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

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

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

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

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

Answer: (b)

∴ ${1 : 2}/{8 : 12}]$ : : 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

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

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