A shopkeeper with a basket of eggs finds that if he sells 3 eggs at a time there is only one egg left if he sells four eggs at a time there is again 1 egg left however if the trader sells 7 is at a time there is no egg left is the capacity of the basket is 108 then find how many days are there in the basket explain with reasoning.
Answers
Hey there!
The trader has one egg left in both cases let him sell 3 eggs or 4 eggs. Thus, we can say that the number of eggs is = [A multiple of (3 x 4)] + 1
= [A multiple of 12 ] + 1
= 13, 25, 37 ,49, etc.
According to second condition, the number of eggs is a multiple of 7!
The only number satisfying both conditions is 49.
Hence,the number of eggs is 49
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[Answer:- 49 eggs.]
Solution:- A shopkeeper with a basket of eggs finds that if he sells 3 eggs at a time there is only one egg left if he sells four eggs at a time there is again 1 egg left however if the trader sells 7 is at a time there is no egg left is the capacity of the basket is 108
LCM of 3 and 4 = 3×4 = 12
The capacity of the basket is 100.
So, there may be:-
= 12 × 8 +1
= 96 + 1
= 97 eggs.
But, 97 is not divisible by 7.
Again, there may be:
12 × 7 +1 = 85 eggs.
12 × 6 +1 = 73 eggs.
12 × 5 +1 = 61 eggs.
12 × 4 +1 = 49 eggs.
Among these numbers 85 , 73 and 61 are not divisible by 7. But 49 is divisible by 7.
So, the number of eggs in the basket is 49.