**Question 1. The Average Age Of A Man And His Son Is 28 Years. The Ratio Of Their Ages Is 3 :1 Respectively. What Is The Man’s Age ?****Answer :**Total sum of man’s age & his son’s age =28 — 2 = 56 Now, the Ratio of their ages is 3 : 1.Therefore, Man’s age = (3/4) — 56 = 42

**Question 2. A Basket Contains 3 Blue, 5 Black And 3 Red Balls. If 3 Balls Are Drawn At Random What Is The Probability That All Are Black ?****Answer :**Ways of selecting 3 black balls out of 5 – 5C3 Total ways of selecting 3 balls – 11C3 The required probability = (5C3 / 11C3 ) = (10/165) = (2/33)

**Question 3. The Ratio Of The Capacity To Do Work Of A And B Is 3 : 2. If They Together Can Complete A Work In 18 Days, Then How Long Does A Take To Complete The Work Alone ?****Answer :**Let A and B take 3x and 2x days to complete the work

1/3x+1/2x=1/18 ;x=15

So A will take 45 days.

**Question 4. How Many Integers Are There Between 300 And 600 That Are Divisible By 9 ?****Answer :**The sequence is 306,… 594

594=306+(n-1)9 ⇒288=(n-1)9n=33

**Question 5. A, B, C And D Are Four Consecutive Odd Numbers And Their Average Is 42. What Is The Product Of B And D ?****Answer :**As there are As diff. Is same so average should lie between B and C so B is 41 & C is 43 so D must be 45 as we have to find the product of B and D so it would be 1845.

**Question 6. Two Taps Can Separately Fill A Cistern 10 Minutes And 15 Minutes Respectively And When The Waste Pipe Is Open, They Can Together Fill It In 18 Minutes. The Waste Pipe Can Empty The Full Cistern In?****Answer :**1/10 + 1/15 – 1/x = 1/18

x = 9

**Question 7. Two Pipes A And B Can Fill A Cistern In 20 And 30 Minutes Respectively, And A Third Pipe C Can Empty It In 40 Minutes. How Long Will It Take To Fill The Cistern If All The Three Are Opened At The Same Time?****Answer :**1/20 + 1/30 – 1/40 = 7/120

120/7 = 17 1/7

**Question 8. Which Letter Should Be In Place Of Question Mark**

B C D

A E C

F A ?**Answer :**A=1,B=2,C=3——–z=26

so now B+C+D= 2+3+4=9

A+E+C = 1+5+3 = 9

So, F+A+? = 9

=> 6+1+? = 9

**Question 9. 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. What Is The Area In Which The Two Goats Can Eat Grass, If They Choose Not To Eat In The Common Approachable Area?****Answer :**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

**Question 10. 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 Families Could, At The Least, Be Subscribing To All The Three Newspapers ?****Answer :**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%.

**Question 11. What Is The Simplified Result Of Following The Steps Below In Order ?****Answer :**X2-X-6=0

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

X=3,-2

**Question 12. 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 ?****Answer :**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.

**Question 13. 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 Another Milestone With Same 2 Digits Separated By 0. Find The Speed Of The Car ?****Answer :**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

**Question 14. If Log 0.317=0.3332 And Log 0.318=0.3364 Then Find Log 0.319 ?****Answer :**log 0.317=0.3332 and log 0.318=0.3364

then

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

=0.3396

**Question 15. There Are 8 People, F, G, H, J, K, L, M, And N. 2 Groups Are To Be Formed. F Will Always Go With J. G And M Will Never Go Together. H Will Always Go With L. N Will Always Go With G. What Are The Two Groups To Be Formed ?****Answer :**8 people namely F,G,H,J,K,L,M,and N respectively.

Now we have to form 2 groups

1st condition: F will always go with J

Meaning: F and J always lie in same group. …………(i)

2nd condition:G and M will never go together.

Meaning: G and M always lie in different groups. ………(ii)

3rd condition:H will always go with L.

Meaning:H and L always lie in same group. ………….(iii)

4th condition:N will always go with G.

Meaning:N and G always lie in same group. ……….(iv)

According to (i),(ii),(iii),and (iv)

2 groups can be formed in following 2 ways

1st Way

Group 1: F, J, G, N

Group 2: M, K, H, L

2nd Way

Group 1: F, J, M, K

Group 2: G, N, H, L

**Question 16. 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 Weight Of C And D Is Found As 102 Kg And That Of B And D Is 116 Kg. What Is D’s Weight ?****Answer :**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

**Question 17. 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 ?****Answer :**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

**Question 18. 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 Know Only One Language ?****Answer :**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%

**Question 19. If A – B = 3 And A^2 + B^2 = 29, Find The Value Of Ab****Answer :**2ab = (a^2 + b^2) – (a – b)^2

= 29 – 9 = 20

ab = 10.

**Question 20. 2 Containers Labeled A And B Are Filled With Red And Blue Marbles In Given Quantities: –**

Container Red Blue

A 6 4

B 60 40

Each Container Is Shaken Vigorously. After Choosing 1 Of The Container, Without Looking, Draw Out A Marble. From Which Container You Have The Max Probability Of Choosing A Blue Marble?**Answer :**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

**Question 21. Below Is A Pseudo Code Read X****While(x < 60) Write X X = X*3****Answer :**The last number in the sequence is 54, what has the user entered as the initial value of 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

**Question 22. If M^2+m^-2=23;then What Is The Value Of M^3+m^-3 ?****Answer :**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

**Question 23. If M=2- _/3**

Find The Value Of:**Answer :**(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)

**Question 24. The Ratio Of The Ages Of Swati And Varun Is 2 : 5, After 8 Years, Their Ages Will Be In The Ratio Of 1 : 2. The Difference In Their Present Ages (in Years) Is ?****Answer :**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.

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