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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

Solution

✅ Correct Option: 3

N=N = Neeta's daily earnings

G=G = Geeta's daily earnings

S=S = Sita's daily earnings


From the question:

  1. (Neeta + Geeta) in 1 day = Sita in 6 days

⇒N+G=6S\Rightarrow N + G = 6S

⇒N+GS=61\Rightarrow \dfrac{N + G}{S} = \dfrac{6}{1}

Hence, we can say that Sita earns 17\frac17th of the total earnings.


  1. (Sita + Neeta) in 1 day = Geeta in 2 days

⇒S+N=2G\Rightarrow S + N = 2G

⇒S+NG=21\Rightarrow \dfrac{S + N}{G} = \dfrac{2}{1}

Hence, we can say that Sita earns 13\frac13rd of the total earnings.


We can find Neeta's share:

Neeta == Total −- Sita −- Geeta

Neeta =1−17−13= 1 - \tfrac{1}{7} - \tfrac{1}{3}

Neeta =2121−321−721=1121= \tfrac{21}{21} - \tfrac{3}{21} - \tfrac{7}{21}= \tfrac{11}{21}


Now we can compare their earnings:

Neeta: 1121\tfrac{11}{21} of total

Geeta: 13=721\tfrac{1}{3} = \tfrac{7}{21} of total

Sita: 17=321\tfrac{1}{7} = \tfrac{3}{21} of total

Converting to same denominator: 1121:721:321=11:7:3\tfrac{11}{21} : \tfrac{7}{21} : \tfrac{3}{21} = 11 : 7 : 3


The highest earner is Neeta (11 units)

The lowest earner is Sita (3 units)

Therefore, the ratio of highest to lowest earnings =11:3= 11 : 3

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