Percentage – 02

Question: In measuring the sides of a rectangle, one side is taken 5% in excess and the other 4% in deficit. Find the error percent in area calculated from the measurement.  [एक आयत की भुजाओं को मापने के क्रम में, एक भुजा को 5% ज्यादा ले लिया जाता है; जबकि दूसरी भुजा की माप में 4% की कमी हो जाती है. बताइए कि आयत के क्षेत्रफल में कितने प्रतिशत की त्रुटि हुई?]

(a) 0.8% deficit (b)1.2% excess (c) 0.8% excess (d) 1.2% deficit (e) none of these 

Soln.

Detailed Explanation: First Method: Let the area of the rectangle be 100 units. It length is increased by 5%, then its area will also be increased by 5%, so it will be 100 + 5% of 100 = 100 + 5 = 105

It breadth is decreased by 4%, then the area will further be decreased by4%, so the resultant area will be 105 – 4% of 105 = 105 – 4.2 = 100.80  Therefore, the decrease = 100.8 -100 = 0.8   So,  error is 0.8% excess  Ans.

  

Second Method: When any quantity is changed by x% and y% successively, then the quantity is changed by