5 x 100 + 9 x 10 + 7 = 597
_______
23 | 13751
| 11500
_______
| 2251
| 2070
_______
| 181
| 161
_______
| 20

Count of mangoes to distribute = 13751
_______
First we give 5 x 100 mangoes to each of 23 boyes
So, we have taken 11500 manogoes out of all the mangoes = 13751 mangoes
_______
Count of mangoes remaining = 2251 mangoes
Then we give 9 x 10 mangoes to each of 23 boyes
So, we have taken 2070 manogoes out of remaining mangoes = 2251 mangoes
_______
Count of mangoes remaining = 181 mangoes
Then we give 7 mangoes to each of 23 boyes
So, we have taken 161 manogoes out of remaining mangoes = 181 mangoes
_______
Count of mangoes remaining = 20 mangoes