Question

A shopkeeper with a basket of apple finds that if he sells 3 apples at a time there is only one apple left if he sells four apple at a time there is again 1 apple left however if the trader sells 7 apple is at a time there is no apple left is the capacity of the basket is 108 apples then find how many days are there in the basket explain with reasoning. ​

Answer 1

Solution:-

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 apples.

But, 97 is not divisible by 7.

Again, there may be:

12 × 7 +1 = 85 apples.

12 × 6 +1 = 73 apples.

12 × 5 +1 = 61 apples.

12 × 4 +1 = 49 apples.

Among these numbers 85 , 73 and 61 are not divisible by 7. But 49 is divisible by 7.

So, the number of apples in the basket is 49.

[Answer:- 49 apples.]

Answer 2

Hello!!

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The trader has one apple left in both cases let him sell 3 apples or 4 apples. Thus, we can say that the number of apples 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 apple is a multiple of 7!

The only number satisfying both conditions is 49.

Hence,the number of apples is 49.

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Thanks!!!