**Question 1. 9 Laboures Can Complete The Construction Of A Wall In 18 Days. How Many Less Days Will 12 Laboures Take To Complete The Same Wall?****Answer :****Work done by a single person = 1/ ( 9* 18) = 1/ 162****Work done by 12 people = 12 / 162****Time taken to finish work = 162 / 12 = 13.5**

**Question 2. The Rectangle Box With Square Base Is Open At The Top. The Maximum Volume Of The Box Made From 1200 M2 Tin,in M3 Is?****Answer :****Let the length be x and the breadth be y.****Now since it has a square base;****x=y****Now the surface area can be given as S= x^2+4xy (Area of square base + Area of Sides)****And Volume can be given as V = x^2y****ATQ, S=1200,so 1200=X2+4xy****y=(1200-x2)/4x****Now for V to be max****V’=0****V'(x)=x2y****Solving for x we get x=20****Now y=20m****Hence volume is 20x20x10=4000 m****3**

**Question 3. A Person Was Fined For Exceeding The Speed Limit By 10 Km/hr. Another Person Was Also Fined For Exceeding The Same Speed Limit By Twice The Same. If The Second Person Was Traveling At A Speed Of 35km/hr,find The Speed Limit?****Answer :****1 person exceeded by 10. Another person twice 10 which is 20. Given he is going at 35 km/h. So speed limit is 35 – 20=15 km/hr**

**Question 4. The Difference Between The Compound And Simple Interest On A Certain Sum For 2 Years At The Rate Of 8% Per Annum Is Rs.80,what Is The Sum?****Answer :****Since we know that SI and CI are same for first year. Difference is due to the SI of 1st year is treated as PRINCIPLE of 2nd year in CI.****So 1st we calculate the amount which treated as P in CI****P = 100*SI/R*T = 100*80/8*1 = 1000****This amount is also the SI for 1 year.****So****SI = 1000****T = 1 Year****R = 8%****P = 100*1000/8*1 = 12500**

**Question 5. The Ratio Between Two Numbers Is 5:7 And Their Product Is 560. What Is The Difference Between These Two Numbers?****Answer :****From the above information****x/y = 5/7****xy = 560****Solving the above equation we get the numbers as 20 and 28****Difference is 8**

**Question 6. The Mean And The Variance Of A Binomial Distribution Are 4 And 2 Respectively. Then The Probability Of 2 Successes Is?****Answer :****Given that variance npq = 2****and mean np = 4****q = 1/2****=> p = 1/2****n = 8****=> 8c2 * (1/2)^8 = 28/256****ans = 28/256**

**Question 7. Take Any Positive Whole Number Not Greater Than 50.if The Number Is Even, Divide It By 2.if The Number Is Odd,multiply It By 3,and Add 1 To The?****Answer :****result. Apply the same method to the resulting numbers until you finally arrive at the number 1.shown below is the chain of numbers that results from****this method if you begin with 15.****15->46->23->70->35->106->53->160->80->40->20->10->5->16->8->4->2->1**

**Question 8. As You Can See, The Number 15 Requires 17 Steps To End Up At 1.of The Numbers Not Greater Than 50,which Takes The Longest To Reach The Number 1 ?****Answer :****27, which takes 111 steps**

**Question 9. After Spending 2/3 Of His Salary On Rent And Food Items And 1/4th Of The Remaining On Transportation, Rajesh Has 6000 With Him. How Much Did He Pay On Transportation?****Answer :****Let x be the salary.****Then if he spends (2/3)x on rent and food then the remaining salary is x/3,****Out of which he spends 1/4 i.e(x/3)1/4 or x/12 on transportation…and the amount left thereafter is : ( x/3 ) – ( x/12 ) = x/4****Given..the amount left with Rajesh is : 6000 = x/4****=> Salary of Rajesh ‘x’ is : 6000 * 4 = Rs.24,000****Amount spent on rent and food = 24000 * (2/3) = Rs.16,000****Remaining amount : 24000 – 16000 = Rs.8000****Amount spent on transportation : 8000 * (1/4) = Rs.2000****Remaining amount : 8000 – 2000 = Rs.6000,the amount left with Rajesh****So answer is : 2000**

**Question 10. E=i*i*r What Is The Effect Of E When I Becomes I/2?****Answer :****E = I * I * R****Now if I = I / 2****Now E = I/2 * I/2 * R****Therefore E will decrease 4 times**

