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

Answer: (b)

8 men ≡ 17 women

12 men ≡ $17/8 × 12 = 51/2$ women

12 men + 24 women

= $51/2 + 24 = 99/2$ women

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

${17 × 33}/1 = {99 × D_2}/{2 × 3}$

$D_2 = {17 × 33 × 6}/99$ = 34 days

Using Rule 12,

Here, A = 8, B = 17, a = 33

$A_1 = 12, B_1$ = 24

Number of days= ${a(A . B)}/{A_1B + B_1A}$

= ${33 × (8 × 17)}/{12 × 17 + 24 × 8}$

= $4488/{204 + 192} = 4488/396$

No. of days to paint 3 houses

= $4488/396 × 3$ = 34 days

Answer: (d)

Using Rule 1,

2 men + 3 women ≡ 4 men

2 men ≡ 3 women

3 men + 3 women ≡ 5 men

$M_1D_1 = M_2D_2$

4 × 20 = 5 × $D_2$

$D_2 = {4 × 20}/5$ =16 days

Answer: (d)

where, x is working hrs/days

Where = number of days

12 : 10 :: 12 : x

12 × x = 10 × 12

$x = {10 × 12}/12 = 10$ days

Using Rule 1,

Here,$M_1 = 10, D_1 = 12, M_2 = 12, D_2$ = ?

$M_1D_1 = M_2D_2$

10 × 12 = 12 × $D_2$

$D_2$ = 10 days

Answer: (c)

$12/18 = 8/x$

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

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: (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