Question 1. A Sphere And A Cube Have The Same Surface Area. Find The Ratio Of Their Volumes?
Answer :
SA of a sphere: 4πr²
SA of a cube: 6x²
4πr² = 6x²
r²/x² = 6 / 4π
(r/x)² = 3 / 2π
r/x = (3 / 2π)^0.5
Volume of a sphere: 4/3 πr³
Volume of a cube: x³
Find the ratio meaning (4/3 πr³)/x³
= (4π/3)(r³/x³)
= (4π/3)(r/x)³
= (4π/3)(3 / 2π)^1.5
= (2²π/3)[3^1.5 / (2^1.5)(π^1.5)]
= √2√3 / √π
= √(6/π).
Answer :
area of square = 63*63=3969 m^2
area inside the square that is grazed =4*area of quadrants of 4 circles
= 4*(1/4)*(22/7)*(63/2)*(63/2) =3118.5
area left ungrazed = 3969-3118.5=850.5.
Question 3. How Many No Between 1000 To 9900 In Which Four Digits Of Number Are Different?
Answer :
Number of 4 digit numbers having all different digits = 9*9*8*7 = 4536
smallest number : 1234, largest number : 9876, all are between 1000 and 9900.
Answer :
Formula for converting from km/hr to m/s: X km/hr = X *( 5/18) m/s.
so Speed = 45 * 5/18 m/sec = 25/2 m/sec.
Total distance to be covered = (360 + 140) m = 500 m.
Required time = 500 * 2/25 sec = 40 sec.
Question 5. The G.c.d. Of 1.08, 0.36 And 0.9 Is?
Answer :
Given numbers are 1.08 , 0.36 and 0.90
H.C.F of 108, 36 and 90 is 18 ( G.C.D is nothing but H.C.F)
So H.C.F of given numbers = 0.18.
Answer :
l = 10m
h = 8m
so r = √(l^2 - h^2) = √(10^2 - 8^2) = 6m
So Curved surface area = (π * r * l) = ( π * 6 * 10) m2 = 60π m2.
Answer :
The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clock only).
So, in a day, the hands point in the opposite directions 22 times.
Answer :
Let Abhay's speed be x km/hr.
So 30/x - 30/2x = 3
=> 6x = 30
x = 5 km/hr.
Answer :
Let the present ages of son and father be x and (60 -x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
=> 54 - x = 5x - 30
=> 6x = 84
=> x = 14.
Son's age after 6 years = (x+ 6) = 20 years.
Question 10. Sum Of Three Even Consecutive Numbers Is 48, And Then Least Number Is?
Answer :
Let the numbers be 2n, 2n+2 and 2n+4
2n + (2n+2) + (2n+4) = 48
6n = 48-6 = 42, n = 7
Hence the numbers are -- > 14, 16 and 18
The least number is 14.
Question 11. Walking At 3/4 Of His Usual Speed ,a Man Is Late By 1/2 Hr. The Usual Time Is?
Answer :
Usual speed = S
Usual time = T
Distance = D
New Speed is ¾ S
New time is 4/3 T
4/3 T T = 5/2
T=15/2 = 7 ½.
Question 12. If 7 Spiders Make 7 Webs In 7 Days, Then 1 Spider Will Make 1 Web In How Many Days?
Answer :
Let the required number days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
Spiders 1 : 7 }
> :: 7 : x
Webs 7 : 1 }
1 x 7 x x = 7 x 1 x 7
=> x = 7.
Answer :
Let the number be x.
Then, error = x*5/3 - x*3/5 = x * 16/15
So Error% = ( x*16/15 * 3/5x * 100)% = 64%.
Answer :
Excess of B's height over A's = [(40/(100 - 40)] x 100%
= 66.66%
Answer :
We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).
Required number of ways = (7C3 * 6C2)+(7C4 * 6C1)+(7C5)
=>[(7*6*5)/(3*2*1) * (6*5)/(2*1)]+(7C3 * 6C1) + (7C2)
=> 525 + [(7*6*5)/(3*2*1)* 6]+[(7*6)/(2*1)]
= (525 + 210 + 21)
= 756.
Answer :
In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.
Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
So,Number of ways of arranging these letters = (8!/2!*2!)=10080.
Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
Number of ways of arranging these letters = (4!/2)=12.
=> Required number of words = (10080 * 12) = 120960.
Question 17. What Will Be The Day Of The Week 15th August, 2010?
Answer :
15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)
Odd days in 1600 years = 0
Odd days in 400 years = 0
9 years = (2 leap years + 7 ordinary years) = (2 * 2 + 7 * 1) = 11 odd days 4 odd days.
Jan. Feb. March April May June July Aug.
(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days
227 days = (32 weeks + 3 days) 3 odd days.
Total number of odd days = (0 + 0 + 4 + 3) = 7 0 odd days.
Given day is Sunday.
Answer :
find the relative speed of the thief and policeman = (11-10)km/hr = 1 km/hr
Distance covered in 6 minutes = (1/60)*6=1/10km => 100meters
So distance between them after 6 minutes = (200-100)=100 meters.
Answer :
Lets assume the time required to weave 25 meters = x sec.
Rule: More cloth means More time (Direct Proportion)
=> 0.128:1::25:x
=>x=[(25*1)/0.128]
=>x=195.31
So time needed ~195 seconds.
Answer :
Given that numbers are co primes,
and two products have the middle number in common.
=> Middle number = H.C.F. of 551 and 1073 = 29
so first number is = 551/29 = 19
=> Third number = 1073/29 = 37
Therefore, sum of these numbers is = (19 + 29 + 37) = 85.
Answer :
Lets assume average weight of the 59 students = x kgs.
=> Total weight of the 59 = 59*x
Given when the weight of this student who left is added, the total weight of the class = (59x + 45)
The average weight decreases by 0.2 kgs, when these students included.
=> (59x+45)/60=(x-0.2)
=> (59x+45)= 60(x-0.2)
=> 59x + 45 = (60A - 12)
=> 45 + 12 = 60x - 59x
=> x = 57.
Answer :
Nirmal:Kapil = 9000*12:(12000*6+6000*6) = 1:1
Kapils share = Rs. [4600 *(1/2)) = Rs. 2300.
Answer :
Total work done by A + B in 1 day = 1/15 + 1/(20 ) = 7/60
Work done in 4 days = 7/60 × 4 = 7/15
Therefore, fraction of work left = 1 - 7/15 = 8/15.
Answer :
Population in 2007 = 480
In 2008 = 1.05 × 480 = 504
In 2009 = 1.25 × 504 = 630.
Question 25. 24% Of 150 × 3/4= ?
Answer :
24% of 150 × 3/4= x = 36 × 4/3 = 48.
3/17 of 20% of 510 + 7 = x2
3/17 of 20% of 510 + 7 = x2
3/17 × 20/100 × 510 + 7 = 18 + 7 = 25 => x = 5.
Answer :
Let the initial salary of Hiten be ‘S’. Then:
(0.55 × 0.4) S = 15400 => S = 70000
After increment, Hiten’s salary = 1.1 × 70000 = 77000.
Answer :
Distance = 120 × 90/60 = 180 km
Speed required to cover 180 km in 1 hr 20 mins
( 4/3 hrs) = 180 × ¾ = 135 km/hr.
Answer :
Ratio of milk : water in Jar A = 120 : 24 = 5 : 1
12 lts of this mixture is taken out => milk = 5/6 × 12 = 10 lts and water = 2 lts taken out
3 lts of water added = 24 – 2 + 3 = 25 lts => new ratio of milk : water
= 110 : 25 = 22 : 5
Now 27 lts of this mixture is again taken out =>
water taken out = 5/27 × 27 = 5 lts
water left = 25 – 5 = 20 lts.
Answer :
Speed of boat = 15 k/h
Let the speed of stream be ‘S’
Given : 30/(15+S) + 30/(15-S) = 9/2
Solving we get, S = 5 km/h.
Answer :
Let the ages of Kunal and Sagar be K and S respectively.
Given : (K-6)/(S-6) = 6/5 => 5K – 6S = -6 ……(i)
And: (K+4)/(S+4) = 11/10 => 10K – 11 S = 4 …..(ii)
Solving (i) & (ii) we get: S = 16 years.
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