1/3 & that of pink 2/3. (h + 2h = 3 ; h = 1/3).
So,
Area of Pink Triangle = 1/2 x Base x Height = 1/2 x 1 x 2/3 = 1/3.
So the area of pink shaded part is 1/3rd of total area occupied by square.
Bruce is an inmate at a large prison, and like most of the other prisoners, he smokes cigarettes. During his time in the prison, Bruce finds that if he has 3 cigarette butts, he can cram them together and turn them into 1 full cigarette. Whenever he smokes a cigarette, it turns into a cigarette butt.
One day, Bruce is in his cell talking to one of his cellmates, Steve.
“I really want to smoke 5 cigarettes today, but all I have are these 10 cigarette butts,” Bruce tells Steve. “I’m not sure that will be enough.”
“Why don’t you borrow some of Tom’s cigarette butts?” asks Steve, pointing over to a small pile of cigarette butts on the bed of their third cellmate, Tom, who is out for the day on a community service project.
“I can’t,” Bruce says. “Tom always counts exactly how many cigarette butts are in his pile, and he’d probably kill me if he noticed that I had taken any.”
However, after thinking for a while, Bruce figures out a way that he can smoke 5 cigarettes without angering Tom. What is his plan?
Bruce takes 9 of his 10 cigarette butts and make 3 cigarettes using those 9 (9/3=3). Now, he smokes all 3 cigarettes. At this point, he has 3 + 1 = 4 cigarette butts.
Using 3 out of 4 cigarette butts, he make one another cigarette and smokes it. Now he has 1 + 1 = 2 cigarette butts & till now has smoked 4 cigarettes.
Now he borrows 1 Tom's cigarette butts making total number of cigarette butts equal to 3. Using these 3 butts he makes one more cigarette and this way he smokes 5th cigarette.
After smoking this 5th, he puts back the cigarette butt left in Tom's pile so that Tom won't find anything missing.
Well, it totally depends on the location of the bus. How? Read further. If you look at it carefully, then you can notice that the doors of the bus are missing. That clearly indicates, those must be on the other side of bus.
Hence if bus is on the roads of India then it must have doors at it's left side & hence the bus must be moving in the right direction.
While in some countries, bus might have doors at the right; in the case the bus must be moving in left direction.
Let r,b and g be the numbers ofred,blue and green marbles in the jar.
There are 73red,blue and green marbles in a jar.
So r + b + g = 73 .....(1)
There are twice as many red marbles as blue marbles.
r = 2b ......(2)
There are 19 moreblue marbles thangreen marbles. b = g + 19
g = b - 19 ......(3)
Putting (2) and (3) in (1), gives 2b + b + b - 19 = 73 4b = 92
b = 23
Putting b = 23 in (3) gives,
g = 23 - 19 = 4
Putting b = 23 in (2), gives r = 2x23 = 46 So there are 46 red,23 blue and 4 green marbles in the jar. Without Algebra : In the case, we need to try trail and error method. If g = 1, then b = 20 and r = 2(20) = 40 giving total 40 + 20 + 1 = 61. If g = 2, then b = 21 and r = 2(21) = 42 giving total 42 + 21 + 2 = 65. If g = 3, then b = 22 and r = 2(22) = 44 giving total 44 + 22 + 3 = 69.
Total is increasing at the rate of 4. So finally,
If g = 4, then b = 23 and r = 2(23) = 46 giving total 46 + 23 + 4 = 73.
So there are 46 red,23 blue and 4 green marbles in the jar.
Once a man steals Rs.100 note from the shop. Later he purchases good of worth Rs.70 from the same shop using that note. The shopkeeper gives back Rs.30 in return.
So did you just answer Rs.130 ? No, that's not correct!
Thief initially steals Rs.100 note. Now imagine instead of Rs.100 he steals goods of worth Rs. 70 + Rs.30 (given by shopkeeper). So eventually, the shopkeeper lost only Rs.100 in the process.
In other words, the thief exchanges Rs.70 with the goods in the case. He pays for those goods to shopkeeper. So he looses Rs.70 from stolen Rs.100 & gains back via goods.
So eventually, the shopkeeper lost only Rs.100in the case.
Mamma:"Let me think, Tommy. Well, our three ages add up to exactly seventy years."
Tommy: "That's a lot, isn't it? And how old are you, Papa?"
Papa: "Just six times as old as you, my son."
Tommy: "Shall I ever be half as old as you, Papa?"
Papa: "Yes, Tommy; and when that happens our three ages will add up to exactly twice as much as to-day."
Tommy: "And supposing I was born before you, Papa; and supposing Mamma had forgot all about it, and hadn't been at home when I came; and supposing..."
Mamma:"Supposing, Tommy, we talk about bed. Come along, darling. You'll have a headache."
Now, if Tommy had been some years older he might have calculated the exact ages of his parents from the information they had given him. Can you find out the exact age of Mamma?
Read the given data first! This could be very tricky one. Let's assume that the Matt is fifth fastest and fifth slowest runner in his school.
Then there are 4 runners ahead of him numbered 1 to 4 and 4 behind him numbered 6 to 9. So there would be total 9 runners in his school in the case.
But Matt is 50th fastest runner meaning 49 are ahead of him numbered 1 to 49. And 49 are behind him numbered as 51 to 99 (total 49) while Matt is at 50th position.
Hence, there are 49 + 1 + 49 = 99 runners in his school.