1. **Problem statement:** Find the number of people who like only one item (either Mobile or Computer) from the survey data. 2. **Given data:** - Total people surveyed, $n = 400$ - People who like Mobile, $n(M) = 180$ - People who like Computer, $n(C) = 150$ - One-fourth do not like either, so people who like neither = $\frac{1}{4} \times 400 = 100$ 3. **Find:** Number of people who like only one item, i.e., $n(\text{only } M) + n(\text{only } C)$. 4. **Step 1: Calculate $n(M \cup C)$** Since 100 people like neither, people who like at least one item: $$ n(M \cup C) = 400 - 100 = 300 $$ 5. **Step 2: Use the formula for union of two sets:** $$ n(M \cup C) = n(M) + n(C) - n(M \cap C) $$ Substitute known values: $$ 300 = 180 + 150 - n(M \cap C) $$ 6. **Step 3: Solve for $n(M \cap C)$:** $$ n(M \cap C) = 180 + 150 - 300 = 330 - 300 = 30 $$ 7. **Step 4: Calculate number of people who like only one item:** People who like only Mobile: $$ n(\text{only } M) = n(M) - n(M \cap C) = 180 - 30 = 150 $$ People who like only Computer: $$ n(\text{only } C) = n(C) - n(M \cap C) = 150 - 30 = 120 $$ 8. **Step 5: Total number who like only one item:** $$ 150 + 120 = 270 $$ **Final answer:** Number of people who like only one item is **270**.