46 - 51
46. There are 4 married couples out of which a group of 3
should be created. But in the group created there should
not be any couples? How many different ways are there.
To select the first person you have 8 choices.
To select the second person you have 6 choices leaving out the spouse.
To select the third person you have 4 choices.
Total ways of selecting is 8 * 6 * 4 / 3! = 32
47. Two men are walking towards each other along a rail track in the opposite
direction.One goods train crossed the first person in 20 sec.
After 10 min the train crossed the other person who is comming in
opposite direction in 18 sec .After the train has passed, when will
the two persons meet?
Let x be the speed of the train.
Let y be the speed of the person.
Let L be the length of the train.
Let Person A walk in the direction of train
Person B walks in the opposite direction.
L / (x-y) = 20 --1
L / (x+y) = 18 --2
From 1 and 2 we have (x+y)/(x-y) = 20/18.
x = 19y
Distance travelled by train in 10 mins = 190y
Distance travelled by Person A = 10y.
so total distance yet to be covered = 180y.
So total time remaing = 180y/2y = 90 minutes.
48. THERE ARE TWO PERSON EACH HAVING SAME AMOUNT OF MARBLES IN THE BEGINING
AND 1st PERSON GAINS 20 MORE FROM THE SECOND PERSON AND HE EVENTUALLY
LOSE TWO THIRDS OF IT DURING THE PLAY AND NOW THE SECOND PERSON HAS
4TIMES MARBLES OF WHAT FIRST PERSON IS HAVING NOW.FIND HOW MUCH MARBLES DID
EACH HAD IN THE BEGINING?
Let us assume X be the initial amount and the persons be A and B
A B
X X
X+20 X-20
(X+20)/3 X-20+(X+20)*2/3
X-20+(X+20)*2/3 = 4(X+20)/3
3X - 60 + 2X + 40 = 4X + 80
5X - 20 = 4X + 80
X = 100
49. THERE WERE TWO CLOCK ONE IS GETTING SLOW BY TWO MINUTES/HR AND
ANOTHER ONE IS GAINING 1 MINUTE EVERY HOUR AND EXACTLY AFTER HOW MANY HOURS
THERE TWO CLOCK HAS A 1HR DIFFERENCE?
Every Hour the Gain of the Faster clock over the slower one is 3 Minutes.
So to have 1 hour difference it will be 60/3 = 20 Hours
50. THERE IS A NUMBER WHICH WHEN ADDED WITH 33/4 GIVES THE SAME ANS AS
MULTIPLIED WITH 33/4
Let the no be X
X + 33/4 = X*33/4
4X + 33 = 33X
X = 33/29
51. Mr. T has a wrong weighing pan.One arm is lengthier than other.1
kilogram on left balances 8 melons on right.1 kilogram on right
balances 2 melons on left.If all melons are equal in weight,what is
the weight of a single melon?
Let the weight of the melons be X
Let the inbalance be W grams.
8X - W = 1.
2X + W = 1
solving we get X = 0.2 Kg
should be created. But in the group created there should
not be any couples? How many different ways are there.
To select the first person you have 8 choices.
To select the second person you have 6 choices leaving out the spouse.
To select the third person you have 4 choices.
Total ways of selecting is 8 * 6 * 4 / 3! = 32
47. Two men are walking towards each other along a rail track in the opposite
direction.One goods train crossed the first person in 20 sec.
After 10 min the train crossed the other person who is comming in
opposite direction in 18 sec .After the train has passed, when will
the two persons meet?
Let x be the speed of the train.
Let y be the speed of the person.
Let L be the length of the train.
Let Person A walk in the direction of train
Person B walks in the opposite direction.
L / (x-y) = 20 --1
L / (x+y) = 18 --2
From 1 and 2 we have (x+y)/(x-y) = 20/18.
x = 19y
Distance travelled by train in 10 mins = 190y
Distance travelled by Person A = 10y.
so total distance yet to be covered = 180y.
So total time remaing = 180y/2y = 90 minutes.
48. THERE ARE TWO PERSON EACH HAVING SAME AMOUNT OF MARBLES IN THE BEGINING
AND 1st PERSON GAINS 20 MORE FROM THE SECOND PERSON AND HE EVENTUALLY
LOSE TWO THIRDS OF IT DURING THE PLAY AND NOW THE SECOND PERSON HAS
4TIMES MARBLES OF WHAT FIRST PERSON IS HAVING NOW.FIND HOW MUCH MARBLES DID
EACH HAD IN THE BEGINING?
Let us assume X be the initial amount and the persons be A and B
A B
X X
X+20 X-20
(X+20)/3 X-20+(X+20)*2/3
X-20+(X+20)*2/3 = 4(X+20)/3
3X - 60 + 2X + 40 = 4X + 80
5X - 20 = 4X + 80
X = 100
49. THERE WERE TWO CLOCK ONE IS GETTING SLOW BY TWO MINUTES/HR AND
ANOTHER ONE IS GAINING 1 MINUTE EVERY HOUR AND EXACTLY AFTER HOW MANY HOURS
THERE TWO CLOCK HAS A 1HR DIFFERENCE?
Every Hour the Gain of the Faster clock over the slower one is 3 Minutes.
So to have 1 hour difference it will be 60/3 = 20 Hours
50. THERE IS A NUMBER WHICH WHEN ADDED WITH 33/4 GIVES THE SAME ANS AS
MULTIPLIED WITH 33/4
Let the no be X
X + 33/4 = X*33/4
4X + 33 = 33X
X = 33/29
51. Mr. T has a wrong weighing pan.One arm is lengthier than other.1
kilogram on left balances 8 melons on right.1 kilogram on right
balances 2 melons on left.If all melons are equal in weight,what is
the weight of a single melon?
Let the weight of the melons be X
Let the inbalance be W grams.
8X - W = 1.
2X + W = 1
solving we get X = 0.2 Kg
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