1) A and B together can complete a work in 3 days. They start together but after 2 days, B left the work. If the work is completed after two more days, B alone could do the work in?
A)5days
B)6days
C)9days
D)10days
Click to View Answer
Answer B)6 days
(A+B)’s one day’s work = 1/3 part;
(A+B) works 2 days together = 2/3 part;
Remaining work = 1-(2/3) = 1/3 part;
1/3 part of work is completed by A in two days;
Hence, one day’s work of A = 1/6;
Then, one day’s work of B = 1/3-1/6=1/6;
So, B alone can complete the whole work in 6 days.
2) A can complete a piece of work in 18 days, B in 20 days and C in 30 days, B and C together start the work and forced to leave after 2 days. The time taken by A alone to complete the remaining work is?
A)10 days
B)12 days
C)15 days
D)16 days
Click to View Answer
Answer C)15days
(B+C)’s 2 days work = 2*(1/20+1/30) = 2*(3+2/60) = 1/6 part.
Remaining work = 1-1/6 = 5/6 part;
A’s one day’s work = 1/18 part;
Time taken to complete the work,
= (5/6)/(1/18) days; Hence, Time taken to complete the work
= (5/6)*18 = 15 days.
3)Working 5 hours a day, A can Complete a work in 8 days and working 6 hours a day, B can complete the same work in 10 days. Working 8 hours a day, they can jointly complete the work in?
A)3days
B)4days
C)4.5days
D)5.4 days
Click to View Answer
Answer A) 3days
Working 5 hours a day, A can complete the work in 8 days i.e.
= 5*8 = 40 hours;
Working 6 hours a day, B can complete the work in 10 days i.e.
= 6*10 = 60 hours;
(A+B)’s 1 hour’s work,
= (1/40+1/60)
=(3+2)/120
= 5/120
= 1/24 =Hence, A and B can complete the work in 24 hours i.e. they require 3 days to complete the work.
4) Ganga and Saraswati, working separately can mow field in 8 and 12 hours respectively. If they work in stretches of one hour alternately. Ganga is beginning at 9 a.m., when will the moving be completed?
A)6pm
B)6:30pm
C)5pm
D)5:30pm
Click to View Answer
Answer B) 6:30 pm
Whenever, workers are working alternatively on one work, we take 2 as 1 unit.
In this case, we take 2 hours as 1 unit.
Part of the field moved by Ganga and Saraswati in 2 hours (1 unit) = 1/8 + 1/12 = 5/24;
Time taken to complete the work,
= 1/(5/24) = 24/5 unit of time;
Then actual time taken by them to complete the work,
= 24*2/5 = 9.5 hours.
The work starts at 9 a.m. then it will complete at 6:30 pm.
5) A complete 7/10 of a work in 15 days, then he completed the remaining work with the help of B in 4 days. In how many day A and B can complete entire work together?
A)10(1/2) days
B)12(2/3) days
C)13(1/3) days
D)8(1/4) days
Click to View Answer
Answer C)13(1/3) days
6) In how many ways can 10 examination papers be arranged so that the best and the worst papers never come together?
A)8*9!
B)8*8!
C)7*9!
D)9*8!
Click to View Answer
Answer A) 8*9!
No. of ways in which 10 paper can arranged is 10! Ways.
When the best and the worst papers come together, regarding the two as one paper, we have only 9 papers.
These 9 papers can be arranged in 9! Ways.
And two papers can be arranged themselves in 2! Ways.
No. of arrangement when best and worst paper do not come together,
= 10!- 9!.2! = 9!(10-2) = 8.9!
7) In how many ways 4 boys and 3 girls can be seated in a row so that they are alternate?
A)144
B)288
C)12
D)256
Click to View Answer
Answer A)144
Let the Arrangement be,
B G B G B G B
4 boys can be seated in 4! Ways.
Girl can be seated in 3! Ways.
Required number of ways,
= 4!*3! = 144.
8) In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together?
A)3! 4! 8! 4!
B)3! 8!
C)4! 4!
D)8! 4! 4!
Click to View Answer
Answer A)3! 4! 8! 4!
9)Three gentlemen and three ladies are candidates for two vacancies. A voter has to vote for two candidates. In how many ways can one cast his vote?
A)9
B)30
C)36
D)15
Click to View Answer
Answer D)15
There are 6 candidates and a voter has to vote for any two of them.
So, the required number of ways is,
= 6C2 = 6!/2!*4! = 15
10)Find the number of triangles which can be formed by joining the angular points of a polygon of 8 sides as vertices?
A)56
B)24
C)16
D)8
Click to View Answer
Answer A) 56
A triangle needs 3 points.
And polygon of 8 sides has 8 angular points.
Hence, number of triangle formed,
= 8C3 = (8*7*6)/(1*2*3)
= 56.
