Q1. 8 Man Work For 6 Days To Complete A Work. How Many Men Are Required To Complete Same Work In 1/2 Day?

To complete a work for 6 days, 8 men require

For complete a work for 1 day = 6*8 = 48 men

For complete a work in half a day(1/2) = 48*2 = 96 men.

Q2. Two Goats Are Tied With A Rope Of Length 40m Outside Of A Rectangular Shed Of Dimensions 50m X 30m. The Goats Are Tied To Different Corners Which Lie On The Opposite Ends Of A Diagonal Of The Shed. Wh

Given rope of length = 40m (radius)

Area of semi circle =(pi*r^2)/2 = (1600 * pi)/2 = 800*pi —(1)

Area of quarter circle = (1/2 * 800 * pi) = 400*pi —– (2)

Area of sector is = r*r*(pi/2)/2 = 25*pi —– (3)

By adding above eq. (1) (2) & (3)

Total area = 1225*pi

As per quesiton there are 2 goats

so area = 1225*pi*2 = 2450pi.

Q3. If A – B = 3 And A^2 + B^2 = 29, Find The Value Of Ab?

2ab = (a^2 + b^2) – (a – b)^2

= 29 – 9 = 20

ab = 10.

Q4. A Man Employs 20 Men, 15 Women And X Children. He Pays Daily Wages Of Rs. 10 Per Men Rs. 8 Per Women And Rs. 4 Per Chil His Daily Average Wages Bill Works Out To Rs. 8.50 Per Person. What The Value Of

20*10 +15*8 +x*4/20+15+x = 8.5

x= 5 child.

Q5. A Batsman Scored 110 Runs Which Included 3 Boundaries And 8 Sixes. What Percent Of His Total Score Did He Make By Running Between The Wickets?

Number of runs made by running = 110 – (3 * 4 + 8 * 6)

= 110 – (60) = 50.

Required percentage = ({50/110}*100)% = 45{5/11}%.

Q6. If M=2- _/3 Find The Value Of: M^6+m^5+m^4+1)/m^3?

m = (2 – ?3)

=> 1/m = (2 + ?3)

(m^6+m^5+m^4+1)/m^3

= m^3 + m^2 + m + 1/m^3

= (m + 1/m)^3 – 3(m +1/m) + m(m+1)

= 4^3 – 3*4 + (2-?3)(3-?3)

= 64 – 12 + 9 – 5?3

= (61 – 5?3).

Q7. The Ratio Of The Ages Of Swati And Varun Is 2 : 5, After 8 Years, Their Ages Will Be In The Ratio Of 1 :

Let Swati’s age = 2X and Varun’s age = 5X

(2X + 8)/(5X + 8) = 1/2 => X = 8

Swati’s age = 16 years

and Varun’s age = 40 years

Difference of their ages = 24 years.

Q8. Below Is A Pseudo Code Read X?

Given Last value int seq. = 54.

and in every Loop result multiplied By 3.

So By Backward Approach

54/3=18 => 18/3=6

=> 6/3=2.

So, The Starting Value Is 2.

Q9. A, B, C And D Go For A Picnic. When A Stands On A Weighing Machine, B Also Climbs On, And The Weight Shown Was 132 Kg. When B Stands, C Also Climbs On, And The Machine Shows 130 Kg. Similarly The Weig

A+B=132

B+C=130

C+D=102

B+D=116

A+2B+C=262

B+C+2D=218

A+B-2D=44

132-2D=44

D=44.

Q10. If M^2+m^-2=23;then What Is The Value Of M^3+m^-3?

m^2+m^-2=23

=> (m + m^-1)^2 – 2 = 23

=> (m + m^-1) = 5

m^3+m^-3 = (m + m^-1)^3 – 3(m + m^-1) = 5^3 – 3*5 = 110.

Q11. What Is The Simplified Result Of Following The Steps Below In Order?

X^{2}-X-6=0

(x-3)(X+2)=0

X=3,-2.

Q12. 1,40,00,000 Pencils Are Put Up Straight. All The Pencils Are Of Length Range 3 To 6 Inches. 80% Of The Pencils Have Average Of Five Inches. So The Find Out The Total Length Spanned By The Pencils?

length covered by 80% of the pencils =80/100 * 14000000 * 5 = 56000000 inches

Minimum length covered by remaining 20% of the pencils =20/100 * 14000000 * 3 = 8400000 inches

Maximum length covered by remaining 20% of the pencils =20/100 * 14000000 * 6 = 16800000 inches

Hence, total length spanned by the pencils is (56000000 +8400000) to (56000000 +16800000 )

ie, 64400000 inches to 72800000 inches.

Q13. A Survey Of A Village Showed That 1 / 10 Of The Total Population Speak Neither Hindi Nor English. 1 / 5 Of Them Cannot Speak English And 3 / 7 Of Them Cannot Speak Hindi. What Percentages Of People Kn

persons who can speak English = 1 – (1/5) = 4/5

persons who can speak Hindi = 1 – (3/7) = 4/7

persons who can speak any or both = 1 – 1/10 = 9/10

so total persons speak both = 4/5 + 4/7 – 9/10 = 33/70

persons speak any = 1 – 33/70 – 1/10 = 3/7

% = 300/7% = 42.86%.

Q14. The Letter Of The Word Labour Are Permuted In All Possible Ways And The Words Thus Formed Are Arranged As In A Dictionary. What Is The Rank Of The Word Labour?

The order of each letter in the dictionary is ABLORU.

Now, with A in the beginning, the remaining letters can be permuted in 5! ways.

