Area Ratio
Area Ratio is a Aptitude concept from the MPSC syllabus, tested in 3 past MPSC questions (2016, 2020). Below are those real questions with their correct answers and explanations, plus the concepts worth being comfortable with first.
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एका वर्तुळात समभुज त्रिकोण अंतर्लिखित केला आहे. वर्तुळाचे क्षेत्रफळ त्रिकोणाच्या क्षेत्रफळाच्या तुलनेत किती पट आहे हे निर्देशित करणारा पर्याय निवडा.
Let side of equilateral triangle be s. Radius of circumscribed circle R = s/√3. Area of circle = πR² = πs²/3. Area of equilateral triangle = (√3/4)s². Ratio of circle area to triangle area simplifies to 4π / (3√3).
सोबतच्या आकृतीत फरशांनी आच्छाडलेला भाग दाखवला आहे. प्रत्येक पाढऱ्या फरशीचे क्षेत्र प्रत्येक काळ्या फरशीच्या दुप्पट आहे. तर आकृतीतील एकूण काळ्या क्षेत्राचे सगळ्या पांढऱ्या फरशांनी आच्छाडलेल्या क्षेत्राशी असलेले गुणोत्तर दाखवणारा पर्याय निवडा. Accompanying figure shows area covered by tiles. Area of each white tile is twice the area of a black tile. Then select the option that indicates the ratio of total black area to the area covered by all the white tiles.
Calculate the total area by assigning relative weights to black and white tiles based on the given area condition and find their ratio.