Shooting Two Hawks with One Arrow (一箭雙鵰)

Killing Two Birds with One Stone
Said of getting two separate results in one go.

During the Southern and Northern Dynasties(420-589A.D), there was a general in Northern Zhou(北周), named Zhangsun Sheng(長孫晟). He was an export in the art of war and was good at archery. One year, his sovereign King Xuanwang ordered him to escort a princess to the northwestern Turkish Kingdom where she was to marry its king Shetu. The Turkish ruler, who wished to see Zhangsun's skill, asked the Northern Zhou general to go hunting with him. Shetu saw two hawks contending for food in the sky. He gave Zhangsun two arrows, asking him to shoot down the birds with them. Zhangsun complied, but he killed the two hawks with only one arrow.

(the soures from the internet and the book "The Best Chinese Idioms")