SSC CGL Tier II 12 Jan 2017 Paper 1

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Question : 73 of 100

Marks: +1, -0

If

a + { 1 } /{ b } = b + { 1 }/ { c } = c + { 1 }/ { a }

(where a ≠ b ≠ c), then abc is equal to

+1
–1
+1 and –1
None of the options

Solution:

(3)

a + { 1 }/ { b } = b + { 1 } /{ c } = c + { 1 }/{ a }

= \± 1 (

let

)

⇒ a + { 1 }/ { b } = 1

⇒ a b + 1 = b⇒ a b = b - 1

b + { 1 }/ { c } = 1 \⇒ { 1 } /{ c } = 1 - b

c = { 1 }/ { 1 - b }

∴a b c = { b - 1 }/ { 1 - b } = - 1

Again,

a + { 1 } /{ b } = - 1

⇒ a b + 1 = - b⇒ a b = - b - 1

b + { 1 }/ { c } = - 1 ⇒ { 1 } /{ c } = - 1 - b

c = { 1 }/ { - 1 - b }

∴ a b c = 1

∴a b c = \± 1

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