Question

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

• A. 7 : 3
• B. 11 : 3
• C. 11 : 7
• D. 3 : 2

Answer 1

The Correct Option is B

Let’s assign variables to the daily earnings of Neeta, Geeta, and Sita: \( N \), \( G \), and \( S \) respectively.

Given:

1. \( N + G = 6S \)
2. \( S + N = 2G \)

Step 1: From the first equation

\[ N + G = 6S \quad \Rightarrow \quad N = 6S - G \quad \text{......(i)} \]

Step 2: Substitute into the second equation

Substituting the value of \( N \) from equation (i) into the second equation \( S + N = 2G \), we get: \[ S + 6S - G = 2G \] Combining like terms: \[ 7S = 3G \] \[ G = \frac{7}{3} S \quad \text{......(ii)} \]

Step 3: Substitute the value of \( G \) into equation (i)

Substituting \( G = \frac{7}{3} S \) from equation (ii) into equation (i): \[ N = 6S - \frac{7}{3} S = \frac{18}{3} S - \frac{7}{3} S = \frac{11}{3} S \quad \text{......(iii)} \]

Step 4: Earnings ratio

The earnings ratio is: \[ N : G : S = \frac{11}{3} S : \frac{7}{3} S : S \] This simplifies to: \[ N : G : S = 11S : 7S : 3S \]

Step 5: Conclusion

Clearly, Neeta earns the most and Sita earns the least. Therefore, the ratio of the daily earnings of the one who earns the most to the one who earns the least is: \[ 11S : 3S = 11 : 3 \]

Final Answer:

The correct option is \( \boxed{(B): 11 : 3} \).

Answer 2

Let the daily earnings be:

• Neeta: \( n \)
• Geeta: \( g \)
• Sita: \( s \)

Given equations:

\[ n + g = 6s \quad (i) \] \[ s + n = 2g \quad (ii) \]

Step 1: Subtract Equation (i) from (ii)

\[ (s + n) - (n + g) = 2g - 6s \implies s - g = 2g - 6s \]

Step 2: Simplify

\[ s - g = 2g - 6s \implies 7s = 3g \implies s = \frac{3}{7} g \]

Step 3: Express in terms of \(a\)

\[ g = 7a, \quad s = 3a \]

Step 4: Use Equation (i) to find \(n\)

\[ n + g = 6s \implies n + 7a = 18a \implies n = 11 a \]

Step 5: Ratio of earnings \(n : s\)

\[ n : s = 11a : 3a = \boxed{11 : 3} \]

Answer:

The ratio of earnings between Neeta and Sita is 11 : 3.