**Question 11. Out Of 55 Eggs 5 Are Defective. What Is % Of Defective Eggs?****Answer :****(5/55)*100 = 9 1/11**

**Question 12. Salary Of A Person Is ‘s’ Per Month,’x’% Of Salary Is Given As Bonus, If 3 Months Salary Is S1,s2 & S3 Then What Is His Salary?****Answer :****s1*x/100 + s2*x/100 + s3*x/100 ****s1 = s2 = s3****Ans = s1*x/100**

**Question 13. In Base 10 Representation For A Rupee 100 Paise,then Base 8 Representation What Is Rupee Value?****Answer :****Octal representation of decimal 100 is 144****100****10**** = 144****8**

**Question 14. A Sum ‘s’ Is Divided Into 4 Parts. Second Person Gets Rs 10 More Than First.3rd Person Is Rs 10 More Than Second, 4th Is 10 More Than 3rd. How Much Amount Do 1st Person Get.?****Answer :****1st person gets Rs.(s-60)/4****Let us assume that 1st person gets Rs.x****Then 2nd will get Rs.x+10****3rd will get Rs.x+20****4th will get Rs.x+30****Then the sum s=x+(x+10)+(x+20)+(x+30)****=> s=4x+60****=> 4x=s-60****=> x=(s-60)/4****Therefore 1st pesron will get (s-60)/4**

**Question 15. 1/8 Is Divided By ‘s’ , If ‘s’ Is Increased By 2 Times, What Is The Result?****Answer :****Answer = 1/(8s/2)****= 1/4s****Increases two times**

**Question 16. X Y Z U V W R S T __?****Answer :****Divide the series into letters of 3. One series starts with next letter of the last character in second series. ****x y z u v w r s t o**

**Question 17. A C F J O __****Answer :****ExplanationDiscuss the solution:****Difference between letter index position increases as 1, 2, 3, 4, 5…****Answer is u.**

**Question 18. Mr. Shah Decided To Walk Down The Escalator Of A Tube Station. He Found That If He Walks Down 26 Steps, He Requires 30 Seconds To Reach The Bottom.?****Answer :****In 12 sec(30-18) he walks down 8(34-26) steps.****therefore, (8*30)/12 =20 steps.****So,the total height of the stair way in steps=(26+20)=46 steps**

**Question 19. The Average Age Of 10 Members Of A Committee Is The Same As It Was 4 Years Ago, Because An Old Member Has Been Replaced By A Young Member.find How Much Younger Is The New Member ?****Answer :****Let the members be Old Having age O + other 9 having ages x and New one having age Y****Sum of their ages = (Y + 9 × x) and average = (Y + 9 × x)/10****Before 4 years sum was (O + 9 x – 10 × 4) and average = (O + 9 x – 10 × 4) /10****equating, Y + 9 x = O + 9x – 40****Y = O – 40****Younger is 40 years younger than Old one.**

**Question 20. Abce Is An Isosceles Trapezoid And Acde Is A Rectangle. Ab = 10 And Ec = 20. What Is The Length Of Ae?****Answer :****From point A we draw the perpendicular****segment AP to the basis EC.****Then EP=(20-10)/2=5****From the rectangular triangle EAC****(A=90) we have****(AE)^2=(EP)(EC)****(AE)^2=5*20****(AE)^2=100****(AE)=10**

**Question 21. Three Containers A, B And C Have Volumes A, B, And C Respectively; And Container A Is Full Of Water While The Other Two Are Empty. If From Container?****Answer :****a , we have to subtract****b/3 and c/2****so water left in container A****= a – (b/3 + c/2)**

**Question 22. Pa And Pb Are Tangents To The Circle At A And B Respectively And The Chord Bc Is Parallel To Tangent Pa. If Ac = 6 Cm, And Length Of The Tangent Ap Is 9 Cm, Then What Is The Length Of The Chord Bc?****Answer :****PA = PB = 9 cm ( Length of tangents from an external point) ****Angle PAB = Angle ABC ( alternate angles PA !! BC)****AC = AB = 6 cm****Triangles PAB and ACB are isosceles and sre similar triangles****( They are equiangular)****Taking the ratios of respective sides****BC/AB = AC/PB****BC/6 = 6/9****BC = 4 cm**

