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Question 23

A poet met a tortoise sitting under a tree. When the tortoise was the poet's age, the poet was only a quarter of his current age. When the tree was the tortoise's age, the tortoise was only a seventh of its current age. If all the ages are in whole number of years, and the sum of their ages is now 264, the age of the tree in years is


Correct Answer: 143

Let the current ages of the poet, tortoise and tree be $$p,t,T$$. The first condition gives $$p=\frac{4t}{3}$$, and the second gives $$t=\frac{7T}{13}$$. Using $$p+t+T=264$$ gives $$\frac{4T}{7}+\frac{7T}{13}+T=264$$, so $$T=143$$.

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