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Question 22

If a, b, c, d are positive integers such that $$a+\cfrac{1}{b+\cfrac{1}{c+\cfrac{1}{d}}} = \frac{43}{30}$$, then d is


Correct Answer: 4

Solution

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Since $$\frac{43}{30}=1+\frac{13}{30}$$, we get $$a=1$$ and the remaining fraction $$\frac{30}{13}=2+\frac{4}{13}$$ gives $$b=2$$. Then $$\frac{13}{4}=3+\frac{1}{4}$$ gives $$c=3$$ and $$d=4$$.

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