Let the number of machines required to produce articles in 54 days be x. The following table is obtained.

Number of machines | 42 | x |

Number of days | 62 | 54 |

More the number of machines, lesser will be the number of days that it will take to produce the given number of articles. Thus, this is a case of inverse proportion. Therefore,

42 × 63 = 54× x

x = (42 x 63)/24 = 49

Hence, the required number of machines to produce the given number of articles in 54 days is 49.