Since they all work for the same number of days, the ratio in which they share the money is equal to the ratio of their work done per day.
That is,\(\cfrac { 1 }{ 4 } :\cfrac { 1 }{ 6 } :\cfrac { 1 }{ 10 } =\cfrac { 15 }{ 60 } :\cfrac { 10 }{ 60 } :\cfrac { 6 }{ 60 } =15:10:6\) 
Here, the total parts = 15 + 10 + 6 = 31
Hence, A’ s share =\(\cfrac { 15 }{ 31 } \times 3100=Rs.1500\), B; share = \(\cfrac { 10 }{ 31 } \times 3100=Rs.1000\) and
C’ s share is Rs.3100 - (Rs.1500 + Rs.1000) = Rs.600

(A+ B) ’s 1 day’s work = \(\cfrac { 1 }{ 16 } \) 
A’s 1 day’s work = \(\cfrac { 1 }{ 48 } \) 
ஃ B’s 1 day’s work = \(\cfrac { 1 }{ 16 } -\cfrac { 1 }{ 48 } \) 
= \(\cfrac { 3-1 }{ 48 } =\cfrac { 2 }{ 48 } =\cfrac { 1 }{ 24 } \)
ஃB alone can complete the work in 24 days

If 15 men can complete the work in 40 days, then the work measured in terms of person days = 15 × 40 = 600. person days.
If the same work is to be done by 30 (15 + 15) men, then the number of days they will take is \(\cfrac { 600 }{ 30 } =20days\)

Multiplicative Factor Method:

Step 1:
Here, less men means more days. So, it is an inverse variation.
ஃ Th e multiplying factor is \(\cfrac { 48 }{ 28 } \) .
Step 2:
Also, more hours means less days. So, it is an inverse variation.
ஃ The multiplying factor is \(\cfrac { 7 }{ 8 } \) .
Step 3:
\(\therefore x=24\times \cfrac { 48 }{ 28 } \times \cfrac { 7 }{ 8 } =36days\) 
Formula Method:
Here, P₁= 48, D₁= 24, H₁ = 7 and W₁ = 1(why?)
P₂ = 28,D₂ = x,H₂ = 8 and W₂ = 1(why?)
Using the formula,\(\cfrac { { P }_{ 1 }\times { D }_{ 1 }\times { H }_{ 1 } }{ { W }_{ 1 } } =\cfrac { { P }_{ 2 }\times { D }_{ 2 }\times { H }_{ 2 } }{ { W }_{ 2 } } \) 
We have,\(\cfrac { 48\times 24\times 7 }{ 1 } =\cfrac { 28\times \times \times 8 }{ 1 } \) 
\(\Rightarrow x=\cfrac { 48\times 24\times 7 }{ 28\times 8 } =36days\)

Proportion Method:

Here, the unknown is the days (x). It is to be compared with the length and the women.
Step 1:
Here, more length means more days. So, it is a direct proportion.
∴ The proportion is 180 : 512 :: 12 : x  ➝1
Step 2:
Also, more women means less days. So, it is an inverse proportion
∴The proportion is 32 : 15 :: 12 : x➝2
Step 3:
Combining 1 and 2
\(\begin{matrix} 180:512 \\ 32:15 \end{matrix}\} ::12:x\) 
We know that the product of the extremes = the product of the means

So,\(180\times 32\times x=512\times 12\times 15\Rightarrow x\cfrac { 512\times 12\times 15 }{ 180\times 32 } =16days\) 
Here, the unknown is the days (x). It is to be compared with the length and the women
Step 1:
Here, more length means more days. So, it is a direct proportion.
ஃ The multiplying factor is \(\cfrac { 512 }{ 180 } \) (take the reciprocal).
Step 2:
Also, more women means less days. So, it is an inverse proportion.
ஃ The multiplying factor is \(\cfrac { 15 }{ 32 } \) (no change)
Step 3:
\(\therefore x=12\times \cfrac { 512 }{ 180 } \times \cfrac { 15 }{ 32 } =16\ days\) 
Formula Method:
Here, P₁ = 15,D₁ = 12 and W₁ = 180
P₂ = 32,D₂ = x and W₂ = 512
Using the formula,\(\cfrac { { P }_{ 1 }\times { D }_{ 1 } }{ { W }_{ 1 } } =\cfrac { { P }_{ 2 }\times { D }_{ 2 } }{ { W }_{ 2 } } \) 
We have,\(\cfrac { 15\times 12 }{ 180 } =\cfrac { 32\times x }{ 512 } \) 
\(\Rightarrow 1=\cfrac { 32\times x }{ 512 } \Rightarrow x=\cfrac { 512 }{ 32 } =16days\)
Remark: Students may answer in any of the three given methods dealt here.