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.
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If our number of apple is divisible by 3 and 4 , than that number we can get by LCM of these numbers , So
So LCM ( 3 and 4 ) = 2 × 2 × 3 = 12
And here when we divide that number of apple by 3 and 4 we get 1 as remainder so our number of eggs could be 12 + 1 = 13
Or Just the multiple of 12 + 1
So
That number could be
12 × 1 + 1 = 13
12 × 2 + 1 = 25
12 × 3 + 1 = 37
12 × 4 + 1 = 49
12 × 5 + 1 = 61
12 × 6 + 1 = 73
12 × 7 + 1 = 85
12 × 8 + 1 = 97
And as the capacity of the basket is 108 apple , SO our number of apple could be one of those number written above
And as our number of apple is divisible by 7 , so that number is also a multiply of 7 ,
So that number could be
7 × 2 = 14
7 × 3 = 21
7 × 4 = 28
7 × 5 = 35
7 × 6 = 42
7 × 7 = 49
7 × 8 = 56
7 × 9 = 63
7 × 10 = 70
7 × 11 = 77
7 × 12 = 84
7 × 13 = 91
7 × 14 =98
7 × 15 = 105
.....
Here we can see that 49 number is common in both the arrangement .
So our number of apple is 49 , that gives 1 as remainder after division by 3 and 4 and there will be no remainder if 49 divide by 7 .
If our number of apple is divisible by 3 and 4 , than that number we can get by LCM of these numbers , So
So LCM ( 3 and 4 ) = 2 × 2 × 3 = 12
And here when we divide that number of apple by 3 and 4 we get 1 as remainder so our number of eggs could be 12 + 1 = 13
Or Just the multiple of 12 + 1
So
That number could be
12 × 1 + 1 = 13
12 × 2 + 1 = 25
12 × 3 + 1 = 37
12 × 4 + 1 = 49
12 × 5 + 1 = 61
12 × 6 + 1 = 73
12 × 7 + 1 = 85
12 × 8 + 1 = 97
And as the capacity of the basket is 108 apple , SO our number of apple could be one of those number written above
And as our number of apple is divisible by 7 , so that number is also a multiply of 7 ,
So that number could be
7 × 2 = 14
7 × 3 = 21
7 × 4 = 28
7 × 5 = 35
7 × 6 = 42
7 × 7 = 49
7 × 8 = 56
7 × 9 = 63
7 × 10 = 70
7 × 11 = 77
7 × 12 = 84
7 × 13 = 91
7 × 14 =98
7 × 15 = 105
.....
Here we can see that 49 number is common in both the arrangement .
So our number of apple is 49 , that gives 1 as remainder after division by 3 and 4 and there will be no remainder if 49 divide by 7 .
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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.
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