If 1/ {a+ {1}/{b+ {1}/{c+ \frac{1}{2}}}}= \frac{16}{23} then the value of a + b + c is

SSC CPO SI and ASI 2016 Paper

Question : 148 of 200

Marks: +1, -0

1/ {a+ {1}/{b+ {1}/{c+ {1}/{2}}}}= {16}/{23}

then the value of a + b + c is

Solution:

(1)

{1}/{a+ {1}/{b+ {1}/{c+ {1}/{2}}}}= 1/{{23} /{16}}

={1}/{1+\ {7}/{16}}

This gives, a = 1 and

{1}/{b+ {1}/{c+ {1}/{2}}}= {7}/{16}

Now,

b+ {1}/{c+ {1}/{2}}= {16}/{7}=2+ {2}/{7}

=2+ {1}/{ {7}/{2}}

This gives, b = 2 and

c+ {1}/{2}= {7}/{2}=3+ {1}/{2}⇒ c=3

Therefore,

a + b + c = 1 + 2 + 3 = 6

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