Model 7 Working with individual wages Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

Since, P men working P hours/ day for P days produce P units of work.

1 man working 1 hour/day for 1 day produce

$P/P^3 =1/P^2$ units of work

n men working n hours a day for n day’s produce $n^3/P^2$ units of work

Using Rule 1,

Here, $M_1 = p, D_1 = p, T_1 =p,W_1$ = p

$M_2 = n, D_2 = n, T_2 = n, W_2$ = ?

$M_1D_1T_1W_2 = M_2D_2T_2W_1$

p × p × p × $w_2$ = n × n × n × p

$w_2 = n^3/p^2$

Answer: (d)

Using Rule 1,

Remaining work = $1 - 2/3 = 1/3$ ;

Remaining days = 124–64= 60

${M_1D_1}/W_1 = {M_2D_2}/W_2$

${120 × 64}/{2/3} = {M_2 × 60}/{1/3}$

$M_2 = {120 × 64}/{2 × 60}$ = 64

No. of men can be discharged

= 120 - 64 = 56 men

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

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Number of men can be withdrawn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

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