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 : 1 [SSC CGL Prelim 2007]
A alone can complete a work in 12 days. A and B together can complete it in 8 days. How long will B alone take to complete the work ?
a) 20 days
b) 16 days
c) 24 days
d) 18 days
Answer »Answer: (c)
A’s 1 day’s work = $1/12$
(A+B)’s 1 day’s work = $1/8$
B’s 1 day’s work =$1/8  1/12 = {3  2}/24 = 1/24$
B alone can do the work in 24 days.
Using Rule 4,
Time taken by B = ${12 × 8}/{12  8}$ = 24 days
Question : 2 [SSC CGL TierI 2010]
If A and B together can complete a piece of work in 15 days and B alone in 20 days, in how many days can A alone complete the work ?
a) 30 days
b) 40 days
c) 60 days
d) 45 days
Answer »Answer: (c)
(A + B)’s 1 day’s work = $1/15$
B’s 1 day’s work = $1/20$
A’s 1 day’s work = $1/15  1/20 = {4  3}/60 = 1/60$
A alone will do the work in 60 days.
Using Rule 4,
A alone do in = ${15 × 20}/{20  15}$
= ${15 × 20}/5$ = 60 days
Question : 3 [SSC (South Zone) Investigator 2010]
If A and B together can complete a work in 12 days, B and C together in 15 days and C and A together in 20 days, then B alone can complete the work in
a) 20 days
b) 24 days
c) 30 days
d) 25 days
Answer »Answer: (a)
(A + B)’s 1 day’s work = $1/12$
(B + C)’s 1 day’s work = $1/15$
(C + A)’s 1 day’s work = $1/20$
On adding,
2 (A + B + C)’s 1 day's work = $1/12 + 1/15 + 1/20$
= ${5 + 4 + 3}/60 = 1/5$
(A+B+C)’s 1 day’s work = $1/10$
B’s 1 day’s work = $1/10  1/20 = {2  1}/20 = 1/20$
B alone can do the work in 20 days.
Using Rule 19,
B alone can do in = ${2 × 12 × 15 × 20}/{12 × 15 + 15 × 20 + 20 × 12}$
= ${24 × 300}/{180 + 300 + 240} = {24 × 300}/360$ = 20 days
Question : 4 [SSC CGL Prelim 2005]
A and B can do a piece of work in 12 days, B and C in 8 days and C and A in 6 days. How long would B take to do the same work alone ?
a) 48 days
b) 40 days
c) 24 days
d) 32 days
Answer »Answer: (a)
(A + B)'s 1 day's work = $1/12$ ...(i)
(B + C)'s 1 day's work = $1/8$ ...(ii)
(C + A)'s 1 day's work = $1/6$ ...(iii)
On adding,
2(A + B + C)'s 1 day's work = $1/12 + 1/8 + 1/6$
= ${2 + 3 + 4}/24 = 9/24$
(A+ B + C)'s 1 day’s work = $9/{24 × 2} = 9/48$ ...(iv)
On, subtracting (iii) from (iv),
B’s 1 day’s work = $9/48  1/6$
= ${9  8}/48 = 1/48$
B can complete the work in 48 days.
Using Rule 19,
B alone can do in = ${2 × 12 × 8 × 6}/{12 × 8 + 8 × 6 + 6 × 12}$
= ${24 × 48}/{96 + 48 + 72} = {24 × 48}/{96 + 120}$
= ${24 × 48}/24$ = 48 days
Question : 5 [SSC CPO 2011]
A and B working together; can do a piece of work in 4$1/2$ hours. B and C working together can do it in 3 hours. C and A working together can do it in 2$1/4$ hours. All of them begin the work at the same time. Find how much time they will take to finish the piece of work.
a) 3·25 hours
b) 2·5 hours
c) 3 hours
d) 2 hours
Answer »Answer: (d)
(A + B)’s 1 hour’s work = $2/9$ .....(i)
(B + C)’s 1 hour’s work = $1/3$ ......(ii)
(C + A)’s 1 hour’s work = $4/9$ .....(iii)
Adding all three equations,
2 (A + B + C)’s 1 hour’s work = $2/9 + 1/3 + 4/9$
${2 + 3 + 4}/9$ = 1
A, B and C together will complete the work in 2 hours.
Using Rule 5,
Time taken = ${2 × 9/2 × 3 × 9/4}/{9/2 × 3 + 3 × 9/4 + 9/2 × 9/4}$
= ${{18 × 27}/8}/{27/2 + 27/4 + 81/8}$
= ${18 × 27}/8 × 8/({108 + 54 + 81})$
= ${18 × 27}/243$ = 2 hours
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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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