Package update fails with Failed dependencies: libcrypto.so.10 on Red Hat Enterprise Linux 6

Issue

When attempting to update a package on Red Hat Enterprise Linux 6 the update fails with errors like

# rpm -ivh bind-libs-9.8.2-0.23.rc1.el6_5.1.x86_64.rpm
warning: bind-libs-9.8.2-0.23.rc1.el6_5.1.x86_64.rpm: Header V3 RSA/SHA256 Signature, key ID fd431d51: NOKEY
error: Failed dependencies:
        libcrypto.so.10(libcrypto.so.10)(64bit) is needed by bind-libs-32:9.8.2-0.23.rc1.el6_5.1.x86_64

or

--> Processing Dependency: libssl.so.10(libssl.so.10)(64bit) for package: ruby-libs-1.8.7.352-13.el6.x86_64
--> Finished Dependency Resolution
Error: Package: ruby-libs-1.8.7.352-13.el6.x86_64 (errata)
           Requires: libssl.so.10(libssl.so.10)(64bit)
Error: Package: ruby-libs-1.8.7.352-13.el6.x86_64 (errata)
           Requires: libcrypto.so.10(libcrypto.so.10)(64bit)