**Question 23. A Number Of Cats Got Together And Decided To Kill Between Them 999919 Mice. Every Cat Killed An Equal Number Of Mice. Each Cat Killed More Mice Than There Were Cats. How Many Cats Do You Think There Were ?****Answer :****Observing the num 999919 which is the total num of rats being eaten, we can write it as****(1000000-81) = (1000^2-9^2) = (1000+9)(1000-9) = (1009)(991)****So total num of rats killed =(1009)(991)****And given that each cat kills more num of rats than the total num of cats****Hence each cat kills 1009 num of rats****And there are 991 num of cats**

**Question 24. If Log2 X – 5 Log X + 6 = 0, Then What Would The Value / Values Of X Be?****Answer :****Log2 x means (log x)^2,****The answer can be found by making the substitution y = log x to give****y^2 – 5y + 6 = 0, which gives the solutions****y = 3****y = 2****ie., log x = 2 or log x = 3****ie., e2 or e3**

**Question 25. The Square Of A Two Digit Number Is Divided By Half The Number. After 36 Is Added To The Quotient, This Sum Is Then Divided By 2. The Digits Of The Resulting Number Are The Same As Those In The Original Number, But They Are In Reverse Order. The Ten’s Place Of The Original Number Is Equal To Twice The Difference Between Its Digits. What Is The Number?****Answer :****Let the number be 10A + B = C****now, (C^2/(C/2) + 36)/2= 10B + A****or, (2C+36)/2 = 10B + A****or C+18=10B+A****or, 10A + B + 18 = 10 B + A****or, 18=9(B-A), giving B-A=2****As per the question, A=twice the difference between A and B****Hence A=2*2=4****B=2+4=6****The original number is 40 + 6 = 46.**

**Question 26. Can You Tender A One Rupee Note In Such A Manner That There Shall Be Total 50 Coins But None Of Them Would Be 2 Paise Coins.?****Answer :****In descending order,****using denominations of 1p,5p,10p,25p which are available.****Thus,****25p coins : 1****10p coins : 2****5p coins : 2****1p coins : 45**

**Question 27. Complete The Sequence A, E ,i ,m ,q ,u , _ , _?****Answer :****Y,C****After each character +3**

**Question 28. A Person Travels 6km Towards West, Then Travels 5km Towards North ,then Finally Travels 6km Towards West. Where Is He With Respect To His Starting Position?****Answer :****C is the answer, 13 km northwest.****When he traveled first 6km, he will b in west.****Then aftr 5km ,he wil b in northwest.****Again he goes to west. So from the given answers, he wil b in north west position.**

**Question 29. If A Speaks The Truth 80% Of The Times, B Speaks The Truth 60% Of The Times. What Is The Probability That They Tell The Truth At The Same Time?****Answer :****Probability of events happening together = Product of individual probabilities****= 0.8 * 0.6 = 0.48.**

**Question 30. A Person Travels 12 Km In The Southward Direction And Then Travels 5km To The Right And Then Travels 15km Toward The Right And Finally Travels 5km Towards The East, How Far Is He From His Starting Place?****Answer :****______****| 5km****| |****| |****15km| |12km****| |****|_____|****5km****Hence 15-12 is 3kms**

**Question 31. Find The Next Number In The Series 1, 3 ,7 ,13 ,21 ,31?****Answer :****k(n) = k(n-1) +2(n-1) with****k(1) =1****k(7) =k(6) +2(7-1)****k(7) =31 +2*6****k(7) =31+12****k(7) =43**

**Question 32. If In A Certain Code “range” Is Coded As 12345 And “random” Is Coded As 123678. Then The Code For The Word “mango” Would Be?****Answer :****M-8****A-2****N-3****G-4****O-7****So for mango the code is 82347**

**Question 33. 1st 3 Letters Are Denoted By Its Next In The Alphabet And The Next 3 Letters Are Denoted By Its Previous In The Alphabets A Monkey Starts Climbing Up A Tree 20ft. Tall. Each Hour, It Hops 3ft. And Slips Back 2ft. How Much Time Would It Take The Monkey To Reach The Top?****Answer :****The first hour, the monkey goes 3 feet up, and slips back 2 feet.****0.1..2..3..4..5..6****|—|—|—|—|—|—|****———->****….<—–****(Imagine that’s going up instead of horizontal.)****So the monkey is 3 ft – 2 ft = 1 ft high after one hour.****In the second hour, the monkey goes up 3 more feet, and slips back 2 feet. So he’s at 1 ft + 3 ft – 2 ft = 2 ft.****Every hour, he gains 3 ft and loses 2 ft, for a total gain of 1 ft. So after the 17th hour, he’s at 17 ft high.****Now, here’s the twist: in the 18th hour, he climbs up 3 feet. Since 17 ft + 3 ft = 20 ft, he’s at the top of the tree!****So, it takes him 18 hours.**

