**Question 1. There Are Two Water Tanks A And B, A Is Much Smaller Than B. While Water Fills At The Rate Of 1 Liter Every Hour In A, It Gets Filled Up Like, 10, 20, 40,80, 160..in Tank B. 1/8 Th Of The Tank B Is Filled In 22 Hours. What Is The Time To Fill The Tank Fully?****Answer :**Tank B is filled in geometric progression, so after 22 hrs water in tank will be = 10 * 2^21 = x/8

where x = volume of tank x = 10 * 2^24 thus by geometric progression we get that n-1 = 24

so n = 25, hence time required is 25 hrs.

**Question 2. A Train Passes A Station Platform In 36 Seconds And A Man Standing On The Platform In 20 Seconds. If The Speed Of The Train Is 54 Km/hr, What Is The Length Of The Platform?****Answer :**Speed = 54 x5/18 m/sec = 15 m/sec.

Length of the train = (15 x 20)m = 300 m.

Let the length of the platform be x metres.

Then,x + 300/36 = 15

x + 300 = 540

x = 240 m.

**Question 3. 12 People {a1, A2, A12} Meet And Shake Hands In A Circular Fashion. In Other Words, There Are Totally 36 Handshakes Involving The Pairs, {a1, A2}, {a2, A3}, {a11, A12}, {a12, A1}. Then Size Of The Smallest Set Of People Such That The Rest Have Shaken Hands With At Least One Person In The Set Is?****Answer :**12 x 11 / 2 = 66 Handshakes.

**Question 4. A Boat Can Travel With A Speed Of 13 Km/hr In Still Water. If The Speed Of The Stream Is 4 Km/hr, Find The Time Taken By The Boat To Go 68 Km Downstream.****Answer :**Speed downstream = (13 + 4) km/hr = 17 km/hr.

Time taken to travel 68 km downstream = (68/17)hrs = 4 hrs.

**Question 5. Tickets Numbered 1 To 20 Are Mixed Up And Then A Ticket Is Drawn At Random. What Is The Probability That The Ticket Drawn Has A Number Which Is A Multiple Of 3 Or 5?****Answer :**Here, S = {1, 2, 3, 4, …., 19, 20}.

Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.

P(E) =n(E)/n(S)=9/20

**Question 6. How Many Four Digit Numbers Can Be Formed Using The Digits 1, 2, 3, 4, 5 (but With Repetition) That Are Divisible By 4? Can You Help Alok Find The Answer ?****Answer :**1= 5^4-1=125, n= no of digits

1 2

2 4

3 2

4 4

5 2

The first two digits in the place can be filled in 5 x 5 ways.

So there are totally 25 x 5 = 125 ways

**Question 7. The Age Of The Two Friends Were In The Ration Of 6:5.if The Sum Of Their Ages Is 66.then After How Many Years Their Ratio Will Become 7:6 ?****Answer :**Let the age of two friends be 6x and 5x

Sum of their ages 66 => 6x + 5x = 66 => 11x = 66 => x=6

The ages will be 36 and 30

(36+k)/(30+k) = 7/6 => 36 x 6 + 6k = 210 + 7k

216 + 6k = 210 + 7k => 6 = k

After 6 years their ages will be in the ratio 7:6

**Question 8. The Age Of The Two Friends Were In The Ratio Of 2:3.if The Sum Of Their Ages Is 55.then After How Many Years Their Ratio Will Become 4:5 ?****Answer :**Let the age be the friends be 2x and 3x. Sum of their ages = 55

2x + 3x = 55 => 5x=55 => x=11

Their ages are 22 and 33

After k years both of them will be 22+k and 33+k years old

Ratio of their age at that time will me 4:5

(22+k)/(33+k)=4/5

5(22+k)=4(33+4) => 110 + 5k = 132+4k

K=132-110 = 22

**Question 9. A Person Is Manufacturing A House. He Bought 20 Ropes Of Wire Which Has A Density Of 300 Kg/m3.the Height Of The Building To Be Constructed Is 40 M. If The Capacity Of The Current Passed In The Wire Is 20 A And The Voltage Capacity Is 80 Volts.then What Will Be The Opposing Force To The Current If The Wire Is Used ?****Answer :****Explanation:**by ohms law

v = ir

so r = v/i

so r = 80/20 = 4

**Question 10. A Horse Chases A Pony 2 Hours After The Pony Runs. Horse Takes 3 Hours To Reach The Pony. If The Average Speed Of The Horse Is 81 Kph.then What Is The Average Speed Of The Pony?****Answer :**Horse covers = 81*3 = 243 kms

