Two women together took 100 eggs to a market, one had more than the ot

1.	Two women together took 100 eggs to a market, one had more than the other. Both sold them for the same sum of money. The first then said to the second: “If I had your eggs, I would have earned Rs 15” , to which the second replied: “If I had your eggs, I would have earned Rs 6(2/3)”. How many eggs did each had in the beginning?
Answer» Number of eggs for the first women be ‘x’ Let the selling price of each women be ‘y’ Selling price of one egg for the first women = y/(100 - x) By the given condition (100 – x) (y/x) = 15 (for first women) y = 15/(100 - x) … (1) (x) x (y/(100 - x)) = 20/3 [For second women] y = 20(100 - x)/3x … (2) From (1) and (2) We get 15/(100 - x) = 20(100 - x)/3x 45x² = 20(100 – x)² (100 – x)² = 45x²/20 = (9/4)x² ∴ 100 – x = √(9/4)x² 100 – x = 3x/2 3x = 2(100 – x) 3x = 200 – 2x 3x + 2x = 200 ⇒ 5x = 200 x = 200/5 ⇒ x = 40 Number of eggs with the first women = 40 Number of eggs with the second women = (100 – 40) = 60

Two women together took 100 eggs to a market, one had more than the other. Both sold them for the same sum of money. The first then said to the second: “If I had your eggs, I would have earned Rs 15” , to which the second replied: “If I had your eggs, I would have earned Rs 6(2/3)”. How many eggs did each had in the beginning?

Answer»

Number of eggs for the first women be ‘x’

Let the selling price of each women be ‘y’

Selling price of one egg for the first women = y/(100 - x)

By the given condition

(100 – x) (y/x) = 15 (for first women)

y = 15/(100 - x) … (1)

(x) x (y/(100 - x)) = 20/3 [For second women]

y = 20(100 - x)/3x … (2)

From (1) and (2) We get

15/(100 - x) = 20(100 - x)/3x

45x² = 20(100 – x)²

(100 – x)² = 45x²/20 = (9/4)x²

∴ 100 – x = √(9/4)x²

100 – x = 3x/2

3x = 2(100 – x)

3x = 200 – 2x

3x + 2x = 200 ⇒ 5x = 200

x = 200/5 ⇒ x = 40

Number of eggs with the first women = 40

Number of eggs with the second women = (100 – 40) = 60