Model 1 Basics On Time & Work Practice Questions Answers Test With Solutions & More Shortcuts
TIME & WORK PRACTICE TEST [7  EXERCISES]
Model 1 Basics On Time & Work
Model 2 Formula Method ‘M1D1W1 = M2D2W2’
Model 3 Man Leaves & Joins
Model 4 Working With Man, Woman, Child
Model 5 Split & Fraction Of Work
Model 6 Efficiency Of The Worker
Model 7 Working With Individual Wages
Question : 6 [SSC CGL Prelim 2002]
A and B can do a piece of work in 10 days, B and C in 15 days and C and A in 20 days. C alone can do the work in :
a) 30 days
b) 80 days
c) 60 days
d) 120 days
Answer »Answer: (d)
According to the question
Work done by A and B together in one day = $1/10$ part
Work done by B and C together in one day = $1/15$ part
Work done by C and A together in one day = $1/20$ part
So, A + B = $1/10$ ....(I)
B + C = $1/15$ ...(II)
C + A = $1/20$ ....(III)
Adding I, II, III, we get
2 (A + B + C) = $1/10 + 1/15 + 1/20$
2 (A + B + C) = ${6 + 4 + 3}/60 = 13/60$
A + B + C = $13/120$ ....(IV)
Putting the value of eqn. (I) in eqn. (IV)
$1/10 + C =13/120$
C = $13/120  1/10 = {13  12}/120 = 1/120$
Work done in 1 day by C is $1/120$ part
Hence, C will finish the whole work in 120 days
Using Rule 19
A and B can do a work in 'x' days, B and C can do the same work in 'y' days. C and A can do the same work in 'z' days. Then, all can do alone the work as following:
A alone can do in =${2xyz}/{xy + yz  zx}$days
B alone can do in =${2xyz}/{xy + yz + zx}$days
C alone can do in =${2xyz}/{xy  yz + zx}$days
Time Taken by C= ${2xyz}/{xy  yz + zx}$
= ${2 × 10 × 15 × 20}/{10 × 15  15 × 20 + 20 × 10 }$
= $6000/{150  300 + 200} = 6000/50$ = 120 days
Question : 7 [SSC CISF ASI 2010]
A and B together can complete a piece of work in 18 days, B and C in 24 days and A and C in 36 days. In how many days, will all of them together complete the work ?
a) 10 days
b) 12 days
c) 16 days
d) 15 days
Answer »Answer: (c)
(A + B)’s 1 day’s work = $1/18$
(B + C)’s 1 day’s work = $1/24$
(A + C)’s 1 day’s work = $1/36$
Adding all three,
2 (A + B + C)’s 1 day’s work= $1/18 + 1/24 + 1/36$
= ${4 + 3 + 2}/72 = 1/8$
(A + B + C)’ 1 day’s work = $1/16$
A, B and C together will complete the work in 16 days.
Using Rule 5,
Total time taken = ${2 × 18 × 24 × 36}/{18 × 24 +24 × 36 + 36 × 18}$
= ${36 × 24 × 36}/{432 + 864 + 648}$
= $31104/1944$ = 16 days
Question : 8 [SSC CGL Prelim 2005]
A and B together can do a work in 8 days, B and C together in 6 days while C and A together in 10 days, if they all work together, the work will be completed in :
a) 4$4/9$ days
b) 5$5/47$ days
c) 3$3/4$ days
d) 3$3/7$ days
Answer »Answer: (b)
(A + B)'s 1 day's work = $1/8$ ...(i)
(B + C)'s 1 day's work = $1/6$ ...(ii)
(C + A)'s 1 day's work = $1/10$ ...(iii)
On adding,
2(A + B + C)'s 1 day's work = $1/8 + 1/6 + 1/10$
= ${15 + 20 + 12}/120 = 47/120$
(A + B + C)'s 1 day’s work= $47/240$
(A + B + C) together will complete the work in
$240/47 = 5{5}/47$ days.
Using Rule 5,
Time taken = ${2 × 8 × 6 × 10}/{8 × 6 + 6 × 10 + 10 × 8}$
= $960/{48 + 60 + 80} = 960/188$
= $240/47 = 5{5}/47$ days
Question : 9 [SSC CHSL 2011]
A and B together can complete a work in 8 days and B and C together in 12 days. All of the three together can complete the work in 6 days. In how much time will A and C together complete the work ?
a) 20 days
b) 12 days
c) 8 days
d) 10 days
Answer »Answer: (c)
Let A and C complete the work in x days
(A + B)’s 1 day’s work = $1/8$
(B + C)’s 1 day’s work = $1/12$
(C + A)’s 1 day’s work = $1/x$
Then (A + B + B + C + C + A)’s 1 day’s work = $1/8 + 1/12 + 1/x$
2(A + B + C)’s 1 day’s work = ${3x + 2x + 24}/{24x}$
(A + B + C)’s 1 day’s work = ${5x + 24}/{24x × 2}$
According to the question,
(A + B + C)’s 1 day’s work = $1/6$
$1/6 = {5x + 24}/{48x}$
30x + 144 = 48x ⇒ x = $144/18$ = 8 days.
Using Rule 5,
Let the time taken by A and C bc x days
Total time taken = ${2 × 8 × 12 × x}/{8 × 12 + 12 × x + 8 × x}$
6 = ${192x}/{96 +20x}$
576 + 120x = 192x
72x = 576 ⇒ x = 8
Time taken by A and C is 8 days.
Question : 10 [SSC CGL Prelim 2000]
A can do a work in 6 days and B in 9 days. How many days will both take together to complete the work?
a) 3 days
b) 3.6 days
c) 7.5 days
d) 5.4 days
Answer »Answer: (b)
According to question,
A can finish the whole work in 6 days.
A’s one day’s work = $1/6$
Similarly, B’s one day’s work = $1/9$
(A + B)’s one day’s work
= $(1/6 + 1/9) = ({3 + 2}/18) = 5/18$
Therefore, (A + B)’s can finish the
whole work in $18/5$ days i.e., 3.6 days.
Using Rule 2
If A completes a piece of work in 'x' days, and B completes the same work in 'y' days, then,
Work done by A in 1 day = $1/x$, Work done by B in 1 day = $1/y$
Work done by A and B in 1 day = $1/x + 1/y = {x + y}/{xy}$
Total time taken to complete the work by A and B both = $({xy}/{x + y})$
Time taken = ${6 × 9}/{9 + 6} = 54/15$ = 3.6 days
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Model 1 Basics On Time & Work Shortcuts »
Click to Read...Model 1 Basics On Time & Work Online Quiz
Click to Start..TIME & WORK SHORTCUTS AND TECHNIQUES WITH EXAMPLES

Model 1 Basics On Time & Work
Defination & Shortcuts … 
Model 2 Formula Method ‘M1D1W1 = M2D2W2’
Defination & Shortcuts … 
Model 3 Man Leaves & Joins
Defination & Shortcuts … 
Model 4 Working With Man, Woman, Child
Defination & Shortcuts … 
Model 5 Split & Fraction Of Work
Defination & Shortcuts … 
Model 6 Efficiency Of The Worker
Defination & Shortcuts … 
Model 7 Working With Individual Wages
Defination & Shortcuts …
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