Question
Download Solution PDFयदि \(\rm \frac{a+b}{b+c}=\frac{c+d}{d+a}\) जहाँ a ≠ c है, तो निम्नलिखित में से कौन-सा सत्य है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
\(\rm \frac{a+b}{b+c}=\frac{c+d}{d+a}\) a ≠ c
प्रयुक्त अवधारणा:
योगानुपात और अन्तरानुपात:
यदि a : b = c : d, तो
(a + b ) : (a – b) = (c + d) : (c – d)
गणना:
\(\rm \frac{a+b}{b+c}=\frac{c+d}{d+a}\)
उपरोक्त अवधारणा के अनुसार
⇒ \(\rm \frac{a+b + b + c}{a + b - b-c}=\frac{c+d+ d + a}{c +d-d-a}\)
⇒ \(\rm \frac{a+2b + c}{a -c}=\frac{c+2d + a}{c -a}\)
⇒ \(\rm \frac{a+2b + c}{a -c}=\frac{c+2d + a}{-{(a-c)}}\)
⇒ a + 2b + c = -c - 2d - a
⇒ 2a + 2b + 2c + 2d = 0
⇒ a + b + c + d = 0
∴ अभीष्ट मान a + b + c + d = 0 है
Last updated on May 29, 2025
-> The UPSC CDS 2 Notification has been released at upsconline.gov.in. for 453 vacancies.
-> Candidates can apply online from 28th May to 17th June 2025.
-> The CDS 2 Exam will be held on 14th September 2025.
-> Attempt UPSC CDS Free Mock Test to boost your score.
-> The selection process includes Written Examination, SSB Interview, Document Verification, and Medical Examination.
-> Refer to the CDS Previous Year Papers to enhance your preparation.