**Core Concept**
The question requires the understanding of lactose intolerance as a common cause of persistent diarrhea in infants and young children. Lactose intolerance is characterized by the inability to digest lactose, a disaccharide sugar found in milk, due to a deficiency of lactase enzyme in the small intestine.

**Why the Correct Answer is Right**
The presence of one percent of reducing substance in the fresh stools indicates the presence of lactose, a reducing sugar. Lactose intolerance is caused by the deficiency of lactase enzyme, which breaks down lactose into glucose and galactose. The acidic nature of the stools suggests the presence of unabsorbed lactose, which is fermented by colonic bacteria, producing short-chain fatty acids and causing acidosis. In lactose intolerance, the body is unable to absorb lactose, leading to its presence in the stool.

**Why Each Wrong Option is Incorrect**
**Option A:** Cystic fibrosis is a genetic disorder that affects the respiratory, digestive, and reproductive systems. While it can cause malabsorption and diarrhea, it is not directly associated with the presence of reducing substances in the stool.

**Option C:** Rotavirus-induced diarrhea is a common cause of diarrhea in infants and young children. However, it does not typically cause the presence of reducing substances in the stool.

**Option D:** Intestinal tuberculosis is a rare cause of diarrhea in children and is not directly associated with the presence of reducing substances in the stool.

**Clinical Pearl / High-Yield Fact**
Lactose intolerance is a common condition in infants and young children, especially those of Asian or African descent. It is essential to diagnose and manage lactose intolerance promptly to prevent malnutrition and other complications.

**✓ Correct Answer: B. Lactose intolerance**