**Question 34. What Is The Missing Number In This Series? 8 2 14 6 11 _ 14 6 18 12?****Answer :****The sum of the first and last number equal 20****The sum of the second and second-to-last number equal 20****The sum of the third and third-to-last number equal 20****So answer is 9**

**Question 35. A Certain Type Of Mixture Is Prepared By Mixing Brand A At Rs.9 A Kg. With Brand B At Rs.4 A Kg. If The Mixture Is Worth Rs.7 A Kg., How Many Kgs. Brand A Are Needed To Make 40kgs. Of The Mixture?****Answer :****A + B = 40.****And at Rs 7 a kg for 40 kg, you want a total of Rs.280.****So the second equation is 9A + 4B = 280****From the first equation: B = 40 – A****and sub into the second equation:****9A + 4(40-A) = 280****9A + 160 – 4A = 280****5A = 120****A = 24.****Your answer, of course, is A = 24.**

**Question 36. A Wizard Named Nepo Says “i Am Only Three Times My Son’s Age. My Father Is 40 Years More Than Twice My Age. Together The Three Of Us Are A Mere 1240 Years Old.” How Old Is Nepo?****Answer :****Let the age of nepo be x years,age of his father is (40+2x),age of his son (x/3)****(40+2x)+x+(x/3)=1240****Solving this equation we get the age of nepo i.e. (x) is 360 years old**

**Question 37. One Dog Tells The Other That There Are Two Dogs In Front Of Me. The Other One Also Shouts That He Too Had Two Behind Him. How Many Are They?****Answer :****dog****dog****dog****So there are 3 dogs**

**Question 38. A Man Ate 100 Bananas In Five Days, Each Day Eating 6 More Than The Previous Day. How Many Bananas Did He Eat On The First Day?****Answer :****Let the number of bananas in first day be x****For consecutive five days it will be like x,x+6,x+12,x+18,x+24****The sum of those are 100, 5x+60=100****So,x = 8**

**Question 39. If It Takes Five Minutes To Boil One Egg, How Long Will It Take To Boil Four Eggs?****Answer :****Five minutes if we keep the four eggs in the same bowl.**

**Question 40. The Minute Hand Of A Clock Overtakes The Hour Hand At Intervals Of 64 Minutes Of Correct Time. How Much A Day Does The Clock Gain Or Lose?****Answer :****Simple explanation by Juned:****The minute hand overtakes hours hand 11 times in 12 hours****Therefore the time taken by the minute to overtake = (12 * 60)/11**** = 65.4545 minutes****In this clock the minute hand is taking 64 minutes to overtake****Therefore in 12 hours it will overtake 720/64 = 11.25 times****That means 0.25 times more in 12 hours or 0.5 times more in a day****Hence, the clock gains = 0.5 times of the normal time****⇒**** 65.4545 * 0.5 = 32.72 minutes or 360/11 minutes****Explanation by a4academics****Let****x be distance traveled by hour hand****Then distance traveled by minute hand = 1 + x****Time = Distance/Rate****⇒**** x/(1/12) = (1 + x)/1****⇒**** x = (1/12)(1 + x) = 1/12 + x/12****⇒**** (11/12)x = 1/12****x = 1/11****Calculate time for minute hand to travel a distance 1 + x.****Time = Distance/Rate****(1 + x)/1 = 1 + x = 1 + 1/11 = 12/11 hour****Actual time to overtake on clock is 64 minutes.****64 min = 64/60 hours = 16/15 hour****Correct Clock Speed/Actual Clock Speed****(12/11) / (16/15) = 12*15 / (11*16) = 180/176 = 45/44****The clock gains:****45/44 – 1 = 1/44 day = 24/44 hour = 6/11 hour = 360/11 min****= 32 min and 434/11 sec.**

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