Model 1 Basics on Time & Work Section-Wise Topic Notes With Detailed Explanation And Example Questions
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The following question based on time & work topic of quantitative aptitude
(a) 4 days
(b) 3${3}/7$ days
(c) $1/4$ day
(d) $7/24$ day
The correct answers to the above question in:
Answer: (b)
A’s 1 day’s work = $1/24$
B’s 1 day’s work = $1/6$
C’s 1 day’s work = $1/12$
(A + B + C)’s 1 day’s work
=$1/24 + 1/6 + 1/12 = {1 + 4 + 2}/24 = 7/24$
The work will be completed by them in $24/7$ i.e., 3$3/7$ days
Using Rule 3If A can do a work in 'x' days, B can do the same work in 'y' days, C can do the same work in 'z' days then, total time taken by A, B and C to complete the work together = $1/{1/x + 1/y + 1/z} = {xyz}/{xy + yz + zx}$and If workers are more than 3 then total time taken by A, B, C ...... so on to complete the work together = $1/{1/x + 1/y + 1/z + ...}$
Time taken = ${24 × 6 × 12}/{24 × 6 + 6 × 12 + 24 × 12}$
= $1728/{144 + 72 + 288}$
= $1728/504 = 24/7 = 3{3}/7$ 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 72 days. B and C can do it in 120 days, A and C can do it in 90 days. In how many days all the three together can do the work ?
a) 150 days
b) 60 days
c) 80 days
d) 100 days
Answer »Answer: (b)
(A+B)’s 1 day’s work = $1/72$,
(B+C)’s 1 day’s work = $1/120$,
(C+A)’s 1 day’s work = $1/90$
On adding all three
2 (A + B + C)'s 1 days work = $1/72 + 1/120 + 1/90$
= ${5 + 3 + 4}/360 = 1/30$
(A+B+C)’s 1 day’s work = $1/60$
(A+B+C) will do the work in 60 days.
Using Rule 5,
Time taken = ${2 × 72 × 120 × 90}/{72 × 120 + 120 × 90 + 72 × 90}$
= $1555200/{8640 + 10800 + 6480}$
= $1555200/25920$ = 60 days
Question : 2
If A and B together can complete a work in 18 days, A and C together in 12 days and B and C together in 9 days, then B alone can do the work in
a) 40 days
b) 30 days
c) 18 days
d) 24 days
Answer »Answer: (d)
(A + B)’s 1 day’s work = $1/18$
(B + C)’s 1 day’s work = $1/9$
(A + C)’s 1 day’s work = $1/12$
Adding all the above three,
2 (A + B + C)’s 1 day’s work = $1/18 + 1/9 + 1/12$
= ${2 + 4 + 3}/36 = 9/36 = 1/4$
(A + B + C)’s 1 day’s work = $1/8$
B’s 1 day’s work = (A + B + C)’s 1 day’s work - (A + C)’s 1 day’s work
= $1/8 - 1/12 = {3 - 2}/24 = 1/24$
Hence, B alone can do the work in 24 days.
Using Rule 19,
B alone can do in = ${2 × 18 × 9 × 12}/{-18 × 9 + 12 × 9 + 12 × 18}$
= ${36 × 108}/{-162 + 108 + 216} = {36 × 108}/162$ = 24 days
Question : 3
A and B together can complete a piece of work in 72 days, B and C together can complete it in 120 days, and A and C together in 90 days. In what time can A alone complete the work ?
a) 150 days
b) 120 days
c) 80 days
d) 100 days
Answer »Answer: (b)
(A + B)’s 1 day’s work = $1/72$
(B + C)’s 1 day’s work = $1/120$
(C + A)’s 1 day’s work = $1/90$
Adding all three,
2(A + B + C)’s 1 day’s work = $1/72 + 1/120 + 1/90$
= ${5 + 3 + 4}/360 = 12/360 = 1/30$
(A + B + C)’s 1 day’s work = $1/60$
Now, A’s 1 day’s work = (A + B + C)’s 1 day’s work - (B + C)’s 1 day’s work
= $1/60 - 1/120 = {2 - 1}/120 = 1/120$
A alone can complete the work in 120 days.
Using Rule 19,
A alone can do in
= ${2 × 72 × 120 × 90}/{72 × 120 + 120 × 90}$ - 72 × 90
= ${2 × 72 × 120 × 90}/{8640 + 10800}$ - 6480
= ${144 × 10800}/12960$ = 120 days
Question : 4
A and B can do a piece of work in 10 days. B and C can do it in 12 days. A and C can do it in 15 days. How long will A take to do it alone ?
a) 30 days
b) 40 days
c) 24 days
d) 20 days
Answer »Answer: (c)
(A+B)’s 1 day’s work = $1/10$
(B + C)’s 1 day’s work = $1/12$
(C + A)’s 1 day’s work = $1/15$
On adding all three,
2(A + B + C)’s 1 day’s work = $1/10 + 1/12 + 1/15$
= ${6 + 5 + 4}/60 = 15/60 = 1/44$
(A + B + C)’s 1 day’s work = $1/8$
A’s 1 day’s work = $1/8 - 1/12$
= ${3 - 2}/24 = 1/24$
A will complete the work in 24 days.
Using Rule 19,
A alone can do in = ${2 × x × y × z}/{xy + yz - zx}$
= ${2 × 10 × 12 × 15}/{10 × 12 + 12 × 15 - 15 × 10}$
= $3600/{120 + 180 - 150}$
= $3600/150$ = 24 days
Question : 5
A and B can complete a piece of work in 30 days, B and C in 20 days, while C and A in 15 days. If all of them work together, the time taken in completing the work will be
a) 13$1/3$ days
b) 12$2/3$ days
c) 10 days
d) 12 days
Answer »Answer: (a)
Work done by (A + B) in 1 day = $1/30$
Work done by (B + C) in 1 day = $1/20$
Work done by (C + A) in 1 day = $1/15$
On adding,
Work done by 2 (A +B + C) in 1 day
= $1/30 + 1/20 + 1/15 = {2 + 3 + 4}/60$
= $9/60 = 3/20$
Work done by (A + B + C) in 1 day = $3/40$
(A + B + C) will do the work in $40/3 = 13{1}/3$ days
Using Rule 5,
Time taken = ${2 × 30 × 20 × 15}/{30 × 20 + 20 × 15 + 15 × 30}$
= $18000/{600 + 300 + 450}$
= $18000/1350 = 13{1}/3$ days
Question : 6
A and B can complete a piece of work in 8 days, B and C can do it in 12 days, C and A can do it in 8 days. A, B and C together can complete it in
a) 7 days
b) 6 days
c) 4 days
d) 5 days
Answer »Answer: (b)
(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 = $1/8$
On adding,
2 (A + B + C)’s 1 day’s work = $1/8 + 1/12 + 1/8$
${3 + 2 + 3}/24 = 8/24 = 1/3$
(A + B + C)’s 1 day’s work = $1/6$
Hence, the work will be completed in 6 days.
Method 2 :
Time = ${2xyz}/{xy + yz + zx}$
(Here, x = 8, y = 12; z = 8)
= ${2 × 8 × 12 × 8}/{96 + 96 + 64}$
${2 × 8 × 12 × 8}/256$ = 6 days.
Using Rule 5,
Time taken = ${2 × 8 × 12 × 8}/{8 × 12 + 12 × 8 + 8 × 8}$
= ${16 × 96}/{96 + 96 + 64} = {16 × 96}/256$ = 6 days
time & work Shortcuts and Techniques with Examples
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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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