So ponies speed = 243/(2+3) = 243/5 = 48.6

**Question 11. The Difference Between Two No Is 9 And The Product Of The Two Is 14.what Is The Square Of Their Sum?****Answer :**One number be x and other y, then x – y = 9

(x – y)2 = 81

x2 + y2 = 81 + 2xy = 109

(x+y)2 = x2 + y2 + 2xy = 109 + 28 = 137

So answer is 137

**Question 12. On Planet Korba, A Solar Blast Has Melted The Ice Caps On Its Equator. 9 Years After The Ice Melts, Tiny Planetoids Called Echina Start Growing On The Rocks. Echina Grows In The Form Of Circle, And The Relationship Between The Diameter Of This Circle And The Age Of Echina Is Given By The Formula D = 4*v (t-9) For T = 9 Where D Represents The Diameter In Mm And T The Number Of Years Since The Solar Blast.jagan Recorded The Radius Of Some Echina At A Particular Spot As 7mm. How Many Years Back Did The Solar Blast Occur ?****Answer :**d = 4*(t-9)

Given r = 12 mm

So, d = 24 mm

So,

24 = 4t – 36

4t = 60

t = 15 years

**Question 13. A Man Goes 50km North , Then Turned Left Walked 40km, Then Turned Right ? In Which Direction He Is?****Answer :**Left and right consecutive movement nullified the change in direction. So, he is in the direction he started with.

**Question 14. Ferrari S.p.a Is An Italian Sports Car Manufacturer Based In Maranello, Italy. Founded By Enzo Ferrari In 1928 As Scuderia Ferrari, The Company Sponsored Drivers And Manufactured Race Cars Before Moving Into Production Of Street-legal Vehicles In 1947 As Ferrari S.p.a. Throughout Its History, The Company Has Been Noted For Its Continued Participation In Racing, Especially In Formula One Where It Has Employed Great Success .rohit Once Bought A Ferrari. It Could Go 4 Times As Fast As Mohan Old Mercedes. If The Speed Of Mohan’s Mercedes Is 35 Km/hr And The Distance Traveled By The Ferrari Is 490 Km, Find The Total Time Taken For Rohit To Drive That Distance.****Answer :**Mohans speed = 35 Km/hr

Rohit speed = 4 x Mohan speed = 4 x 35 = 140 Kmph

Time taken =Distance / Speed = 490 / 140 = 49/14 = 7/2

**Question 15. A Man Goes North 37 Km. Turns Left Goes 2 Km.turns Right Goes 17 Km.turns Right Goes 2 Km. Find Distance B/w Starting Ending Point.****Answer :**Distance between the starting and end point is 37 + 17 = 54.

**Question 16. If There Are 30 Cans Out Of Them One Is Poisoned If A Person Tastes Very Little He Will Die Within 14 Hours So If There Are Mice To Test And 24 Hours To Test, How Many Mices Are Required To Find The Poisoned Can ?****Answer :**Have 6 mice for testing,

Give each mice contents from 5 cans each

5 5 5 5 5 5

After 14 hours, one of the mice will die

So, we will know which 5 cans must have the poison

Then , take the contents of these 5 cans and give to the remaining 5 mice each.

We will know in due time which can is poisoned

5C1+5C2+5C3+5C4 = 5 + 10 + 10 + 5 = 30

**Question 17. If A And B Are Mixed In 3:5 Ratio And B And C Are Mixed In 8:5 Ratio If The Final Mixture Is 35 Liters, Find The Amount Of B?****Answer :**a: b = 3:5

b: c = 8: 5

a:b:c = 24 : 40 : 25 and total is 24+40+25 = 89

(40/89) x 35 = 15.73

**Question 18. It Is Dark In My Bedroom And I Want To Get Two Socks Of The Same Color From My Drawer, Which Contains 24 Red And 24 Blue Socks. How Many Socks Do I Have To Take From The Drawer To Get At Least Two Socks Of The Same Color ?****Answer :**The Answer is 25. First he will select 24 in that the maximum chance is all are red so if we take one more socks, it has to be the other color. Hence, the answer is 24 + 1 = 25

**Question 19. If The Valentines Day In 2005 Falls On Monday, Then On Which Day Will The Valentines Day Fall On 2010 ?****Answer :**FEB. 14, 2005 IS A MONDAY

From Feb. 14, 2005 to Feb. 14 2006, there will be 365 days which means one odd day.

So, FEB. 14, 2006 WILL BE A TUESDAY

From Feb. 14, 2006 to Feb. 14 2007, there will be 365 days which means one odd day.

So, FEB. 14, 2007 WILL BE A WEDNESDAY

From Feb. 14, 2007 to Feb. 14 2008, there will be 365 days which means one odd day.

