One guy has Rs. 100/ in hand. He has to buy 100
balls. One football costs Rs. 15/, One
Cricket ball costs Re. 1/ and one table tennis ball
costs Rs. 0.25 He spend the whole Rs. 100/ to buy the
balls. How many of each balls he bought?
F + C + T = 100eq1
15F + C + 0.25T = 100eq2
eq1=eq2 .solve to get F=3T/56 ;F=3,T=56,C=41
1.Bird and the train:
The distance between Station Atena and Station Barcena
is 90 miles. A train starts from Atena towards
Barcena. A bird starts at the same time from Barcena
straight towards the moving train. On reaching the
train, it instantaneously turns back and returns to
Barcena. The bird makes these journeys from Barcena to
the train and back to Barcena continuously till the
train reaches Barcena. The bird finally returns to
Barcena and rests. Calculate the total distance in
miles the bird travels in the following two cases:
(a) the bird flies at 90 miles per hour and the speed
of the train is 60 miles per hour
there is no need to consider their meeting pt at
all.the train has been running for
90miles/(60miles/hr)=1.5hrs.bird flies till train
reaches destination frm strting pt.so bird flies
for1.5hrs at the vel given(90).so dist=1.5*90=135miles
(b) the bird flies at 60 miles per hour and the speed
of the train is 90 miles per hour
time of train=1hr.so dist of bird=60*1=60miles
2.Tennis Championship
A tennis championship is played on a knockout basis,
i.e., a player is out of the tournament when he loses
a match.
(a) How many players participate in the tournament if
15 matches are totally played?
C u don't need to sum it up.since it's a knock out
only 1 person emerges winner finally.so15+1=16is
answer.becos after15 matches finally we shud've
15losers and 1winner.
(b) How many matches are played in the tournament if
50 players totally participate? > 49.its always
one less thn no of players as per the idea ive given
above.so no need to check okay cos its always
true.ans is 49.
old enough:
Mark:
"When I add 4 times my age 4 years from now to 5
times my age 5 years from now, I get 10 times my
current age. How old will I be 3 years from now?"
Let x= current age
4(x+4)+5(x+5)=10x ;so x=Ò 41 years
3.Gold coins:
A rich merchant had collected many gold coins. He did
not want anybody to know about them. One day, his wife
asked, "How many gold coins do we have?"
After pausing a moment, he replied, "Well! If I divide
the coins into two unequal numbers, then 37 times the
difference between the two numbers equals the
difference between the squares of the two numbers."
The wife looked puzzled. Can you help the merchant's
wife by finding out how many gold Ò
37(xy)=x^2y^2. u no tht x^2y^2=(xy)(x+y).so (xy)
cancels on both sides to give x+y=37.so sum of unequal
halves=37 which is the req answer.
4.Football Matches
A set of football matches is to be organized in a
"roundrobin" fashion, i.e., every participating team
plays a match against every other team once and only
once.
If 21 matches are totally played, how many teams
participated?
Ò ans:7 teams okay.for a match u need 2 teams.suppose
there r totally 'n 'teams.
Now uve to choose 2 teams out of 'n' teams.so answer
=no of such choices=no. of possible combinations. So
we've ans = nC2(ncombination2)=21;solve to get n=7.
Sol: n(n1)/2=21. so n=7.if u don't understand c the
graph below
each team plays no. of matches=no of teams ahead of
it. One bar '|' represents one team.
| | | | | | | 7
6 5 4 3 2 1 0 21
last team is written as 0 matches becos this team has
already played with all other teamshence sum of
matches =6+5+4+3+2+1=21 which is correct only if no of
teams =7
5. Glenn and Jason each have a collection of cricket
balls. Glenn said that if Jason would give him 2 of
his balls they would have an equal number; but, if
Glenn would give Jason 2 of his balls, Jason would
have 2 times as many balls as Glenn. How many balls
does Jason have? Ò 14
1. G+2=j2
2. 2(G2)=J+2.
solve these 2 to get
J=14
6. Monkeys and bananas:
Suppose 8 monkeys take 8 minutes to eat 8 bananas.
(a) How many minutes would it take 3 monkeys to eat 3
bananas?
Sol:each mky takes 8 min to eat a banana
(b) How many monkeys would it take to eat 48 bananas
in 48 minutes
ans:8m=48 m=6
7.Vacation time
It was vacation time, and so I decided to visit my
cousin's home. What a grand time we had! In the
mornings, we both would go for a jog. The evenings
were spent on the tennis court. Tiring as these
activities were, we could manage only one per day,
i.e., either we went for a jog or played tennis each
day. There were days when we felt lazy and stayed home
all day long.
Now, there were 12 mornings when we did nothing, 18
evenings when we stayed at home, and a total of 14
days when we jogged or played tennis. For how many
days did I stay at my cousin's place?
Use sets and venn diagram to solve such questions.a,b
,aub,anb etc.
12=tennis+leave
18=jog +leave
so jogtennis=6
again jog+tennis=14.so solve and get
jog=10,leave=8,tennis=4.so tot=22
8.The Carpenter and the Nails
A 31" x 31" square metal plate needs to be fixed by a
carpenter on to a wooden board. The carpenter uses
nails all along the edges of the square such that
there are 32 nails on each side of the square. Each
nail is at the same distance from the neighboring
nails. How many nails does the carpenter use?
Ans= 32*2 + 30*2=124
9.Old Man Wrinkle
Man Wrinkle spent onefourth of his life as a boy,
oneeighth as a youth, and onehalf as an active man.
If Man Wrinkle spent 8 years as an old man, then how
many years did he spend as an active man?
(1/4)y+(1/8)y+(1/2)y =p; where y =tot life time.
yp=8.since p=(14/16)y
we've y=64
active age=32
10 A farmer has C chickens.A sack of feed comes for 9
days.As the feed cost is increasing the
farmer sells some chickens and retains 12 chicken.If
he reduces the feed quantity by 10% .Then
he observesthat the feed comes for 30 days.What is C?
sol:
C chickens can b fed for 9 days.so C chick can eat 1/9
in 1 day.
so 1 chick can eat
(1/9C)in one day.
after his reduction one chick gets to eat only 90% of
wht it used to eat in one day.
so new feed value=0.9*(1/9C)for 1day.but now he has
only 12 chicks.
that means as per new rule feed is suitable for 12
chicks for 30 days.
i.e.
0.9*(1/9C)*12*30=1. solve to get C=36
Ans:36
23. to be 10 min earlier means car has been driven for 10
min less thn usual.
i.e 5 min in fwd jrney and 5min in bwd jrny.normally
car reaches station at 6pm.
today since it has to drive only 5 min less it reaches
at 5:55.since he
strtd to walk at 5pm.hes been walking till 5:55 since
thts wen he sees the car.so 55 min
27.m:n t1:t2
ans:(mt2mt1)/(t1t2).don't remember how this eq is
obtained but its given in lower class
mathematics texts.
38. its not ur mistake tht u don't get this answer.this
question of shak devi is confusing becos of its
grammar.
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