जर A : B = 7 : 8 आणि B : C = 7 : 9 असेल, तर A : B : C चे गुणोत्तर किती आहे?

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SSC GD Previous Paper 2 (Held On: 11 Feb 2019 Shift 2)
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  1. 56 : 49 : 72
  2. 49 : 56 : 72
  3. 56 : 72 : 49
  4. 72 : 56 : 49

Answer (Detailed Solution Below)

Option 2 : 49 : 56 : 72
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दिलेल्याप्रमाणे:

A : B = 7 : 8

B : C = 7 : 9

संकल्पना:
 
जर N ला a : b मध्ये विभागले असेल तर
 
पहिला भाग = N × a/(a + b)
 
दुसरा भाग = N × b/(a + b)
 
गणना:
 
A/B = 7/8 ----(i)
 
तसेच B/C = 7/9 ----(ii)
 
समीकरण (i) आणि (ii) गुणाकार करून आपल्याला मिळते,

⇒ (A/B) × (B/C) = (7/8) × (7/9)

⇒ A/C = 49/72

∵ A : B = 49 : 56

∴ A : B : C = 49 : 56 : 72

पर्यायी पद्धत:

A : B = 7 : 8 = 49 : 56

B : C = 7 : 9 = 56 : 72

⇒ A : B : C = 49 : 56 : 72

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