Model 5 Split & Fraction of 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) 20
(b) 40
(c) 15
(d) 30
The correct answers to the above question in:
Answer: (a)
Using Rule 1,
Days | Work | Men |
60 | $3/4$ | 60 |
↑ | ↓ | ↓ |
30 | $1/4$ | x |
∴ ${30 : 60}/{3/4 : 1/4}]$ : : 60 : x
$30 × 3/4 × x = 60 × 1/4 × 60$
$x = {60 × 60}/{30 × 3}$ = 40
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Read more split and fraction of work Based Quantitative Aptitude Questions and Answers
Question : 1
A, B and C contract a work for Rs. 440. A and B together are to do $9/11$ of the work. The share of C should be :
a) Rs. 90
b) Rs. 75
c) Rs. 80
d) Rs. 100
Answer »Answer: (c)
Work done by A and B together = $9/11$ parts
Work done by C = $1 - 9/11 = 2/11$ parts
Total amount = Rs. 440
∴ C’s share = Rs.$(2/11 × 440)$ = Rs.80
Question : 2
A and B together can complete a work in 24 days. B alone does $1/3$ rd part of this work in 12 days. How many days will A alone take to complete the remaining work?
a) 36 days
b) 24 days
c) 72 days
d) 48 days
Answer »Answer: (d)
B completes $1/3$ work in 12 days.
B will complete 1 work in 12 × 3 = 36 days.
B’s 1 day’s work = $1/36$
(A + B)’s 1 day’s work = $1/24$
A’s 1 day’s work = $1/24 - 1/36$
= ${3 - 2}/72 = 1/72$
Time taken by A in doing 1work = 72 days
∴ Remaining work
= $1 - 1/3 = 2/3$
Time taken by A in doing $2/3$ work
= $2/3$ × 72 = 48 days
Question : 3
Janardan completes $2/3$ of his work in 10 days. Time he will take to complete $3/5$ of the same work, is
a) 6 days
b) 8 days
c) 4 days
d) 9 days
Answer »Answer: (d)
Using Rule 1,
${M_1D_1}/W_1= {M_2D_2}/W_2$
$10/{2/3} = D_2/{3/5}$
$30/2 = {5D_2}/3$
$D_2 = 30/2 × 3/5$ = 9 days
Question : 4
A does half as much work as B in three- fourth of the time. If together they take 18 days to complete a work, how much time shall B take to do it alone?
a) 35 days
b) 30 days
c) 45 days
d) 40 days
Answer »Answer: (b)
Using Rule 2,
Let B completes the work in x days.
Work done by A in ${3x}/4$ days = $1/2$
Time taken by A in completing the work = $2 × {3x}/4 = {3x}/2$ days
(A + B)’s 1 day’s work
= $1/x + 2/{3x} = {3 + 2}/{3x} = 5/{3x}$
$5/{3x} = 1/18$ ⇒ 3x = 90 ⇒ x = 30
Hence, time taken by B in completing the work = 30 days
Question : 5
P can complete $1/4$ of a work in 10 days, Q can complete 40% of the same work in 15 days, R, completes $1/3$ of the work in 13 days and S, $1/6$ of the work in 7 days. Who will be able to complete the work first ?
a) Q
b) P
c) S
d) R
Answer »Answer: (a)
Time taken by P in completing 1 work
= 10 × 4 = 40 days
Time taken by Q in completing 1 work
= ${15 × 5}/2 = 75/2$ days
Time taken by R in completing 1 work
= 13 × 3 = 39 days
Time taken by S in completing 1 work
= 7 × 6 = 42 days
Clearly, Q took the least time i.e. $75/2$ or 37${1}/2$ days.
Question : 6
A and B can do a piece of work in 72 days, B and C can do it in 120 days, and A and C can do it in 90 days. When A, B and C work together, how much work is finished by them in 3 days.
a) $1/30$
b) $1/40$
c) $1/10$
d) $1/20$
Answer »Answer: (d)
Using Rule 5If 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 total time taken, when A, B and C work together =$2/{(1/x + 1/y + 1/z)}$ OR ${2xyz}/{xy + yz + zx}$ days
(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 day’s 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)’s 3 days’ work = $3/60 = 1/20$
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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