7 x 100 + 1 x 10 + 4 = 714
_______
24 | 17143
| 16800
_______
| 343
| 240
_______
| 103
| 96
_______
| 7

Count of mangoes to distribute = 17143
_______
First we give 7 x 100 mangoes to each of 24 boyes
So, we have taken 16800 manogoes out of all the mangoes = 17143 mangoes
_______
Count of mangoes remaining = 343 mangoes
Then we give 1 x 10 mangoes to each of 24 boyes
So, we have taken 240 manogoes out of remaining mangoes = 343 mangoes
_______
Count of mangoes remaining = 103 mangoes
Then we give 4 mangoes to each of 24 boyes
So, we have taken 96 manogoes out of remaining mangoes = 103 mangoes
_______
Count of mangoes remaining = 7 mangoes