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### Mathmetics

ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams

##### Directions: Study the following information carefully and answer the given questions.In a bag X there are some identical green balls and rest other are blue balls (blue balls greaterthan the green balls).(i) Probability of getting 1 green and 1 blue ball without replacement is 40/87.(ii) Probability of getting both green is A.(iii) If there is another bag (Y) in which some blue balls and rest others are green.(iv) If a number of blue balls taken out from Y is 4 more than the green balls taken out from bag Y and added to bag X. Then the probability of getting both green from bag X is 13/123.Find the number of blue balls taken out from bag Y.
 1) 2 2) 4 3) 5 4) 6
Explanation :
Bag X:
Two balls taken from bag x, total probability,
According to the question,
40/87 = (Probability of getting 1st green and second blue * Probability of getting 1st blue and second green)
Take green = 10 and blue = 20
According to the question,
40/87 = 10 * 20 * 2/(30 * 29)
40/87 = 40/87
Let us take number of green balls taken out from bag Y be a
Number of blue balls taken out from bag Y = a + 4
According to the question,
(10 + a)C2/(30 + 2a + 4)C2 = 13/123
(10 + a) * (9 + a)/[(34 + 2a) * (33 + 2a)] = 13/123
Simplify the equation we get, a = 4
Number of blue balls taken out from bag Y = a + 4 = 4 + 4 = 8
##### Directions: Study the following information carefully and answer the givenquestions.In a bag X there are some identical green balls and rest other are blue balls (blue balls greaterthan the green balls).(i) Probability of getting 1 green and 1 blue ball without replacement is 40/87.(ii) Probability of getting both green is A.(iii) If there is another bag (Y) in which some blue balls and rest others are green.(iv) If a number of blue balls taken out from Y is 4 more than the green balls taken out frombag Y and added to bag X. Then the probability of getting both green from bag X is 13/123.What should be total number of balls in bag X ?
 1) 10 2) 20 3) 29 4) 30
Explanation :
Bag X:
Two balls taken from bag x, total probability,
According to the question,
40/87 = (Probability of getting 1st green and second blue * Probability of getting 1st blue and
second green)
Take green = 10 and blue = 20
According to the question,
40/87 = 10 * 20 * 2/(30 * 29)
40/87 = 40/87
This satisfies the given condition.
So, total number  balls in box X should be 30.
##### Directions : Study the following information carefully and answer the given questions.In a bag X there are some identical green balls and rest other are blue balls (blue balls greater than the green balls).(i) Probability of getting 1 green and 1 blue ball without replacement is 40/87.(ii) Probability of getting both green is A.(iii) If there is another bag (Y) in which some blue balls and rest others are green.(iv) If a number of blue balls taken out from Y is 4 more than the green balls taken out from bag Y and added to bag X. Then the probability of getting both green from bag X is 13/123.What should be the value of A ?
 1) 2/29 2) 3/29 3) 4/29 4) 5/29
Explanation :
Bag X:
Two balls taken from bag x, total probability,
According to the question,
40/87 = (Probability of getting 1st green and second blue * Probability of getting 1st blue and second green)
Take green = 10 and blue = 20
According to the question,
40/87 = 10 * 20 * 2/(30 * 29)      or  40/87 = 40/87
This satisfies the given condition.
Probability of both green ball (A) = 10C2/30C2
= (10 * 9)/(29 * 30) = 3/29
##### Direction: Data below represent the number of people required for various projects to be completed in various days:Project                      Situation 1                                                             Situation 2                 Number of workers       Days required          Number of workers       Days required A              X                                   88                                                  X+8             66 B              Y                                  Y-1                                                  Y+6                    Y-6 C              Z2                           75                                                   M2                    108
 1) 60 days 2) 80 days 3) 90 days 4) 120 days 5) None of these
Answer : 90 days
Explanation : Total workers = 0.5Z * 2 M = 0.5 * (1.2 M) * 2 M = 1.2 M2 Total work = M2 * 108 = 1.2 M2 * No of days = > No of days = (M2 * 108) / (1.2 M2 ) = 90 days
##### Direction: Data below represent the number of people required for various projects to be completed in various days:Project                      Situation 1                                                             Situation 2                 Number of workers       Days required                  Number of workers       Days required A              X                                   88                                                  X+8             66 B              Y                                  Y-1                                                  Y+6                    Y-6 C              Z2                           75                                                   M2                    108If 64 people were working for Project A, how many days did it take to complete the work?
 1) 33 days 2) 22 days 3) 36 days 4) 44 days 5) None of the
Answer : 33 days
Explanation :
Solutions:
Project A:
X * 88 = (X + 8) * 66
= > 88X = 66X + 8 * 66 = > 22X = 8 * 66   = > X = 24

Project B:
Y * (Y - 1) = (Y + 6) * (Y - 6)
Y2 – Y = Y2 – 62
= > Y = 36

Project C:
Z2 * 75 = M2 * 108
= > Z2 / M2 = 108/75
= > Z2 / M2 = 36/25
= > Z / M = 6/5
= > Z = 6/5 * M
= > Z = 1.2 M

M1 * D1 = M2 * D2
24 * 88 = 64 * D2
= > D2 = (24 * 88)/64
= > D2 = 33 days
##### In a 96 litre mixture of water and milk, water is only 40%. The milkman sold 12 litres of the mixture to a customer and then added 10 litres of pure milk and 15 litres of water in the mixture. What is the approximate percentage of water in the final mixture?
 1) 40 2) 42 3) 45 4) 48
##### Direction: Each question below is followed by three statements I,II and III. You have to determine whether the data given in the statement/statements is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer.What is the speed of boat in still water ?I. The boat can cover 25 km downstream distance in 5 hours.II. Speed of the stream us two-third of the speed of boat in still water.III. The boat can cover 25 km upstream distance in 10 hours.
 1) I and II together 2) Only II 3) I and II together 4) I and either II or III 5) Any two statements together.
Answer : Any two statements together.
Explanation : Explanations : Let speed of boat in sill water be x kmph and velocity of stream be y kmph respectively.
So, from I , we get x+y = 5kmph

From II, it given y = 2x/3 , we get x = 3kmph and y = 2kmph
From III, w get, x - y = 2.5 kmph

Therefore, to find out the speed of the boat any two statements together is sufficient.

##### A rectangular container, whose base is square of side 15cm,stands on a horizontal table and holds water up to 3cm from the top. When a cube is  placed in the water and is completely submerged, the water rises to the top and 54cm^3 of water overflows. What is its surface area?
 1) 448cm2 2) 464cm2 3) 486cm2 4) 524cm2 5) None of these