LIC AAO | QUANT QUIZ - 12 | S W A G

TOPIC:-TIME AND WORK 

Directions (Q. 1-10): Study the following information carefully and answer the given questions.

1. A can do a work in 50 days and B in 40 days . They work together for 10 days. and then A leaves B to finish the work alone. How long will B take to finish it??
(a)    11 days
(b)    18 days
(c)    22 days
(d)    26 days
(e)    None of these

(c) 22 days
EXPLANATION :-
Let the total work be 200 work
Efficiency of
A = 200/50 = 4 work/day
B = 200/40 = 5 work/day
A+B’s efficiency = 9/day
A+B’s 10 days work = 9*10 = 90
Remaining work = 200-90 = 110
Time taken by B alone to finish the remaining wrk = 110/5 = 22days

2. 30 men, working 4 hrs a day can do a piece of work in 10 days. Find the number of days in which 45 men working 8 hrs a day can do twice the work. Assume that 2 men of the first group do as much wrk in 2 hrs as 4 men of the second group do in 1 hr.
(a)    6(1/3) days
(b)    6(2/3) days
(c)    5(3/6) days
(d)    3(1/6) days
(e)    None of these

(a) 6(2/3) days
EXPLANATION :-
M1D1H1E1W2 = M2D2H2E2W1 (From MDH Rule)
Efficinecy of first grp : 2nd grp = 2*2 :4*1 = 1:1
Now, D2 = M1D1H1E1W2 / M2H2E2W1
D2 = 30*4*10*1*2 / 45*8*1*1
D2 = 20/3 = 6(2/3) days

3. A alone would take 27 hrs more to complete the job than if both A and B would together. If B worked alone, he took 3 hrs more to complete the job than A and B worked together. What time, would they take if both A and B worked together?
(a)    8 hours
(b)    10 hours
(c)    9 hours
(d)    6 hours
(e)    None of these

(c) 9 Hours
EXPLANATION :-
Let A+B together takes X hours
A will take X+27 hrs
B will take X+3 hrs
Let the total work be (X+27)(X+3)
Efficiency of A= X+3
B = X+27
Total efficiency = 2X+30
Time working together = (X+27)(X+3) / 2X+30 = X
==> X^2 +30X + 81 = 2X^2 + 30X
or, X^2 = 81 or X= 9 hrs (neglecting –Ve time )


4. A and B together can do a piece of work in 12 days which B and C together will do in 16 days. After A has been working on it for 5 days, and B for 7 days, C finishes it in 13 days. In how many days A,B and C alone will do the work ?
(a)    16, 48 and 26 days respectively
(b)    16, 48 and 24 days respectively
(c)    26, 48 and 24 days respectively
(d)    16, 46 and 24 days respectively
(e)    None of these

(b) 16, 48 and 24 days respectively
EXPLANATION :-
Let the total work be 48
Efficiency of
A+B = 4/day…… (i)
B+C = 3/day……..(ii)
Now, A works for 5 days, B works for 7 days and C works for 13 days and completes the total work of 48.
This can be rewritten as
A+B for 5 days + B+C for 2 days + C for 11 days completes the total work of 48
Now, A+B’s 5 days work = 20
B+C’s 2 days work = 6
Therefore, 20+6+ C’s 11 days work = 48
C’s  11 days work = 48-26 = 22
C’s efficiency = 2/day.. (iii)
From (i),(ii),(iii)
C’s efficiency = 2
B’s Efficiency = 1
A’s efficiency = 3
Time taken by
A= 16 days, B= 48 days, and C= 24 days

5. Two women Ganga and Jamuna, working separately can mow a field in 8 and 12 hours respectively. If they work for an hour alternately, Ganga beginning at 9 am, when will the mowing be finished?
(a)    9:30 PM
(b)    8:30 PM
(c)    6:00 AM
(d)    7:00 PM
(e)    None of these

(e) None of these (6:30PM)
EXPLANATION :-
Let the total work be 24
Efficiency of Ganga = 24/8 = 3/hr
Efficiency of Jamuna= 24/12 = 2/hr
They work alternately starting from Ganga
First 2 hrs work = 3+2 = 5
First 8 hrs work = 20
Remaining = 24-20 = 4
9th hr work to be done by Ganga = 3
Remaining work = 4-3 = 1 to be done by Jamuna in 1/2 hr.
Total time = 8+1+(1/2) hrs = 9.5 hrs or 9 Hr 30 minutes
So work will be completed by 9AM + 9 hrs 30 minutes = 18 hrs 30 minutes or 6:30 PM

6. A, B and C together can do a work in 12 days. A alone can do the work in 36 days and B alone can do the same work in 54 days. Find in what time C alone can do that work?
(a)    9 days
(b)    18 days
(c)    24 days
(d)    27 days
(e)    None of these

(d) 27 Days
EXPLANATION :-
Let the total work be 108 (Common Multiple of 12,36 and 54)
Efficiency of A+B+C =108/12=  9,
of A alone = 108/36 = 3 and
of B alone = 108/54 = 2
Therefore of C alone = 9-(3+2) = 4
Time taken by C = 108/4 = 27 days

7. A, B and C together can do a work in 4 days. A alone can do the work in 12 days B alone can do the same work in 18 days. Find in what time C alone can do the same work alone?
(a)    9 days
(b)    18 days
(c)    27 days
(d)    8 days
(e)    None of these

(a) 9 Days
EXPLANATION :-
Let the total work be 36 ( Can take any value Preferably Common Multiple )
Efficiency of
A+B+C = 36/4 = 9
A alone= 36/12 = 3
B alone = 36/18 = 2
C alone = A+B+C- (A+B) = 9-(3+2) = 4
Time taken by C alone = 36/4 = 9 days

8. A can complete a work in 35 days and B can do the same work in 28 days. If A after doing 10 days, leaves the work , find in how many days B will do the remaining work?
(a)    15 days
(b)    10 days
(c)    27 days
(d)    24 days
(e)    None of these

(e) None of these (20 days)
EXPLANATION :-
Let the total work be 140
Efficiency of A = 4
Efficiency of B = 5
A works for 10 days = 4*10 = 40
Remaining work = 140-40 = 100 to be done by B
B will do it in 100/5 = 20 days

9. A can complete a work in 24 days and B can complete the same work in 18 days. If A after doing 4 days leaves the work find in how many days B will complete the remaining work?
(a)    11 days
(b)    15 days
(c)    12 days
(d)    10 days
(e)    None of these

(b) 15 days
EXPLANATION :-
Let the total work be 72
Efficiency of A = 3 and Of B = 4
A’s 4 days work = 3*4 = 12 remaining work = 72 -12 = 60
Work completed by B in 60/4 = 15 days


10. A and B together can do a piece of work in 6 days, B alone could do it in 8 days. Supposing B works at it for 5 days, in how many days A alone could finish the remaining work?
(a)    9 days
(b)    8 days
(c)    24 days
(d)    12 days
(e)    None of these

(a) 9 days
EXPLANATION :-
Let the total work be 24
Efficiency of A+B = 4
Efficiency of B = 3
Efficiency of A = 1 as A+B = 4 and B= 3
Work done by B in 5 day = 3*5 = 15
Remaining work = 24-15 = 9
Remaining work to be done by A in 9/1 = 9 days

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