The product of the ages of the three members is 2450 = 2*5*5*7*7. The table below lists the
possible ages of the members (columns 1-3) and the age of the bell ringer (column 4).

1 | 25 | 98 | 62 |

5 | 5 | 98 | 54 |

1 | 35 | 70 | 53 |

1 | 49 | 50 | 50 |

5 | 7 | 70 | 41 |

2 | 25 | 49 | 38 |

2 | 35 | 35 | 36 |

7 | 7 | 50 | 32 |

5 | 10 | 49 | 32 |

5 | 14 | 35 | 27 |

7 | 10 | 35 | 26 |

7 | 14 | 25 | 23 |

If the bell ringer’s age appeared only once in the table then he could immediately deduce
the ages of the three members. However he cannot. Therefore we know that his age appears
more than once in the table. The only bell ringer age that appears more than once is 32,
i.e., the bell ringer’s age is 32 and the ages of three members either are (7, 7, 50) or
(5, 10, 49). The vicar is older than any of them. If he were 51 or older the bell ringer
still would not be able to deduce the ages. However he can so the vicar’s age must be 50.