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
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)
Let A and B take 3x and 2x days to complete the work
So A will take 45 days.
The sequence is 306,... 594
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?
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?
1/20 + 1/30 - 1/40 = 7/120
120/7 = 17 1/7
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?
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 ?
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
So, common families who take all newspaper = 10%.
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 ?
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)
but since x and y are digits so only possible combination is x=1 and y=6,
So average speed = 45 Kmph
log 0.317=0.3332 and log 0.318=0.3364
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 ?
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
Group 1: F, J, G, N
Group 2: M, K, H, L
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 ?
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 ?
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%
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?
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
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
So, The Starting Value Is 2
=> (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
m = (2 - ?3)
=> 1/m = (2 + ?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)
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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