Tuesday, 19 June 2012

Quantitative Aptitude 101

1.  A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :
A.
1
4
B.
1
10
C.
7
15
D.
8
15


Answer: Option D
Explanation:


A's 1 day's work = 1 ;
15


B's 1 day's work = 1 ;
20


(A + B)'s 1 day's work = ( 1 + 1 ) = 7 .
15 20 60


(A + B)'s 4 day's work = ( 7 x 4 ) = 7 .
60 15

Therefore, Remaining work = ( 1 - 7 ) = 8 .
15 15
2.  A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:
A.
9 1 days
5
B.
9 2 days
5
C.
9 3 days
5
D. 10

Answer: Option C
Explanation:


(A + B + C)'s 1 day's work = 1 ,
4


A's 1 day's work = 1 ,
16


B's 1 day's work = 1 .
12


Therefore C's 1 day's work = 1 - ( 1 + 1 ) = ( 1 - 7 ) = 5 .
4 16 12 4 48 48
So, C alone can do the work in48= 93
55   











3.  A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
A.12 daysB.15 days
C.16 daysD.18 days

Answer: Option B
Explanation:


A's 2 day's work = 1 x 2 = 1 .
20 10


(A + B + C)'s 1 day's work = 1 + 1 +1 = 6 = 1 .
20 30 60 60 10


Work done in 3 days = 1 + 1 = 1 .
10 10 5


Now, 1 work is done in 3 days.
5

Whole work will be done in (3 x 5) = 15 days.


4.  A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:
A. 20 daysB.
22 1 days
2
C. 25 daysD. 30 days

Answer: Option B
Explanation:

Ratio of times taken by A and B = 1 : 3.
The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.
If difference of time is 2 days, B takes 3 days.

If difference of time is 60 days, B takes 3 x 60 = 90 days.
2

So, A takes 30 days to do the work.

A's 1 day's work = 1
30


B's 1 day's work = 1
90


(A + B)'s 1 day's work = 1 + 1 = 4 = 2
30 90 90 45

A and B together can do the work in 45 = 22 1 days.
5.  A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
A. Rs. 375B. Rs. 400
C. Rs. 600D. Rs. 800

Answer: Option B
Explanation:


C's 1 day's work = 1 - 1 + 1 = 1 - 7 = 1 .
3 6 8 3 24 24


A's wages : B's wages : C's wages = 1 : 1 : 1 = 4 : 3 : 1.
6 8 24

C's share (for 3 days) = Rs. 3 x 1 x 3200 = Rs. 400.
24

6.  If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:
A. 4 daysB. 5 days
C. 6 daysD. 7 days


Answer: Option A
Explanation:

Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.

Then, 6x + 8y = 1 and 26x + 48y = 1 .
10 2


Solving these two equations, we get : x = 1 and y = 1 .
100 200


(15 men + 20 boy)'s 1 day's work = 15 + 20 = 1 .
100 200 4

15 men and 20 boys can do the work in 4 days.


7.  A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
A. 8 hoursB. 10 hours
C. 12 hoursD. 24 hours
Answer: Option C
Explanation:


A's 1 hour's work = 1 ;
4


(B + C)'s 1 hour's work = 1 ;
3


(A + C)'s 1 hour's work = 1 .
2


(A + B + C)'s 1 hour's work = ( 1 + 1 ) = 7 .
4 3 12


B's 1 hour's work = ( 7 - 1 ) = 1 .
12 2 12

Therefore B alone will take 12 hours to do the work.


8.  A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:
A. 15 daysB. 20 days
C. 25 daysD. 30 days
Answer: Option C
Explanation:


(A + B)'s 1 day's work = 1
10


C's 1 day's work = 1
50


(A + B + C)'s 1 day's work = 1 + 1 = 6 = 3 . .... (i)
10 50 50 25

A's 1 day's work = (B + C)'s 1 day's work .... (ii)

From (i) and (ii), we get: 2 x (A's 1 day's work) = 3
25


A's 1 day's work = 3 .
50


B's 1 day's work 1 - 3 = 2 = 1 .
10 50 50 25

So, B alone could do the work in 25 days.


9.  A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
A. 23 daysB. 37 days
C. 371/2D. 40 days
Answer: Option C
Explanation:


Whole work is done by A in ( 20 x 5 ) = 25 days.
4


Now, ( 1 - 4 ) i.e., 1 work is done by A and B in 3 days.
5 5

Whole work will be done by A and B in (3 x 5) = 15 days.

A's 1 day's work = 1 , (A + B)'s 1 day's work = 1 .
25 15


Therefore B's 1 day's work = ( 1 - 1 ) = 4 = 2 .
15 25 150 75


So, B alone would do the work in 75 = 37 1 days.
2 2
10.  A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished ?
A. 11:30 A.M.B. 12 noon
C. 12:30 P.M.D. 1:00 P.M.
Answer: Option D
Explanation:


(P + Q + R)'s 1 hour's work = ( 1 + 1 + 1 ) = 37 .
8 10 12 120


Work done by P, Q and R in 2 hours = ( 37 x 2 ) = 37 .
120 60


Remaining work = ( 1 - 37 ) = 23 .
60 60


(Q + R)'s 1 hour's work = ( 1 + 1 ) = 11 .
10 12 60


Now, 11 work is done by Q and R in 1 hour.
60


So, 23 work will be done by Q and R in ( 60 x 23 ) = 23 hours = 2 hours.
60 11 60 11

So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.


11.  A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
A. 5B.
5 1
2
C. 6D. 8
Answer: Option C
Explanation:


B's 10 day's work = ( 1 x 10 ) = 2 .
15 3


Remaining work = ( 1 - 2 ) = 1 .
3 3


Now, 1 work is done by A in 1 day.
18


Therefore 1 work is done by A in ( 18 x 1 ) = 6 days.
3 3

12.  4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
A. 35B. 40
C. 45D. 50
Answer: Option B
Explanation:

Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y.

Then, 4x + 6y = 1 and 3x + 7y = 1 .
8 10


Solving the two equations, we get: x = 11 , y = 1
400 400


1 woman's 1 day's work = 1 .
400


10 women's 1 day's work = 1 x 10 = 1 .
400 40

Hence, 10 women will complete the work in 40 days.


13.  A and B can together finish a work 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the work?
A. 40B. 50
C. 54D. 60
Answer: Option D
Explanation:


(A + B)'s 20 day's work = ( 1 x 20 ) = 2 .
30 3


Remaining work = ( 1 - 2 ) = 1 .
3 3


Now, 1 work is done by A in 20 days.
3

Therefore, the whole work will be done by A in (20 x 3) = 60 days.

14.  P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?
A.
5 5
11
B.
5 6
11
C.
6 5
11
D.
6 6
11
Answer: Option A
Explanation:

P can complete the work in (12 x 8) hrs. = 96 hrs.
Q can complete the work in (8 x 10) hrs. = 80 hrs.

P's1 hour's work = 1 and Q's 1 hour's work = 1 .
96 80


(P + Q)'s 1 hour's work = 1 + 1 = 11 .
96 80 480


So, both P and Q will finish the work in 480 hrs.
11


Number of days of 8 hours each = 480 x 1 = 60 days = 5 5 days.
11 8 11 11
15.  10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
A. 3B. 5
C. 7D. Cannot be determined
E. None of these
Answer: Option C
Explanation:


1 woman's 1 day's work = 1
70


1 child's 1 day's work = 1
140


(5 women + 10 children)'s day's work = 5 + 10 = 1 + 1 = 1
70 140 14 14 7

5 women and 10 children will complete the work in 7 days.






































No comments:

Post a Comment

Recent Posts