Man walked 6 km at 1.5 kmph, again he walked 8 km at speed of 2 kmph and 32 km at a speed of 8kmph
time taken indivisually:
=> 6/1.5 = 4 m
=> 8/2 = 4 m
=> 32/8 = 4 m
Average speed of man= total distance/ total time
=> 46/12 = 3 (5/6)
Let the distance be x km. Then,
x/3 - x/4 =1/2
(4x - 3x)/12 = 1/2
x = 6 km
Let the percentage of benzene =X
(30 - X)/(X- 25) = 6/4 = 3/2
=> 5X = 135 or
X = 27 so,
required percentage of benzene = 27 %
%age of liquid Base in the original mixture
=1/5 x 100 = 20%
In the final mixture % of the liquid Base
= 3/5 x 100 = 60%
Now using the rule of allegation
Hence reduced quantity of the first mixture and the quantity of mixture B which is to be added are the same.
Total mixture = 10 + 10 = 20 liters and quantity of liquid A = 20/5 x 4 = 16 lts
Let X be the required number, then
(7 + X) : (11 + X) :: (11 +X) : (19 + X)
(7 + X) (19 + X) = (11 + X)2
X2 + 26X + 133 = X2 + 22X + 121
4X = - 12 or X = - 3
If X be the required number, then
(45 x X)1/2 = 3 x (5 x 22)1/2
45X = 9 x 110
X = 22
Let total number of employees be X.
Then, 8000 x X = 7 x 12000 + (X - 7) x 6000
X = 26.
Thus, the total number of employees in the organization is 26.
Let the total distance to be covered is 48 kms.
Time taken to cover the distance without stoppage = 48/42 hrs = 2 hrs
Time taken to cover the distance with stoppage = 48/28 = 3 hrs.
Thus, he takes 60 minutes to cover the same distance with stoppage.
Therefore, in 1 hour he stops for 20 minutes. .
The sum of numbers appeared is 6 or 7. Therefore, the required sums are 6 or 7, i.e., the required events are
(1,5), (5,1), (2,4), (4,2), (3,3), (1,6), (6,1), (2,5), (5,2), (3,4), (4,3)
i.e., for 6, n(E) = 5 and for 7, n(E) = 6
Therefore, the required probability = n(E)/n(S) = 11/36.
The probability that Alex will not solve a problem = 4/5.
The probability that Alex will not solve 10 problems = (4/5)4 = 256/625.
Hence, the probability that Alex will solve at least one problem = 1 - 256/625
= 369/625.