Will EIGRP perform one to one load balancing across two paths with different end to end Bandwidths?

Without using the variance command and assuming switch A & B are purely layer two and do not participate in the EIGRP process.

 +-----------------------------------------------------------+ | EIGRP AS 10 | | | | +--------------+ 1Gbps | | | +------------------+ | | | Router_A | 10.2.2.1/30 | | | | | | | | | | | | | +--+-----------+ +------+-------+ | | | 10.1.1.1/30 | | | | | | Switch_A | | | | | | | | | | | | | | +---+----------+ | | | | | | | | | | Path A | 1Gbps Path B | 100Mbps | | | | | | | | | | | | | | | +---+----------+ | | | | | | | | | Switch_B | | | | | | | | | 10.1.1.2/30 | | | | +--+-----------+ +------+-------+ | | | | | | | | Router_B | | | | | | 10.2.2.2/30 | | | | +------------------+ | | +--------------+ 1Gbps | | | +-----------------------------------------------------------+