Similarly, with B in the beginning, the remaining letters can be permuted in 5! ways.

With L in the beginning, the first word will be LABORU, the second will be LABOUR.

Hence, the rank of the word LABOUR is 5!+5!+2 =242.

Q15. When A Square Of An Odd Number Is Divided By 8?

Let’s call the odd number 2a+1, where a is an integer.

Then (2a+1)^2 = 4a^2 + 4a + 1 = 4a(a+1) + 1.

Since a is odd, a+1 is even.

So, 4a(a+1) has to be a multiple of 8

Therefore 4a(a+1) + 1 must leave a remainder of 1 when divided by 8.

Q16. A Father Is 30 Years Older Than His Son However He Will Be Only Thrice As Old As The Son After 5 Years What Is Father’s Present Age ?

Lets assume son’s age = x

So, father’s age = x + 30

**After 5 years:**

Son’s age = x + 5

Father’s age = x + 35

In 5 years the father is thrice as old as his son so:

3(x + 5) = x + 35

x = 10

So, current father’s age = 40 Years.

Q17. If Each Of The Three Nonzero Numbers A , B , And C Is Divisible By 3, Then Abc Must Be Divisible By Which One Of The Following The Number?

Since each one of the three numbers a, b, and c is divisible by 3, the numbers can be represented as 3p,3q, and 3r, respectively, where p, q, and r are integers.

The product of the three numbers is 3p*3q*3r =27(pqr).

Since p, q, and r are integers, pqr is an integer and therefore abc is divisible by 27.

Q18. Containers Labeled A And B Are Filled With Red And Blue Marbles In Given Quantities: -container Red Blue?

If any one choose container A then prob = (1/2)*(4/10)=1/5

If any one choose container A then prob = (1/2)*(40/100)=1/5.

Q19. A Cylinder Is 6 Cms In Diameter And 6 Cms In Height. If Spheres Of The Same Size Are Made From The Material Obtained, What Is The Diameter Of Each Sphere?

The volume of the cylinder is Pi x r^2 x h = Pi x 3^2 x 6 = 54Pi

Volume of a cylinder is 4/3 x Pi x r^3

Now 54Pi = 12 x 4/3 x Pi x r^3

54 = 16 x r^3

r^3 = 54/16 = 27/8

r = 3/2

Therefore diameter is 3 cms.

Q20. How Many Ways Can 360 Be Written As Product Of Two Numbers?

1*360, 2*180, 3*120, 4*90, 5*72, 6*60, 8*45, 9*40, 10*36, 12*30, 15*24, 18*20

SOL 2) 360 => 2^3 * 3^2 * 5^1 [i.e. a^x * b^y * c^z)

No. of ways can be written as a prod of 2 no’s is

(x+1)*(y+1)(z+1)/2

=> (3+1)*(2+1)*(1+1)/2

=> 24/2 = 12.

Q21. Two Students Appeared At An Examination. One Of Them Secured 9 Marks More Than The Other And His Marks Was 56% Of The Sum Of Their Marks. The Marks Obtained By Them Are?

Let their marks be (x + 9) and x.

Then, x + 9 = (56/100)(x + 9 + x)

25(x + 9) = 14(2x + 9)

3x = 99

x = 33

So, their marks are 42 and 33.

Q22. A Person Travels In A Car With Uniform Speed. He Observes The Milestone,which Has 2 Digits. After One Hour He Observes Another Milestone With Same Digits Reversed. After Another Hour He Observes Anoth

Let 10’splace digit is x and unit’s place digit y

**First milestone :** 10x+y

**Second milestone :** 10y+x

**Third milestone:** 100x+y

Since the speed is uniform so

Distance covered in first Hr = Distance covered in Second Hr

(10y+x)-(10x+y) = (100x+y)-(10y+x)

By solving,

y=6x

but since x and y are digits so only possible combination is x=1 and y=6,

So average speed = 45 Kmph.

Q23. A Class Photograph Has To Be Taken. The Front Row Consists Of 6 Girls Who Are Sitting. 20 Boys Are Standing Behin The Two Corner Positions Are Reserved For The 2 Tallest Boys. In How Many Ways Can The

Two tallest boys can be arranged in 2! ways, rest 18 can be arranged in 18! ways.

Girls can be arranged in 6! ways.

Total number of ways in which all the students can be arranged = 2! * 18! * 6! = 18! *1440.

Q24. In A Society Of 80 Resident Families Who Subscribe Newspapers, 60% Of Them Subscribe The Hindu Newspaper, 80% Of Them Subscribe Regional Language Newspaper And 70% Of Them Subscribe Toi. How Many Fami

Total no. of families who take newspaper=80

Hindu newspaper = 60% = (80*60/100) = 48

Regional newspaper = 80% = (80*80/100) = 64

TOI newspaper = 70% = (70*80/100) = 56

Find common families take H.C.F (48,64,56) = 8

Therefore,(8/80)*100=10%

So, common families who take all newspaper = 10%.

Q25. If Log 0.317=0.3332 And Log 0.318=0.3364 Then Find Log 0.319 ?

log 0.317=0.3332 and log 0.318=0.3364

then

log 0.319=log0.318+(log0.318-log0.317)

=0.3396.

Q26. A Works Thrice As Much As B. If A Takes 60 Days Less Than B To Do A Work Then Find The Number Of Days It Would Take To Complete The Work If Both Work Together?

Given A works trice as much as B

So the ratio between A and B = 3:1

so 3x-x=60

and x = 30

so 1/90+1/30=221/2 days.