self Maths Puzzle Numerical Ability Alligation or Mixture

A circle is drawn on a plane with center as P and diameter AB. Another is drawn inside this circle by taking AP as the diameter and Q as the center. Another circles is drawn inside the second circle by taking AQ as diameter and R as the center. This process is repeated infinitely. The ratio of the sum of the areas of all the circles to the area of the biggest circle is

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self Other Question

If the third, first and second term of an arithmetic progression forms a geometric progression in the given order, then what can be the common ratio of the geometric progression? A certain gentleman has plenty of time at his disposal. He puts his pencil to paper one day and draws a square. He then decides to create a design, so he draws another square inside the earlier one by joining its mid points. He then draws a third square inside the second in a similar fashion. He likes the design and hence goes on making squares inside squares in this manner. The side of the first square drawn is 8 cm. What is the ratio of the sum of area to the sum of perimeter of all the squares?