Quantitative Aptitude Questions and Answers with Explanation

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Anil
2015-04-09 13:59:29
1) A water tank is hemispherical below and cylindrical at the top. If the radius is 12m and capacity is 3312*pi cubic metre the height of the cylindrical portion in metres is:

2) If three metallic spheres of radii 6 cms, 8 cms and 10 cms are melted to from a single sphere, the diameter of the new sphere will be:

3) Sixty men can build a wall in 40 days, but though they begin the work together, 5 men quit every ten days. The time needed to build the wall is:

4) Shyam is travelling on his cycle and has calculated to reach point 'A' at 2 PM If he travels at 10 kmph. he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach point 'A' at 1 PM:

5) An aeroplane travelling at 700 km. p. h. in level flight drops a bomb from a height of 1000 metres on a target. The time taken from releasing the bomb to hitting the target is nearest to the figure:

6) In a History examination, the average for the entire class was 80 marks. If 10% of the students scored 95 marks and 20% scored 90 marks. What was the average marks of the remaining students of the class
Ashutosh R
2015-08-11 12:47:55
If three metallic spheres melted down and formed a new sphere, volume of all three sphere will be equivalent to the volume of new sphere and final equation will be
(r1^3)+(r2^3)+(r3^3) = R^3

here,
(6^3)+(8^3)+(10^3) = R^3
=>216+512+1000 = R^3
=> R = (1728)^1/3
i.e. R = 12 cm.

Hence, diameter of the new sphere will be (2R) i.e 24cm.
Yash
2015-07-31 05:52:28
4.   Since distance is same,
S1*t1=s2*t2.            (Speed 1=10 kmh, s2 is 15)
10*(14-t)=15*(12-t).  (2 o'clock on 24 hrs clock is 14, while 12 is 12)
140-10t=180-15t.      (t is the start time)
5t=40
t=8 hrs, means he had started journey at 8AM

D=s1*(14-t)
D=10*(14-8)
D=60 km
Time to reach destination=13-8=5 hrs
Speed=d\t=60/5=12kmh
Titas
2015-07-28 21:30:00
4. Since we do not know at what time Shyam actually sets on his journey,we will consider any one of the time limits provided (either 12 p.m or 2 p.m) to be taking x hours from the time he started,that is we have consider either duration to be x (or y or z or whatever you wish to take) hours.Now, if we consider this for 2 p.m,then by time = distance/speed,we have

x = d/10 ......Eqn 1.

Now,(x - 2) = d/15 or 15x - 30 = d or 15x = 30 + d or x = (d + 30)/15......Eqn 2.

From eqns 1 and 2,we have (d + 30)/15 = d/10 or 10d + 300 = 15d or 5d = 300 or d = 60 km.

Now,
x -1 = d/10 - 1 or x - 1 = 60/10 - 1 = 5 [We are talking about 1 p.m and we have chosen the time duration of upto to p.m to be x,so upto 1 p.m,it is (x -1) hours]

So,the time taken upto 1 p.m is 5 hours.Therefore,the speed = distance/time = 60/5 km/hr
= 12 km/hr
dinesh
2015-07-27 17:17:08
As many discussed on 3rd problem I would like to give my answer that it is exactly 47.5 days.

Try it. Work done by 1 person in one day is  work/2400.
After every 10 days, 5 will go off. So for 1st 10 days there will be 60, then 55 and so on...

now, it follows as
10*(60+55+50+45)/2400 +40*x/2400=1. (here x is no of more days required and 1 is the total work)

solving this we get
2100/2400+40x/2400=1
40x=300
x=7.5

so the total no of days required to do the given work as per the condition is 40+x=40+7.5=47.5.....
Anusree
2015-07-13 17:50:54
Que.3

60 men can do work in 40 days
Thus for one man completes 1/2400 in one day

Every 10 days 5 men quit,thus
On the first 10 days,60 men were working
Next 10 days,55 men were working
Next 10 days, 50 men were working,
Next, 45 men and so on

ie:
60 men * 10days + 55men * 10days + 50 men * 10 days + 45men * 10days+ ... + 5men*10 days
= 600 man days + 550 man days + 500 man days + ... + 50 man-days

This follows an arithmetic progression, A.P formula to find sum of n numbers is
Sn=n(a1+aL)/2 where a1 is the first term and aL is the last or the n th term,n is the no. of terms.

Using this formula
12(600+50)/2
=650*6
=3900 man-days
The total amount of work  done before there are zero workers is 3900/2400.
Yash
2015-07-25 12:33:14
3. If 60 people would have worked for 40 days, it will complete the work after applying 2400 man-days (i.e. 60*40)

But here we have, 60 people for 10 days = 60*10 = 600 MD ;(MD refers man-days, Shortened for time ease)

55 people for next 10 days = 55*10 = 550 MD ;
50 people for other 10 days = 50*10 = 500 MD ;
45 people for more 10 days = 45*10 = 450 MD ;   (10+10+10+10=40 days, considering our  initial time budget)

Adding our calculated database for MD, we get a total of 2100MD ;   (i.e. (600+550+500+450)MD)

Now, we can conclude that the manpower must work for 2400 MD to complete the work,instead, we are getting it as 2100 days as according to the question's statement, means it is causing a lack of 300 days, which must be replenished an excessive time period of work and that can be calculated as follows:

we can solve that, 2400 is 1.14 times the 2100
equating the manpower, the time must also have a leap of 1.14 times, thats 40*1.14=45.6 days.
clearly causing an increase of 5.6 days, certainly let to the sign out of approximately 2.8 people.
(ie 5 people leave after 10 days, 2.5 people in 5 days, 0.25 people in 0.5 days, giving an rough idea for so)
it will then also leap an lack of MD of 2.8 * 5.6=15.68~15.5 MD, which will cause a minor decrease in MD and the time period to increase as well by 0.00625 days. hence, it will require about 45.6+0.00625= 45.606 days for the so work to complete.

Thanking careerbless as platform and greeting the readers
I do regard Ms. Anusreeji for her contribution, but it can be noticed that she got out the mandays and man work until the no. of labours become 0, but not time which was required by the question (as i identify her solution), to the above extent. I am a grade 9 student and so not know the progressions, this is my answer for the question for those having same as me. Any modifications are kindly welcomed.
sony
2015-07-29 12:22:02
didnt understand 1.14 times of 2100 is 2400
Karan
2015-08-02 10:49:01
@yash, 1.14×2100= 2394. But I guess, you are taking the approximation.
yash
2015-07-30 13:51:55
2400/2100=1.14
or, 2100*1.14=2400
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