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.
Answers
Let the no of apples be x.
First customer: x/2+1/2
Remaining apples: x-(x/2+1/2)= x/2–1/2
Second customer: x/4–1/4+1/2= x/4+1/4
Remaining apples: (x/2–1/2)-(x/4+1/4)=x/4–3/4
Third customer: x/8–3/8+1/2= x/8+1/8
Remaining apples: (x/4–3/4)-(x/8+1/8)=x/8–7/8
Fourth customer: x/16–7/16+1/2=x/16+1/16
Remaining apples: (x/8–7/8)-(x/16+1/16)=x/16–15/16
Given remaining no of apples =15
=> x/16–15/16= 15
=> x-15 =15×16= 240
=> x=255
So the answer is option b(255).
Also u can verify.
For the first customer : 255/2+1/2= 128
Remaining : 255–128=127
Second customer: 127/2+1/2=64
Remaining: 127–64= 63
Third customer: 63/2+1/2=32
Remaining : 63–32=31
Fourth customer: 31/2+1/2= 16
Remaining apples: 31–16=15.
[Answer:- 49 apples.]
Solution:- 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
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.