In which year there was maximum decrease in registration of patients in…

Concept: On a line graph the value for a year is read from a single plotted point, but a change is read from a pair of consecutive points — change in a year = (that year’s value) − (previous year’s value). A downward segment means a decrease, and the size of that decrease is the vertical drop between the two points. So "maximum decrease" asks for the largest downward step between two consecutive years; it is a property of a segment, not of how high any single point sits.

Application: read the hospital X line (filled circles) point by point and take successive differences.

The years that show a fall are 2003 (2,000), 2004 (4,000) and 2006 (10,000). The largest of these is a fall of 10,000, recorded in 2006, when the count drops from 12,000 to 2,000. So the maximum decrease in registration at hospital X occurs in 2006.

Cross-check:

• Relative fall: 2003 loses 2,000 out of 10,000 = 20%; 2004 loses 4,000 out of 8,000 = 50%; 2006 loses 10,000 out of 12,000 ≈ 83%. The ordering is the same, so the answer does not change whether the fall is read in absolute or in percentage terms.

• On the graph, the steepest downward segment of the hospital X line runs from the 2005 point down to the 2006 point, a drop of five grid intervals of 2,000 each.

• Common trap: 2005 carries the highest count (12,000) and sits at the top of that steep segment, but the fall is registered in 2006; during 2005 itself the count rose by 8,000.

Answer: 2006.