Challenging

There is a big fruit tree in a garden. It bears fruits at a constant rate everyday. Paul will pick the fruits and sell. Animals will pluck and eat the fruits. 25 men can pick all the fruits in 15 days and 66 animals can eat all the fruits in 10 days. If 1 man can pick twice the number of fruits as 1 animal, find the number of days it take for 10 men to pick and 10 animals to eat all the fruits together.


25M (15 days) [ ][ ][ ] [][][][][][][][][][][][][][][]
50A (15 days)
66A (10 days)  [ ][ ][ ] [][][][][][][][][][]
                      Number of fruits at the beginning

50A (10 days) [ ][ ] [][][][][][][][][][]


16A (10 days) [ ]


32A (10 days) [ ][ ]


18A (10 days) [][][][][][][][][][] --> 10 u


16A (10 days) --> 16/18 x 10 u = 80/9 u


[ ][ ] --> 2 x 80/9 u = 160/9 u
                                   
[ ][ ][ ] --> 3 x 80/9 = 80/3 u



25M (10 days) --> 160/9 + 10 = 250/9 u
10M (10 day) --> 10/25 x 250/9 = 100/9 u


10A (10 days) --> 10/18 x 10 = 50/9 u    [which is half of 10M (10 days)]

10M + 10A (10 days) --> 100/9 + 50/9 = 50/3 u

10M + 10A (x days) --> x/10 x 50/3 = 5/3 x

5/3 x --> 80/3 + x    [ ][ ][ ][   x u    ]

2/3 x --> 80/3

x --> 3/2 x 80/3 = 40 days

It takes 40 days for 10 men to pick and 10 animals to eat all the fruits.