So, FEB. 14, 2008 WILL BE A THURSDAY

From Feb. 14, 2008 to Feb. 14 2009, there will be 366 days

– add one more odd day for Feb.29. Total is 2 odd days.

So FEB. 14, 2009 WILL BE A SATURDAY

From Feb. 14, 2009 to Feb. 14 2010, there will be 365 days

one odd day .

So FEB. 14, 2010 WILL BE A SUNDAY

**Question 20. An Athlete Decides To Run The Same Distance In 1/4th Less Time That She Usually Took. By How Much Percent Will She Have To Increase Her Average Speed ?****Answer :**(3/4)t=1

t=4/3=1+1/3

She will have to increase her speed by 33.333% to run the same distance in 3/4s of the time

**Question 21. In A Building There Are 5 Rooms. Each Having A Equal Area .the Length Of The Room Is 4m And Bread Ht Is 5 M.the Height Of The Rooms Are 2m.if 17 Bricks Are Needed To Make A Square Meter Then How Many Bricks Are Needed To Make The Floor Of A Particular Room?****Answer :**Dimensions = 4 x 5 x 2

TSA = 2 (4 x 5 + 5 x 2 + 4 x 2) = 2(20+10+8)=2×38 = 76 sq m

So bricks required = 76 x 17 = 1292

For 5 rooms 1292 x5 = 6460

**Question 22. One Man Want To Build A Wall .the Length And Breadth Of The Wall Are 20 And 30 Respectively. He Need 35 Bricks For One Square Centimeter Then How Many Bricks He Need ?****Answer :**Area = 20 x 30 = 600 cm^2

Bricks = 600 x 35 = 21000

**Question 23. In A Hotel We Can Order Two Types Of Varieties,but We Can Make 6 More Varieties In Home.one Can Choose The Four Varieties With Two From Hotel As Must.find How Many Ways One Can Order.****Answer :**No of ways of selecting 2 from hotel (6 choices) = 6C2

And from home (2 choices) = 2C2

2C2 x 6C2 = 1 x 15 = 15 ways

**Question 24. If A Pipe Can Fill The Tank Within 6hrs. But Due To Leak It Takes 30 Min More.now The Tank Is Full Then How Much Time Will It Take To Empty The Tank Throught The Leak.?****Answer :**Let the capacity of the tank be 6 litre.

Then time to fill this tank is 6 hour ,when there is no leakage .

so in 1 hour it fills 1 litre.

when leakage is there then it takes 6.5 hour to fill 6 litre

so in 1 hour it fills 6/6.5 litre.

Time to vacate will be 1-(6/6.5) = 1/13 litre in 1 hour

time to vacate 1 litre will be 13 hour.

For 6 litre it will be 13*6 =78

**Question 25. The Bacteria Has The Probability Of Split Into 3 And Probability To Die Is 1/3rd Of The Total Bacteria.let The Probability Is P. Some Of Them Survived With Probability 1/5.then Which Among The Following Relation Is True ?****Answer :**Probability for the bacteria to be dying = 1/3

Hence probability of survival = 1/5

if they survive, they will be split into 3 more bacteria hence, p = (1/3) + (3* 1/5)

**Question 26. There Is A Bacteria Which Has The Probability Of Die 1/3 Of Its Total Number Or It May Tripled. Find Out The Probability ?****Answer :**Probability of bacteria to die is 1/3

or its get tripled, hence the probability of getting tripled is (2/3)*p*p*p that is (2/3)*p^3

so both the probability combined as P=1/3+(2/3*p^3)

**Question 27. Amrith Told To Anand In Front Of A Photo That He Is The Son Of My Fathers Son.find Who Is In The Picture If Amrith Have No Brothers And Sisters.****Answer :**Amriths son

**Question 28. One Grand Father Has 3 Grand Children Two Of The Age Difference Is 3.eldest Child Age Is 3 Times The Youngest Childs Age And The Eldest Child Age Is Two Year More Than The Sum Of Other Two Children. Find What Is The Age Of The Elders Child ?****Answer :**Let the age of eldest child is E , that of elder child is M and that of youngest child is Y, then according to the given conditions

E = 3Y (1) and E = 2 + M + Y (2)

Third condition is somewhat complicated, according to this condition two of the age difference is 3 so three cases will arise

1) E – M = 3, ……(3)

2) M – Y = 3, ……(4)

3) E – Y = 3, ……(5)

if we take first of the 3 conditions then on solving (1), (2) and (3) we will get E = 3, M = 0, Y = 1 which is wrong now on solving (1), (2) and (4) we will get E = 15, M = 8, Y = 5

similarity on solving (1), (2) and (5) we will get E = 4.5, M = 1, Y = 1.5

only E = 15, M = 8, Y = 5 is correct so age of elder child is 8 years.

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