Model 2 Formula method ‘M1D1W1 = M2D2W2’ 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) 12$1/4$ days
(b) 14 days
(c) 12 days
(d) 24$1/2$ days
The correct answers to the above question in:
Answer: (c)
A's 1 day's work = $1/21$
B's 1 day's work = $1/28$
Total work done by both
= $1/21 + 1/28 = {4 + 3}/84 = 1/12$
Amount is sufficient to pay 12 days wages of both.
Using Rule 2If 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 = $({xy}/{x + y})$
Here, x = 21, y = 28
Required days
= ${xy}/{x + y}= {21 × 28}/{21 + 28}$
= ${21 × 28}/49$ = 12 days
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Read more formula method m1d1w1 m2d2w2 Based Quantitative Aptitude Questions and Answers
Question : 1
Suman can do a work in 3 days. Sumati can do the same work in 2 days. Both of them finish the work together and get Rs.150. What is the share of Suman ?
a) Rs.30
b) Rs.60
c) Rs.75
d) Rs.70
Answer »Answer: (b)
Ratio of Suman’s and Sumati’s 1 day’s work
= $1/3 : 1/2 = 2 : 3$
Sum of the ratios = 2 + 3 = 5
Suman’s share = $2/5 × 150$ = Rs.60
Using Rule 24A can do a work in 'm' days and B can do the same work in 'n' days. If they work together and total wages is R, then.Part of A = $n/{m + n} × R$Part of B = $m/{m + n} × R$
Here, m = 3, n = 2, R = 150
Share of suman = $n/{m + n} × R$
= $2/{3 + 2} × 150 = 2/5 × 150$ = 60
Question : 2
A and B can complete a piece of work in 15 days and 10 days respectively. They contracted to complete the work for Rs.30,000. The share of A in the contracted money will be :
a) Rs.18,000
b) Rs.16,500
c) Rs.12,000
d) Rs.12,500
Answer »Answer: (c)
A’s 1 day’s work = $1/15$
B’s 1 day’s work = $1/10$
Ratio = $1/15 : 1/10$ = 2 : 3
Sum of the ratios = 2 + 3 = 5
A’s share
= Rs.$2/5 × 30000$ = Rs.12000
Using Rule 24,
Here, m = 15, n = 10, R = 30,000
Share of A = $n/{m + n} × R$
= $10/{15 + 10} × 30000$
= $10/25 × 30 000$ = Rs.12,000
Question : 3
Two men undertake a job for Rs.960. They can complete it in 16 days and 24 days respectively. They work along with a third man and take 8 days to complete it. Then the share of the third man should be
a) Rs.155
b) Rs.165
c) Rs.150
d) Rs.160
Answer »Answer: (d)
Using Rule 25,
Work done by the third person in 1 day
= $1/8 - 1/16 - 1/24 = {6 - 3 - 2}/48 = 1/48$
Ratio of their 1 day’s work
= $1/16 : 1/24 : 1/48$ = 3 : 2 : 1
Share of the third person
= $1/(3 + 2 + 1) × 960 = 960/6$ = Rs.160
Question : 4
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs.3200. With the help of C they completed the work in 3 days. How much is to be paid to C ?
a) Rs.375
b) Rs.400
c) Rs.800
d) Rs.600
Answer »Answer: (b)
Using Rule 25,
A’s 1 day’s work = $1/6$
B’s 1 day’s work = $1/8$
(A + B + C)’s 1 day’s work = $1/3$
C’s 1day’s work
= $1/3 - 1/6 - 1/8 = {8 - 4 - 3}/24 = 1/24$
Ratio of their one day’s work respectively
= $1/6 : 1/8 : 1/24$ = 4 : 3 : 1
Sum of the ratios = 4 + 3 + 1 = 8
C’s share = Rs.$1/8$ × 3200 = Rs.400
Question : 5
Stanie and Paul take a piece of work for Rs.28,800. One alone could do it in 36 days, the other in 48 days. With the assistance of an expert, they finish it in 12 days. How much remuneration the expert should get ?
a) Rs.10000
b) Rs.18000
c) Rs.12000
d) Rs.16000
Answer »Answer: (c)
Expert’s 1 day’s work
= $1/12 - 1/36 - 1/48$
= ${12 - 4 - 3}/144 = 5/144$
Ratio of their respective work for 1 day
= $1/36 : 1/48 : 5/144$ = 4 : 3 : 5
Expert’s share
= $5/12 × 28800$ = 12000
Question : 6
A, B and C are employed to do a piece of work for Rs.575. A and C are supposed to finish $19/23$ of the work together. Amount shall be paid to B is
a) Rs.210
b) Rs.100
c) Rs.475
d) Rs.200
Answer »Answer: (b)
Work done by B
= $1 - 19/23 = {23 - 19}/23 = 4/23$
(A + C) : B = $19/23 : 4/23$ = 19 : 4
Sum of ratios = 19 + 4 = 23
B’s share = $4/23 × 575$ = Rs.100
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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