Quantitative Aptitude - Arithmetic Ability Questions

Given,

P can fill in 12 hrs

Q can fill in 15 hrs

R can fill in 20 hrs

=> Volume of tank = LCM of 12, 15, 20 = 60 lit

=> P alone can fill the tank in 60/12 = 5 hrs

=> Q alone can fill the tank in 60/15 = 4 hrs

=> R alone can fill the tank in 60/20 = 3 hrs

Tank can be filled in the way that

(P+Q) + (P+R) + (P+Q) + (P+R) + ....

=> Tank filled in 2 hrs = (5+4) + (5+3) = 9 + 8 = 17 lit

=> In 6 hrs = 17 x 6/2 = 51 lit

=> In 7th hr = 51 + (5+4) = 51 + 9 = 60 lit

=> So, total tank will be filled in 7 hrs.

Speed of the Train K is given by s = d/t = 240/20 = 12 m/s
Distance covered by Train K in 50 seconds = 12 x 50 = 600 mts.
But it crosses Train L in 50 seconds
Therefore, the length of the Train L is = 600 - 240 = 360 mts.

From the given data,

The part of honey in the first mixture = 1/4

The part of honey in the second mixture = 3/4

Let the part of honey in the third mixture = x

Then,

1/4             3/4

           x

(3/4)-x     x-(1/4) 

Given from mixtures 1 & 2 the ratio of mixture taken out is 2 : 3

=> 34-xx-14=23

=> Solving we get the part of honey in the third mixture as 11/20

=> the remaining part of the mixture is water = 9/20

Hence, the ratio of the mixture of honey and water in the third mixture is 11 : 9 .

But at x=-1/3, log x is not defined.

The only admissible value of x is 1.

We first count the number of committee in which

(i). Mr. Y is a member
(ii). the ones in which he is not

Case (i): As Mr. Y agrees to be in committee only where Mrs. Z is a member.
Now we are left with (6-1) men and (4-2) ladies (Mrs. X is not willing to join).

We can choose 1 more in5+2C1=7 ways.

Case (ii): If Mr. Y is not a member then we left with (6+4-1) people.
we can select 3 from 9 in 9C3=84 ways.

Thus, total number of ways is 7+84= 91 ways.

 P1+20100n>2P⇔65n>2

 65×65×65×65>2

so, answer is 4 years