LeenaSai wrote:
Is there any short cut for solving the three equations ?
I am ending up taking more than 2 mins to solve this question
There's a shortcut to solve this problem, which avoids equations altogether. We know from the last piece of information, if we subtract 2 from the 'Aged' bottle's age, we must get a multiple of 20, and therefore of 10. Notice that means if we add 8 to the 'Aged' bottle's age, we must also get a multiple of 10, since multiples of ten are ten apart (if a-2 is a multiple of 10, a+8 will always also be a multiple of 10). But from the first piece of information, we also know that if we add 8 to the 'Aged' bottle's age, we must get a multiple of 7. So when we add 8 to the 'Aged' bottle's age, we must get a multiple of both 7 and 10, and thus of 70, and unless, from the answer choices, we need to consider the possibility that this bottle is centuries old, we can conclude the bottle will be 70 years old in 8 years, and is 62 years old now. Then it's easy to work out (if we even need to -- again there should be answer choices) the other bottles' ages.
With answer choices you could also just use the fact that adding 8 to the 'Aged' age must produce a multiple of 7, subtracting 2 from the 'Aged' age must produce a multiple of 20, and subtracting 1 from the 'Vintage' age must produce a multiple of 4; those observations alone would almost always let you pick the right answer without doing algebra. That would work even if you couldn't find a relationship similar to the one I explain in the paragraph above (which relied on a detail specific to the numbers in the question).
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