Model 7 Working with individual wages 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) 28
(b) 18
(c) 30
(d) 10
The correct answers to the above question in:
Answer: (c)
Using Rule 1,
We know that
$W_1/{M_1D_1} = W_2/{M_2D_2}$
$280/{72 × 21} = 100/{x × 18}$
Where x = number of men
x × 18 × 280 = 100 × 72 × 21
$x = {100 × 72 × 21}/{18 × 280}$ = 30
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Read more working with individual wages Based Quantitative Aptitude Questions and Answers
Question : 1
If 4 men or 8 women can do a piece of work in 15 days, in how many days can 6 men and 12 women do the same piece of work ?
a) 30 days
b) 15 days
c) 20 days
d) 5 days
Answer »Answer: (d)
4 men ≡ 8 women
1 man ≡ 2 women
6 men + 12 women
≡ 12 women + 12 women ≡ 24 women
$M_1D_1 = M_2D_2$
8 × 15 = 24 × $D_2$
$D_2 = {8 × 15}/24$ = 5 days
Using Rule 12,
Here, A = 4, B = 8, a = 15
$A_1 = 6, B_1$ = 12
Required number of days = ${a(A . B)}/{A_1B + B_1A}$
= ${15(4 × 8)}/{6 × 8 + 12 × 4}$
= ${15 × 32}/96$ = 5 days
Question : 2
3 men and 7 women can do a job in 5 days, while 4 men and 6 women can do it in 4 days. The number of days required for a group of 10 women working together, at the same rate as before, to finish the same job is :
a) 20 days
b) 40 days
c) 30 days
d) 36 days
Answer »Answer: (a)
3 × 5 men + 7 × 5 women
= 4 × 4 men + 6 × 4 women
16 men - 15 men
= 35 women - 24 women
1 man = 11 women
3 men + 7 women = 40 women
$M_1D_1 = M_2D_2$
40 × 5 = 10 × $D_2$
$D_2$ = 20 days
Using Rule 11If $A_1$ men and $B_1$ boys can do a certain work in $D_1$ days, Again, $A_2$ men and $B_2$ boys can do the same work in $D_2$ days, then, $A_3$ men and $B_3$ boys can do the same work inRequired time = ${D_1D_2(A_1B_2 - A_2B_1)}/{D_1(A_1B_3 - A_3B_1) - D_2(A_2B_3 - A_3 B_2)}$ days
Here, $A_1 = 3, B_1 = 7, D_1$ = 5
$A_2 = 4, B_2 = 6, D_2$ = 4
$A_3 = 0, B_3$ = 10
Required days = ${D_1D_2(A_1B_2 - A_2B_1)}/{D_1(A_1B_3 - A_3B_1) - D_2(A_2B_3 - A_3 B_2)}$ days
= ${5 × 4(3 × 6 - 4 × 7)}/{5 × (3 × 10 - 0) - 4(4 × 10 - 0)}$
= ${20 × (-10)}/{150 - 160}$ = 20 days
Question : 3
Working 8 hours a day, Anu can copy a book in 18 days. How many hours a day should she work so as to finish the work in 12 days ?
a) 13 hours
b) 11 hours
c) 12 hours
d) 10 hours
Answer »Answer: (c)
Days | Working hours/day |
18 | 8 |
↑ | ↓ |
12 | x |
$12/18 = 8/x$
where x is hours/days
12x = 18 × 8
$x = {18 × 8}/12$ = 12 hours
Using Rule 1,
Here, $M_1 = 1, D_1 = 18, T_1$ = 8
$M_2 = 1, D_2 = 12, T_2$ = ?
$M_1D_1T_1 = M_2D_2T_2$
1 × 18 × 8 = 1 × 12 × $T_2$
$T_2 = {18 × 8}/12 = 12$ hours
Question : 4
Two persons can complete a piece of work in 9 days. How many more persons are needed to complete double the work in 12 days?
a) 1
b) 4
c) 3
d) 2
Answer »Answer: (c)
Work | Days | Persons |
1 | 9 | 2 |
↓ | ↑ | ↓ |
2 | 12 | x |
where x = number of persons
∴ ${1 : 2}/{12 : 9}]$ : : 2 : x
1×12 × x = 2 × 9 × 2
$x = {2 × 9 × 2}/12$ = 3
Using Rule 1,
Here, $M_1 = 2, W_1 = 1, D_1$ = 9
$M_2 = ?, W_2 = 2, D_2$ = 12
$M_1D_1W_2 = M_2D_2W_1$
2 × 9 × 2 = $M_2$ × 12 × 1
$M_2 = 36/12$ = 3
Question : 5
7 men can complete a piece of work in 12 days. How many additional men will be required to complete double the work in 8 days ?
a) 7
b) 14
c) 28
d) 21
Answer »Answer: (b)
Work | Days | Men |
1 | 12 | 7 |
↓ | ↑ | ↓ |
2 | 8 | x |
∴ ${1 : 2}/{8 : 12}]$ : : 7 : x
where, x is no. of men
1 × 8 × x = 2 × 12 × 7
$x = {7 × 12 × 2}/8 = 21$
Number of additional men = 21 - 7 = 14
Metod 2 : Using Rule 1,
$M_1D_1W_2 = M_2D_2W_1$
7 × 12 × 2 = $M_2$ × 8 × 1
$M_2 = {7 × 12 × 2}/8 = 21$
No. of additional men = 21 - 7 = 14
Question : 6
20 men or 24 women can complete a piece of work in 20 days. If 30 men and 12 women undertake to complete the work, the work will be completed in
a) 16 days
b) 15 days
c) 10 days
d) 12 days
Answer »Answer: (c)
20 men ≡ 24 women
5 men ≡ 6 women
30 men + 12 women = 40 men
$M_1D_1 = M_2D_2$
20 × 20 = 40 × $D_2$
$D_2 = {20 × 20}/40$ = 10 days
Using Rule 12If A men or B boys can do a certain work in 'a' days, then $A_1$ men and $B_1$ boys can do the same work inTime taken = $a/{A_1/A + B_1/B} = {a(A . B)}/{A_1B + B_1A}$ days
Here, A = 20, B = 24, a = 20
$A_1 = 30, B_1$ = 12
Required time = ${a(A . B)}/{A_1B + B_1A}$
= ${20(20 × 24)}/{30 × 24 + 12 × 20}$
= $9600/{720 + 240} = 9600/960$ = 10 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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