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) \(S + N = 2G\)

From the first equation: 

\(N = 6S - G\) .......(i) 

Substituting the value of \(N\) from (i) into the second equation: 

\(S + 6S - G = 2G\)

Combining like terms: 

\(7S = 3G\)

Or, \(G = \frac{7}{3} S\) .......(ii) 

Substituting the value of \(G\) from (ii) into (i): 

\(N = 6S - \frac{7}{3} S,\space   N = \frac{11}{3} S\) .......(iii) 

So, the earnings ratio is: 

\(N : G : S = \frac{11}{3} S : \frac{7}{3} S : S\)

This simplifies to: 

\(N : G : S = 11S : 7S : 3S\)

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 that of the one who earns the least is: 

\(11S : 3S = 11 : 3\)

So, the correct option is (B): 11 : 3.

Answer 2

Let the daily earnings of Neeta, Geeta, and Sita be \(n, g\) and \(s\) respectively.
Given that:
\(n+g=6s \)     \(………. (i)\)
\(s+n=2g \)      \(……….. (ii)\)
From eq \((ii)\) - eq \((i)\)
\(s-g = 2g-6s\)
\(7s = 3g\)
Let \(g\) be \(7a\), then \(s\) earns \(3a\).
Earning of \(n= 6s-g = 18a-7a = 11 a\)
Now, the ratio \(=11 a:3a = 11:3\)

So, the correct option is (B): \(11:3\)