Question

2/7 of the eggs at a store were quail eggs. 2/3 of the remaining eggs
were chicken eggs and the rest were duck eggs. The shopkeeper sold 3/5
of the chicken eggs, 1/2 of the quail eggs and 1/2 of the duck eggs. He
then had 104 chicken eggs left. How many eggs did he have left?

Answer 1

quail: 2/7 x
chicken: 2/3 * 5/7 = 10/21 x
duck: 5/21 x
2/5 * 2/7 x = 104
x = 910 at the start
Now you can finish it off

Answer 2

Let the total No. of eggs = x
∴ A/q
No. of quail eggs = 2x/7
Remaining eggs = x - 2x/7
∴ No. of chicken eggs = 2/3 (x - 2x/7)

And No. of duck eggs = (x - 2x/7) - 2/3 (x - 2x/7)

= 1/3 (x - 2x/7)
shopkeeper sold 3/5 of the chicken eggs.
∴ remaining chicken eggs = 2/3 (x - 2x/7)
- 2/3 * 3/5 (x - 2x/7)
=> 2x/3 - 4x/21 - 2x/5 + 4x/35 = 104 (A/q)
=> 70x - 20x - 42x + 12x/105 = 104
=> 20x = 10,920
=> x = 546 eggs. (Total eggs)
No. of quail egg = 2 * 546/7 = 156 egg
No. of duck egg = 1/3 (546 - 2 * 546/7)
= 130
shopkeeper sold 1/2 of the quail and 1/2
of the duck.
∴ Remaining eggs = 104 + 78 + 65
= 247 eggs.
He have left 247 eggs.