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) 30
(b) 25
(c) 15
(d) 20
The correct answers to the above question in:
Answer: (c)
Using Rule 1,
7 men ≡ 10 women
or 1 man = $10/7$ women
14 men + 20 women
= $({10 × 14}/7 + 20)$ women = 40 women
Now, more work, more days
More women, less days
∴ ${Work - {1 : 6}}/{Women - {40 : 10}}]$ : : 10 : x
Where x = number of days
1 × 40 × x = 6 × 10 × 10
or $x = 600/40$ = 15
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Read more working with individual wages Based Quantitative Aptitude Questions and Answers
Question : 1
A man undertakes to do a certain work in 150 days. He employs 200 men. He finds that only a quarter of the work is done in 50 days. The number of additional men that should be appointed so that the whole work will be finished in time is :
a) 50
b) 125
c) 75
d) 100
Answer »Answer: (d)
Using Rule 1,
200 men do $1/4$ work in 50 days.
${M_1D_1}/W_1 = {M_2D_2}/W_2$
${200 × 50}/{1/4} = {M_2 × 100}/{3/4}$
$M_2 × 100 = 200 × 50 × 3$
$M_2$ = 300
Additional men = 100
Question : 2
A contractor undertook to finish a work in 92 days and employed 110 men. After 48 days, he found that he had already done $3/5$ part of the work, the number of men he can withdraw so that the work may still be finished in time is :
a) 30
b) 35
c) 45
d) 40
Answer »Answer: (a)
Using Rule 1,
${M_1D_1}/W_1 = {M_2D_2}/W_2$
${110 × 48}/{3/5} = {M_2 × 44}/{2/5}$
$M_2$ × 44 × 3 = 110 × 48 × 2
$M_2 = {110 × 48 × 2}/{44 × 3}$ = 80
Number of men can be withdrawn
= 110 - 80 = 30
Question : 3
One man, 3 women and 4 boys can do a piece of work in 96 hours, 2 men and 8 boys can do it in 80 hours, 2 men and 3 women can do it in 120 hours. 5 men and 12 boys can do it in
a) 44 hours
b) 43$7/11$ hours
c) 39$1/11$ hours
d) 42$7/11$ hours
Answer »Answer: (b)
Using Rule 1,
1 hour’s work of 1 man and 4 boys = $1/160$
[Since,2 men and 8 boys can do the work in 80 hrs.]
1 hour’s work of 1 man 3 women and 4 boys = $1/96$
1 hour’s work of 3 women
= $1/96 - 1/160 = {10 - 6}/960 = 1/240$
1 hour’s work of 2 men
= $1/120 - 1/240 = 1/240$
1 hour’s work of 4 boys
= $1/160 - 1/480$
= ${3 - 1}/480 = 1/240$
2 men = 3 women = 4 boys
2 men + 8 boys = 12 boys
5 men + 12 boys = 22 boys
By $M_1D_1 = M_2D_2$
12 × 80 = 22 × $D_2$
$D_2 = {12 × 80}/22 = 480/11 = 43{7}/11$ hours
Question : 4
4 mat-weavers can weave 4 mats in 4 days. At the same rate how many mats would be woven by 8 mat-weavers in 8 days ?
a) 16
b) 12
c) 4
d) 8
Answer »Answer: (a)
Using Rule 1,
Weaver | Days | Mats |
4 | 4 | 4 |
↓ | ↓ | ↓ |
8 | 8 | x |
∴ ${4 : 8}/{4 : 8}]$ : : 4 : x
where, x is no. of mats
4 × 4 × x = 8 × 8 × 4
$x = {8 × 8 × 4}/{4 × 4}$ = 16
Question : 5
Some persons can do a piece of work in 12 days. Two times the number of such persons will do half of the work in
a) 3 days
b) 5 days
c) 9 days
d) 6 days
Answer »Answer: (a)
Using Rule 1,
${M_1D_1}/W_1 = {M_2D_2}/W_2$
${M × 12}/W = {2M × D_2}/{W/2}$
${M × 12}/W = {4MD_2}/W$
$D_2$ = 3 days
Question : 6
39 persons can repair a road in 12 days working 5 hours a day. In how many days will 30 persons working 6 hours a day complete the work ?
a) 15 days
b) 14 days
c) 10 days
d) 13 days
Answer »Answer: (d)
Less persons, more days (Indirect)
More working hours/day, less days (Indirect)
Let required no. of days be x.
Persons | Working hours /day | Days |
39 | 5 | 12 |
↑ | ↑ | ↓ |
30 | 6 | x |
∴ ${30 : 39}/{6 : 5}]$ : : 12 : x
30 × 6 × x = 39 × 5 × 12
$x = {39 × 12 × 5}/{30 × 6}$ = 13 days
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, $M_1 = 39, D_1 = 12, T_1$ = 5
$M_2 = 30, D_2 = ?, T_2$ = 6
$M_1D_1T_1 = M_2D_2T_2$
39 × 12 × 5 = 30 × $D_2$ × 6
$D_2 = {39 × 12 × 5}/{30 × 6}$ = 13 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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