The total area of the smaller circle is what percent of the total area

Solution

Given:
• Two circles are there – smaller and larger

To find:
• The total area of the smaller circle is what percent of the total area of the larger circle

Approach and Working:
• If we assume the radius of the smaller circle as r and the radius of the larger circle as R, then

o Area of the smaller circle = πr2

o Area of the larger circle = πR2

• Therefore, area of the smaller circle as a percentage of the area of the larger circle = πr2/ πR2 = r2/R2 = (r/R)2
• Or, if we can find out the ratio of their radii, we can find out the answer

Analysing Statement 1
• As per the information given in Statement 1, R is 300% longer than r.

o Or, [(R – r)/ r] * 100 = 300

Solving, R = 4r

Or, r/R = ¼

• From this Statement we can find out the ratio of r and R

o Therefore, Statement 1 alone is sufficient to answer

Analysing Statement 2
• As per the information given in Statement 2, the ratio of R and r = 4:1

o Therefore, r/R = 1:4

• From this Statement also, we can find out the ratio of r and R

o Therefore, Statement 2 alone is sufficient to answer

Hence, the correct answer is Option D

Answer: D