Question

One night the king couldn't sleep, so he went down into the royal kitchen, where he found a bowl full of mangoes. being hungry, he took 1/6 of the mangoes. later that same night, the queen was hungry and couldn't sleep. she, too, found the mangoes and took 1/5 of what the king had left. still later, the first prince awoke, went to the kitchen, and ate 1/4 of the remaining mangoes. even later, his brother, the second prince, ate 1/3 of what was then left. finally, the third prince ate 1/2 of what was left, leaving only three mangoes for the servants. how many mangoes were originally in the bowl? is there more than one solution?

Answer 1

If you think in picture, it will be easier
1. king --1/6 of all
2. queen -- 1/5 of what king had left (remaining)
3. 1st prince -- 1/4 of remaining
4. 2nd prince -- 1/3 of remaining
5. 3 rd prince -- 1/2 of remaining
6. there are 3 mangoes left

so if we think that there are 6 parts of all
1. king took 1st part (5 parts left)
2. queen took 1 of what king had left which he left 5 parts (4 parts left)
3. 1st prince took 1 of 4 (3 parts left)
4. 2nd prince took 1 of 3 (2 parts left)
5. 3rd prince took 1 of 2 (1 part left)
that means 1 part equals 3 mangoes
so we have 6 parts at first then there were 18 mangoes originally in the bowl.

i think there is only 1 answer.