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To solve this problem, we can set up a system of equations based on the information provided.
Let:
– ( w ) = earnings of 1 woman per day
– ( g ) = earnings of 1 girl per day
From the first scenario:
5 women and 9 girls earn ₹18,720 in 9 days.
The equation can be set up as:
[
9(5w + 9g) = 18720
]
This simplifies to:
[
5w + 9g = frac{18720}{9} = 2080 quad text{(Equation 1)}
]
From the second scenario:
9 women and 16 girls earn ₹52,080 in 14 days.
Setting up the equation:
[
14(9w + 16g) = 52080
]
This simplifies to:
[
9w + 16g = frac{52080}{14} = 3720 quad text{(Equation 2)}
]
Now we have the system of equations:
1. ( 5w + 9g = 2080 )
2. ( 9w + 16g = 3720 )
We can solve these equations simultaneously.
From Equation 1, we can express ( g ) in terms of ( w ):
[
9g = 2080 – 5w
]
[
g =