Question

Two women together took 100 eggs to a market, one had more
Both sold them for the same sum of money. The first then said to the second: "Itxa
I had your eggs, I would have earned 15”, to which the second replied: "If I had
your eggs, I would have earned "20/3. How many eggs did each had in the
beginning?
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Answer 1

Answer:

Let say One had = E eggs

Then other had = 100 - E eggs

Let Say Both sold the eggs for = S Rs

Selling Price with E eggs = S/E

She would have got rs 15 by selling other's egg

=> (S/E)(100 - E) = 15 - Eq 1

Selling Price with 100-E eggs = S/(100-E)

She would have got rs 20/3 by selling other's egg

=> (S/(100-E))E = 20/3 Eq 2

Eq1/E2

=> (100-E / E)² = 15/(20/3)

=> (100-E / E)² = 9/4

=> 100- E / E = 3/2

=> 200 - 2E = 3E

=> 5E = 200

=> E = 40

One had 40 Eggs

Other Had = 60 eggs