A trader with a basket of eggs finds that if he sells 3 eggs at a time there is only 1 egg left.If he sells 4 eggs at a time there is again 1 egg left.However if the trader sells 7 eggs at a time,there are no egg left.If the capacity of the basket is 100 eggs, find how many eggs are in the basket? Explain with reasoning
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Answered by
261
We know that the LCM of 3 and 4 is 12. We have also been given that the maximum capacity of the egg basket is 100.
Lets list down the multiples of 12 till the number reaches 100.
12, 24, 36, 48, 60, 72, 84, 96
To leave a remained with 3 as well as 4, these numbers list above need to be one more; so we get the new numbers as follows:
13, 25, 37, 49, 61, 73, 85, 97.
The given statement also states that when 7 eggs are selected, no eggs remain. That mean we are looking for a number that is divisible by 7.
From 13, 25, 37, 49, 61, 73, 85, 97, we see that only 49 matches all the three criteria.
Hence the total number of eggs in the basket is 49
Lets list down the multiples of 12 till the number reaches 100.
12, 24, 36, 48, 60, 72, 84, 96
To leave a remained with 3 as well as 4, these numbers list above need to be one more; so we get the new numbers as follows:
13, 25, 37, 49, 61, 73, 85, 97.
The given statement also states that when 7 eggs are selected, no eggs remain. That mean we are looking for a number that is divisible by 7.
From 13, 25, 37, 49, 61, 73, 85, 97, we see that only 49 matches all the three criteria.
Hence the total number of eggs in the basket is 49
Answered by
60
Answer:49
Step-by-step explanation:
logically the answer must be a multiple of 7
so the multiples of 7 from 100 decreasingly 98,91,84,77,70,63,56,49,42,......
the number which leaves remainder 1 when divided by both 3 and 4 is 49....so basket contains 49 eggs
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