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SSC Selection Post 2022 PYQ — Question 62

SSC Selection Post - Higher Secondary Level - 14 March 2022 - Shift 2 • Quantitative Aptitude • Q62

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In △ABC, D and E are the points on sides AB and BC, respectively, such that DE || AC. If BD = 3 cm and AD = 4 cm, then AreaofΔBDEAreaofquadrilateralADEC=pq{Area of \Delta BDE \over Area of quadrilateral ADEC} = {p \over q} , where p, q are coprime. What is the value of |p - q|? 

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 31.

△BDE ~ △ABC

⇒ BD2AB2=ar△BDEar△ABC{BD^2\over AB^2}={ar△BDE\over ar△ABC}

⇒ 32(3+4)2=ar△BDEar△ABC{3^2\over(3+4)^2}={ar△BDE\over ar△ABC}

⇒ 949=ar△BDEar△ABC{9\over49}={ar△BDE\over ar△ABC}

Area of quadrilateral ADEC = area of △ABC - area of △BDE

Area of quadrilateral ADEC = 49 - 9 = 40

According to the question,

⇒ AreaofΔBDEAreaofquadrilateralADEC=pq=940{Area of \Delta BDE \over Area of quadrilateral ADEC} = {p \over q} = {9\over40} 

Value of |p - q| = |9 - 40| = 31