📄 puzzles.html
字号:
bg plastic bottles. Pramatha got thirsty and drank half the water
in her bottle.A little later on she drank 1/3 f what was left.Sometime
afterwards she drank 1/4 of what remained and so on Pranathi also had
a bottle of the same size.She drank half the bottle at the first
instance ,half of what remained when she drank next and so on.
Aftr each took 10 drins ,the water Pramatha left was how many times
greatr than the water Pranathi had left?
Soltuion:
Pramatha for the first drink 1/2
for the second drink 1/3
for the third drink 1/4
She drank 10 times and hence by the end of the 10th drink 1/11
of water she had in the bottle was over.
Pranathi for the first drink 1/2
for the second drin 1/4
for the third drink 1/8
So Pranathi as per the given information has drunk 1/1024 of water
she had in the bottle.
Water left for Pramatha/Water left for Pranathi=1/11 / 1/1024 =1024/11
13.NAME OF THE EXCHANGE
In GreatBritain some years ago the first threeletters of a telephone
number usd to indicate the name of the exchangeHow many such
arrangements of 3 letters is it possible to devise from the 26
letters of the alphabet?
Solution:
For permutations the no.of ways to select is npr=n!/(n-r)!
Hence out of 26 letters the possible outcomes are 26p3=26!/23!=15600
14.VALUE OF THE SERIES
Take a good look at the following series.
1-1/3+1/5-1/7+1/9-1/11+1/13....................
Find the value of the series and multiply the answer by 4.You will
notce that a well-known vale approximates this product.Even more
interestng is that as you add more terms the approximation becomes
closer.
Solution:
Ths is an Arithmetic progresson with value .76 when two terms
added becomes .77 and multiplidd by 4 it becomes 3.04 and 3.08
repeatition it is 3.14 which pi value adjusted to 2 decimals.
15.PLANTING TREES
If you wished to plant some trees so that each was equidistant from
every pther tree,what is the largest number you would plant?
Solution:
From the above informatin,as per equidstant formula of triangle,it is
an equilateral triangle.
Planting at all the three corners only 3 can be planted.
The centroid is the middle point placed exactly equidistant from
all the corners.
Hence 4 plants can be planted at euqidistant.
16.LENGTH OF A TRAIN
A train is travelling at the speed of 96 kmph.It takes 3 seconds to
enter a tunnel and 30 seconds more to pass thorugh it completely.
What is the length of the train and the tunnel?
Solution:
Speed of the train=95*5/18 m/sec
Time taken=3ssec
Length of the train=96*5/18*3=80m
Length of the tunnel=96*5/18*30=800m
17.A GAME OF BILLIARDS
Rajv,Sanjiv,Vinay were playing a game of Billiards.Rajiv can give
Sanjiv 10 points in 50 and Sanjiv can give 10 points in 50.How
many points in 50 must Rajiv gve Sanjiv to make an even game?
Solution:
Rajiv 50 Sanjiv 40
Sanjiv 50 Vinay 40
Sanjiv 40 Vinay 40*40/50=32
Rajiv 50 Sanjiv 40 Vinay 32
Rajiv gains 18 points than Vinay (50-32=18)
18.WOMEN AT CLUB SOCIALS
Women outnumbered men by 16 at a club social.Seventimes the no.of
women exceeds nine times the no.of men by 32.What was the number
of men and women at club?
Solution:
Let W and M be the no.of women and men respectively.
Given W=M+16.................(1)
7W=9M+32................(2)
7*(1)=>7W=7M+112........(3)
(3)-(2) =>M=40
W=56
<font size=3> <a href="puzzles.html"><b>Top</b></a></font>
19.FILLING WINE IN BARRELS
A friend of mine in London has a very nice cellar.He has two large
barrels in the cellar.The larger barrel is mostly empty.But the
smaller barrel is only 5/6 th full f wine while it can hold
536 litres.Supposing he empties the smaller barrel and fills the
bigger barrel to find that the wine fills only 4/9 of it.How much
wine would the larger barrel hold when full?
