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Continued Fraction Algebra

CMAT 2026 · Quantitative Techniques & Data Interpretation · Medium · Algebra

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If A+1B+1C−9=295A + \frac{1}{B + \frac{1}{C - 9}} = \frac{29}{5}, then the value of A+B+CA + B + C is

  1. A.

    17

  2. B.

    12

  3. C.

    19

  4. D.

    28

Answer

C

Explanation

295=5+45=5+15/4=5+11+1/4\frac{29}{5} = 5 + \frac{4}{5} = 5 + \frac{1}{5/4} = 5 + \frac{1}{1 + 1/4}. So A=5A = 5, B=1B = 1, and C−9=4  ⟹  C=13C - 9 = 4 \implies C = 13. Then A+B+C=5+1+13=19A + B + C = 5 + 1 + 13 = 19.

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