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) Rs.18,000
(b) Rs.16,500
(c) Rs.12,000
(d) Rs.12,500
The correct answers to the above question in:
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
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Read more formula method m1d1w1 m2d2w2 Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
A can do a piece of work in 12 days while B alone can do it in 15 days. With the help of C they can finish it in 5 days. If they are paid Rs.960 for the whole work how much money A gets ?
a) Rs.480
b) Rs.240
c) Rs.400
d) Rs.320
Answer »Answer: (c)
Rule 2 and Rule 25,
Work done by A and B in 5 days
= $5(1/12 + 1/15) = 5({5 + 4}/60)$
= $9/12 = 3/4$
Time taken by C in doing $1/4$ work = 5 days
C will complete in 20 days.
Ratio of wages = $1/12 : 1/15 : 1/20$ = 5 : 4 : 3
Amount received by A
=$5/12 × 960$ = Rs.400
Question : 3
If 6 persons working 8 hours a day earn Rs.8400 per week, then 9 persons working 6 hours a day will earn per week
a) Rs.8400
b) Rs.16800
c) Rs.16200
d) Rs.9450
Answer »Answer: (d)
More persons, more earning, Less working hours, less earning = Direct proportion
∴ ${6 : 9}/{8 : 6}]$ : : 8400 : x
where x = required earning
Therefore, 6 × 8 × x = 9 × 6 × 8400
or $x ={9 × 6 × 8400}/{6 × 8}$ = Rs.9450
Using Rule 1If $M_1$ men can finish $W_1$ work in $D_1$ days and $M_2$ men can finish $W_2$ work in $D_2$ days then, Relation is${M_1D_1}/{W_1} = {M_2D_2}/{W_2}$ andIf $M_1$ men finish $W_1$ work in $D_1$ days, working $T_1$ time each day and $M_2$ men finish $W_2$ work in $D_2$ days, working $T_2$ time each day, then${M_1D_1T_1}/{W_1} = {M_2D_2T_2}/{W_2}$
Here, $M_1 = 6, T_1$ = 8, wages = x
$M_2 = 9, T_2$ = 6, wages = 8400
6 × 8 × x = 9 × 6 × 8400
$x = {9 × 6 × 8400}/{6 × 8}$ = Rs.9450
Question : 4
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 : 5
A sum of money is sufficient to pay A’ s wages for 21 days and B’s wages for 28 days. The same money is sufficient to pay the wages of both for :
a) 12$1/4$ days
b) 14 days
c) 12 days
d) 24$1/2$ days
Answer »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
Question : 6
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
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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