Solution:
5/6-------------------536
4/9-------------------?
5/6*536=4/9*x
=>x=1005 litrs
20.WEIGHT OF A BRICK
We have a brick of regular size.It weighs 4 kilograms.How much do
you think asmaller brick four times small, but made of the same
material weigh?
Solution:
The weight of the given brick = 4 Kilograms = 4000 grams
It is given that the smaller brick's volume is 4 times smaller
than the given one.
The volume of smaller brick = 4 * 4 * 4 = 64 times smaller
The smaller brick's weight = 4000/64 = 62.5 grams
21.A JUMPING FROG
A frog starts climbing a 30 ft wall. Each hour it climbs 3 ft and
slips back 2. How many days does it take him to reach the top and
get out?
Solution:
Hours Feets
1 3ft - 2ft = 1ft
2 3ft - 2ft = 1ft
3 3ft - 2ft = 1ft
: :
: :
27 3ft - 2ft = 1 ft
At the end of 27th hour the frog climbs 27fts and on 28th hour it
climbs the remaining 3fts and comes out.
22.QUESTION OF PROBABILITY
My friend Parveen teaches at a school. One day she conducted a
test for 3 of her students and when they handed back the test
papers, they had forgotten to write their names. Parveen returned
the papers to the students at random.What is the probability that
none of the 3 students will get the right paper?
Solution:
The possible combinations for the given condition are:
1 2 3 condition met
1 2 3 No
1 3 2 Yes
2 1 3 No
2 3 1 Yes
3 1 2 Yes
3 2 1 No
The required probability = 2/6 = 1/3
23.MATHEMATICAL ODDITY
In the 20th century there are only seven years whose numbers are a
mathematical oddity because their numbers signify a prime number.
The first one of its kind was the year 1951.Can you name the other sin?
Solution:
1973,1979,1987,1993,1997,1999.
24.DOWN THE ESCALATOR
Recently,while in London,I decided to walk down the escalator of a
tube station.I did some quick calculation in my mind.I found that
if I wa down 26 steps, I require 30 seconds to reach the bottom.
However ,if I am able to step down 34 stairs I would only require
18 secionds to get to the bottom. If the time is measured from the
moment the top step begins to descend to the time I step off the
last step at the bottom , can you yel the height of the stairway
in steps?
Solution:
Given that after walking 26 steps time needed to reach the bottom is
30 seconds ---(1)
Similarly after walking 34 steps, it needs
18 seconds more to reach the bottom ---(2)
from (1) & (2) it is clear that
for (34-26) steps it took (30-18) seconds.
i.e; 12 seconds for 8 steps
in 1 second --------?
(1*8)/12=2/3 steps/sec.
i.e; 2 steps in 3 seconds
for 30 seconds -----------how many steps?
=> (30*2)/3=20 steps.
Finally Total number of steps = 26 + (steps covered in 30 seconds)
=26+20=46 steps.
25.A COMPUTING PROBLEM
Compute (100-1)(100-2)(100-3).................(100+1)(100+2)(100+3)=?
Solution:
=>(100-1)(100-2)(100-3).........(100-100)(100+1)(100+2)(100+3)
=>(100-1)(100-2)(100-3).........(0)(100+1)(100+2)(100+3)
=0
26.A CIRCLE AND A TRIANGLE
What do you call a circle which passes through the vertices of of
a triangle?
Solution:
Circumscribed.The meaning to circumscribe is to describe a figure
round another so as to touch it at points without cutting.This is
exactly what takes place with the circumscribed circle.
To find the center of such a circle,we have to bisect the sides of
a triangle and errect perpendiculars which are concurrent at the
circumcentre. The radius r of the circumscribed circle of the
triangle ABC is given by R=a/2SinA=b/2SinB=c/2Sinc
27.MISSING TERMS
48,60,58,72,68,104.......
