How is zakat calculated after a partner joins a business, knowing that zakat was previously paid four months before he joined?

If the partnership is on a 50/50 basis, you own half of the trade goods and he owns the other half. You pay zakat on half the value of the goods when your year ends in Jumada (one-quarter of a tenth), and he pays zakat on his half when the year ends on his wealth. Mixing does not affect trade goods, and each partner pays zakat on his share individually, according to the majority of scholars.