The amount neeta and geeta together earn in a day equals what sita alone earns in 6 days. the amount sita and neeta together earn in a day equals what geeta alone earns in 2 days

General
1

the amount neeta and geeta together earn in a day equals what sita alone earns in 6 days. the amount sita and neeta together earn in a day equals what geeta alone earns in 2 days. the ratio of the daily earnings of the one who earns the most to that of the one who earns the least is

2

The amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days. The amount Sita and Neeta together earn in a day equals what Geeta alone earns in 2 days. What is the ratio of the daily earnings of the one who earns the most to that of the one who earns the least?

Answer:
Let’s denote the daily earnings of Neeta, Sita, and Geeta as x, y, and z, respectively.

From the information given in the problem, we can set up the following equations:

  1. Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days:
    x + z = \frac{y}{6}

  2. Sita and Neeta together earn in a day equals what Geeta alone earns in 2 days:
    y + x = 2z

To find the ratio of the daily earnings of the one who earns the most to that of the one who earns the least, we need to determine the maximum and minimum values among x, y, and z.

Solving these two equations simultaneously:

From equation 1:
x = \frac{y}{6} - z

Substitute this into equation 2:
y + \frac{y}{6} - z = 2z
\frac{7y}{6} = 3z
y = \frac{18z}{7}

Therefore, Neeta earns x = \frac{\frac{18z}{7}}{6} - z = \frac{3z}{7} - z = \frac{-4z}{7}, Sita earns y = \frac{18z}{7}, and Geeta earns z = z.

The ratio of the daily earnings of the one who earns the most (Neeta) to that of the one who earns the least (Geeta) is:
\frac{-4z/7}{z} = \frac{-4}{7}

So, the ratio of the daily earnings of the one who earns the most to that of the one who earns the least is \frac{-4}{7}.