Directions: Read the following information to answer the question.
Solution:
From the given information Q is thrice as efficient as P.
R is thrice as efficient as Q.
S is thrice efficient as R.
If work done by P in a day is 'n' units, the work done in a day by Q, R and S would be 3n, 9n and 27n units respectively.
It can be seem that, P,Q and R working together can do 13n units in a day while P,Q and S working together can do 31n units in a day.
Hence, the ratio of times taken to complete the work by the former and later groups is 31:13
P,Q and S take 13 days.
Directions: Read the following information to answer the question.
Solution:
Let the total distance to be covered be d
On each day under normal weather conditions they travel d/20
of the distance.
On 1st day they would travel =d/20
On 2nd day they would travel =0.8×d/20
On 3rd day they would travel =0.8×(0.8×d/20)
Let he will reach the point B in nth day
⇒ d/20+0.8 *d/20+0.82*d/20+…….+0.8n*d/20=d
⇒ d/20×(−(0.8)n+1)/(−0.8+1)=d
⇒ 1−(0.8)n=4(0.8)n=−3
Since (0.8)n>0, thus it is never equal to -3
The man will never reach the point B.
Directions: Read the following information to answer the question.
There are four varieties of pipes Pipe A, Pipe B, Pipe C and Pipe D. Each pipe can be either an inlet pipe or an outlet pipe but cannot be both. there are 5 tanks of equal volume.
Tank P is filled by Pipe A and Pipe B
Tank Q is filled by Pipe A and Pipe C
Tank R is filled by Pipe A and Pipe D
Tank S is filled by Pipe B and Pipe C
Tank T is filled by Pipe C and Pipe D
Time taken for the first 3 tanks (P, Q and R) to get filled are in the ratio 1:2:4 and the time taken for the S and T tanks to be filled are in the ratio 7:10.
Find the outlet pipes among the 4 varieties.
Solution:
Let A,B,C and D do a,b,c and d with of work in an hour.
Let A and B fill the tank in 1 hour.
Then A and C would fill the tank in 2 hours while A and D in 4 hours.
a+b=1 ---------- (i)
a+c=1/2 ----------- (ii)
a+d=1/4 ------------ (iii)
Let B and C take 7k hours while c and D take 10k hours to fill the tank
⇒ b+c=1/7k --------------- (iv)
c+d=1/10k -------------- (v)
a=[(i)+(ii)−(iv)]/2 = [(ii)+(iii)−(v)]/2
⇒ a={1+1/2−1/7k}/2={1/2+1/4−1/10k}/2 ---------- (vi)
⇒ k=4/70
On substituting value of k in equation (vi) we get a<0
⇒ a<0,b>0,c>0 and d>0
Hence only A is the outlet pipe.
Directions: Read the following information to answer the question.
Solution:
When A and B work together, they will take √5×15=√225= 15 days.
Where 5 and 45 are the extra time that A and B take to complete the job if they work alone compared to the time that they will take if they worked together.
Directions: Read the following information to answer the question.
Solution:
Let us take the complete work to be 20 units (LCM of 5 and 4) to make things easier.
3a + 4b = 4 ---(1)
4 < 4a + 2b < 5 ---(2)
Double (1) and add it to (2) to get:
12 < 10 (a+b) < 13 -----(3)
Now,
Multiply (1) by 4 and subtract (3) from it
12a + 16b - 10 (a+b) [= 2a+6b]
= 4(4) - (12,13)
= (3,4) [ since 16 - 12 = 4, 16 - 13 = 3 =>the value will be between 12 and 3 and 4 ]
=> they will complete the work between 20/3 and 20/4 days (inclusive)
Thus, the work can get completed in 5th, 6th, 7th day.