Question

Mr. Shyam wants to display his oranges neatly for sale. Doing this he discovers that one orange is left over when he places them in groups of three. The same happens if he tries to place them in groups of 5, 7, or 9 oranges. Only when he makes groups of 11 oranges, it fits exactly.

How many oranges does the Shyam have at least?

Answer 1

Answer :
As mention that if Mr. Shyam arrange in group of 3 , 5 , 7 , 9 then one orange is left .
And
When arrange in group of 11 than they fits exactly.
So,
Here we know that total number of Oranges is divisible by 11 , And also divisible by 3 , 5 , 7 , 9 when we take one seprate .
SO,
Total number of Oranges = 3 $\times$ 5 $\times$ 7 $\times$ 9 + 1
= 946
Now we check that number is divisible by 11 or not . So,
$\frac{946}{11}$ = 86

Hence we can say that Mr. Shyam have 946 oranges ( Ans )