AP Police Constable practice question
In trapezium ABCD, AB is parallel to CD, with AB = 12 cm and CD = 27 cm. A line PQ is drawn parallel to AB and CD, meeting leg AD at P and leg BC at Q, such that AP : PD = 2 : 3. Find the length of PQ.
From a AP Police Constable Quantitative Aptitude practice set · Quantitative Aptitude
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Correct answer: (B) 18 cm
When a line parallel to the two parallel sides of a trapezium divides a leg AD in the ratio AP:PD = 2:3 (measuring from the side AB), its length is the weighted average PQ = (PD-part × AB + AP-part × CD)/(AP+PD) = (3×AB + 2×CD)/(2+3). So PQ = (3×12 + 2×27)/(5) = (36 + 54)/5 = 90/5 = 18 cm.
हिंदी में प्रश्न
समलंब ABCD में, AB, CD के समांतर है, जहाँ AB = 12 सेमी और CD = 27 सेमी है। एक रेखा PQ, AB और CD के समांतर खींची जाती है, जो भुजा AD को P पर तथा भुजा BC को Q पर इस प्रकार काटती है कि AP : PD = 2 : 3 है। PQ की लंबाई ज्ञात कीजिए।
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सही उत्तर: (B) 18 cm
जब समलंब की दोनों समांतर भुजाओं के समांतर कोई रेखा भुजा AD को AP:PD = 2:3 (AB की ओर से मापने पर) के अनुपात में बाँटती है, तो उसकी लंबाई भारित औसत (weighted average) होती है: PQ = (3×AB + 2×CD)/(2+3)। अतः PQ = (3×12 + 2×27)/5 = 90/5 = 18 सेमी।
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