Model 1 Basics On Time & Work SectionWise Topic Notes With Detailed Explanation And Example Questions
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The following question based on Time & Work topic of Quantitative Aptitude
(a) 20 days
(b) 24 days
(c) 30 days
(d) 25 days
The correct answers to the above question in:
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
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Read more basics on time and work Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
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
Question : 3
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 : 4
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 : 5
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
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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