I am underweight girl..height is 5'4 and weight is just 43..please suggest me some good and quick way to gain weight and fat?

See Dr., then eat...: If one is truly underweight (based on height, family background, and body type), a dr. Can evaluate for a hormonal, digestive, or other disorder. If no medical cause is found, then one can add weight by eating more calories of nutritious foods, while also doing weight-training to increase muscle. Proteins: egg white, chicken breast, salmon, ... Better fats: olive oil, peanuts, almonds, tofu, ....

Emergency: If this is not a typo and you are at 43lbs, this is an emergency situation. Your body mass index is at 7.38 which is usually not life sustainable. You must go to the hospital immediately for medical stabilization and weight restoration. At your bmi you cannot gain weight fast as this will lead to a condition called refeeding syndrome which can also lead to sudden death.