In measuring the sides of a rectangular plot, one side is taken 5% in excess…

Concept

When two dimensions of a figure are each altered by a percentage, the percentage change in their product (the area) is not the plain sum of the two percentages. Because (1 + x/100)(1 + y/100) expands to 1 + x/100 + y/100 + xy/10000, an extra cross-term appears whenever both changes act together. So a percentage increase in one side combined with a percentage decrease in the other side must be found by multiplying the two adjusted factors together, not by simply adding or subtracting the two given percentages.

Applying it here

1. Let the original length be l and the original breadth be b, so the original area is l × b.

2. The length is measured 5% in excess, so the new length is 1.05l.

3. The breadth is measured 6% in deficit, so the new breadth is 0.94b.

4. The new area is 1.05l × 0.94b = 0.987lb.

5. Percentage change in area = [(new area − original area) ÷ original area] × 100 = (0.987lb − lb) ÷ lb × 100 = −1.3%.

Cross-check

Multiplying the two adjustment factors directly, 1.05 × 0.94 = 0.987, confirms the new area is 98.7% of the original area — an independent check on the same figure obtained above.

Result

So the calculated area differs from the true area by 1.3%, matching the option that states a 1.3% error.