SBI PO – 2015 - 02

Question: If radius of a sphere is increased by 20%, then by what percent the surface area of the sphere will be changed? [यदि किसी गोले की त्रिज्या 20% से बढ़ा दी जाये, तो गोले के पृष्ठीय क्षेत्रफल में कितने प्रतिशत का परिवर्तन आएगा?]

Solution:

Detailed Explanation: First Method: Let the initial area of the sphere is 100 square units. If radius of the sphere is increased by 20%, then there will be two successive changes of 20% each. After the first increase of 20% it will be 100 + 20% of 100 = 100 + 20 = 120. After the second change of 20%, the new area will be 120 + 20% of 120 = 120 + 24 = 144

Area of 100 square units becomes 144 square units. That is, the percentage change in area is (144 – 100)% = 44% Ans.

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