Here is a sequenc.Can you find the two missing terms?
Solution:
The odd terms are in the decimal system and differ by 10.And each
even term is the preceeding odd term expressed in the octonamy
system.78-8=70,remainder 6:9:8=1,remainder 1.Therefore the next
two terms are: 78,116
<font size=3> <a href="puzzles.html"><b>Top</b></a></font>
28.PACKETS OF CANDY
If 6 men can pack 6 packets of candy in 6 minutes.How many are
required to pack 60 packets in 60 minutes?
Solution:
Given that for 6 men to pack 6packets of candy it takes 6 miutes
i.e., for 1 man to pack 1 packet it takes 1 miute.
Hence,for 60 packets to be packed in 60 miutes we need 60 men.
29.A PROBLEM OF WEIGHT
In my neighbourhood lives a man who weighs 200 pounds.He has
two sons.They both weigh 100 pounds each.On a festival day they
decide to go across the river on a boat to vissit some relations.
But the boat could carry a maximum load at only 200 pounds.Yes
they managed to come across the river by boat.How did they?
Solution:
Let us assume that c1 ----------------->first son
c2 ---------------->second son
f ------------------>father
First the two sons c1,c2rowed across the river and c1 stayed
behind while c2 returned in the boat to his father.The son remained
behind while the father crossed the river.Then the other son
brought back and the two brothers c1,c2 rowed over together.
30.A PROBLEM OF CANDY BARS
Recently I attended a birthday party.All the children in the
party were given candy bars.All the children got 3 candy bars each
except the child sitting in the end.She got only 2 candy bars.If
only child had been given 2 candy bars there would have been
8 candy bars remaining.How many candy bars were there altogether
to begin with?
Solution:
Suppose that there were x children at the party.
If we distribute the candies in the above mentioned ways,then
the resulting expressions
3(x-1)+2---------------------(1)
2x+8-------------------------(2)
3(x-1)+2=2x+8
3x-3+2=2x+8
3x-1=2x+8
x=9
Therefore the no.of candies for distribution 2x+8=2*9+8=18+8=26
31.FIND OUT THE SUM
What is the sum of all numbers between 100 and 1000 which are
divisible by 14?
Solution:
Let us assume that the sum is S
s=112+126+........+994
s=14(8+9+10+.....................+71)
s=14(8+71)(71-8+1)/2=7(79)(64)=35392
32.WALKING ALL THE WAY
One day I decided to walk all the way from Banglore to Tumkur.
I started exactly at noon and some one I know in Tumkur decided
to walk all the way from Tumkur to Banglore and she started
exactly at 2 PM on the same day. We met on the Banglore - Tumkur
road at 5 past four and we both reached our destination at exactly
the same time.At what time did we both arrive?
Solution:
There fore Total time = 2:00 PM + 3:55 PM + 1:55 PM = 7:50PM
33.THE TRAINS AND THE FALCON
Two trains start from two opposite directions towards each other.
The stations from which they start are 50 miles apart.Both the trains
start at the same time towards the other train. As soon as it
reaches the second one, it fies back to the first train and so on
and so forth. It continues to do so, flying bacwards and forwards
from one train to other until the trains meet. Both the trains travel
at a speed of 25 miles per hour,and the bird flies at 100 miles per
hour. How many miles will the falcon have flown before the trains meet?
Solution:
The trains travel at 25 miles per hour.
Hence they will meet after travelling for one hour and the falcon also
must have been flyingfor one hour. Since it travels at 100 miles per
hour the bird must have flown 100 miles
34.VALUE OF 'S'
S434S0, what number must be substituted with to make it divisible by 36?
Solution:
To be divisible by 36, the number has to be divided by 4 and 9
To be divisible by 4 , the number 'S' must be an even number and to be
divisible by 9, the sum of all the digits of the number must be either
equal to 9 or a multiple of 9
⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -