After 21 men and 21 women board, Men : Women = 3 : 2 and total adults = 60.

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• At the end: Men = \(\frac{3}{5}\) × 60 = 36, Women = \(\frac{2}{5}\) × 60 = 24
• At first: Men = 36 − 21 = 15, Women = 24 − 21 = 3
• Adults at first = 15 + 3 = 18
• Check: Men : Adults at first = 15 : 18 = 5 : 6

There were 60 adults on the bus in the end.
Check: 36 + 24 = 60. 36 : 24 = 3 : 2. ✓