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

Questions : 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

The correct answers to the above question in:

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

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Read more formula method m1d1w1 m2d2w2 Based Quantitative Aptitude Questions and Answers

Question : 1

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: (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 1
If $M_1$ 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
${M_1D_1}/{W_1} = {M_2D_2}/{W_2}$ and
If $M_1$ 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 : 2

A skilled, a half skilled and an unskilled labourer work for 7, 8 and 10 days respectively and they together get Rs.369 for their work. If the ratio of their each day’s work is $1/3 : 1/4 : 1/6$, then how much does the trained labourer get (in rupees) ?

a) 164

b) 102.50

c) 143.50

d) 201.50

Answer: (c)

Using Rule 25,

Skilled : half skilled : unskilled

= $1/3 : 1/4 : 1/6$

= $(1/3 × 12) : (1/4 × 12) : (1/6 × 12)$

= 4 : 3 : 2

Share of the trained labourer

= $28/{7 × 4 + 8 × 3 + 2 × 10} × 369$

= $28/{(28 + 24 + 20)} × 369$

= $28/72 × 369$ = Rs.143.50

Question : 3

A man and a boy received Rs.800 as wages for 5 days for the work they did together. The man’s efficiency in the work was three times that of the boy. What are the daily wages of the boy ?

a) Rs.76

b) Rs.56

c) Rs.40

d) Rs.44

Answer: (c)

Man : boy = 3 : 1

Boy's share = $1/4 × 800$ = Rs.200

The daily wages of boy

= Rs.$(200/5)$ = Rs.40

Using Rule 16
If the efficiency to work of A is twice the efficiency to work of B, then, A:B (efficiency) = 2x:x and A:B (time) = t:2t

A:B = 3x:x and A:B = t:3t

Share of boy

= $t/{t + 3t} × 800$ = 200

Daily wages of boy = $200/5$ = Rs.40

Question : 4

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: (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 : 5

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: (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 : 6

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: (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 24
A 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

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GET time & work PRACTICE TEST EXERCISES

Model 1 Basics on Time & Work

Model 2 Formula method ‘M1D1W1 = M2D2W2’

Model 3 Man leaves & joins

Model 4  Working with Man, Woman, Child

Model 5  Split & Fraction of work

Model 6  Efficiency of the worker

Model 7 Working with individual wages
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