Final answer:
The original number of mangoes in the pile was 18. We arrived at this number by working backward from the fact that the youngest child took the last 3 mangoes and retracing the shares taken by the other family members.
Step-by-step explanation:
To solve the problem of finding the number of mangoes in the pile, we can work backwards from the small clues we have. We know the youngest child took the three remaining mangoes, which is our starting point. Here's the step-by-step explanation:
- The youngest child takes the last 3 mangoes, which means this is the remaining amount after the three princes have taken their shares.
- The third prince takes one-half of the remaining mangoes before the youngest child. If the youngest child is left with 3, the third prince took 3 mangoes as well, making the total 6 mangoes before the third prince's turn.
- The second prince takes one-third of the remaining mangoes. To find the original amount before the second prince's share, we calculate 2/3 (as 1 - 1/3 = 2/3) of the total before the third prince, which is 9, because 6 is 2/3 of 9.
- The first prince takes one-fourth of the remaining mangoes before the second prince. So, we calculate 3/4 of what was before the second prince, which means the total was 12 before the first prince's turn, because 9 is 3/4 of 12.
- The queen took one-fifth of the remaining pile of mangoes. To find the amount before the queen's share, we calculate 4/5 of the pile before the princes, which gives us 15 (since 12 is 4/5 of 15).
- Finally, the king took one-sixth of the original pile. To find the initial number of mangoes, we look for a number that gives us 15 when we take 5/6 of it, which is 18 (since 15 is 5/6 of 18).
Therefore, the original number of mangoes in the pile was 18.