What is the number of cans Soham had if it is known that the number of cans were more than 15 and no can was put........

Question

Soham works at a soft drink company and was arranging some particular number of cylindrical aluminium soft drink cans in a square box but the box became full and there were 8 cans remaining to be put in.
Then, he started arranging all cans in a rectangular box where he could arrange 6 cans more along the length than the breadth after putting all the cans in the rectangular box.
He found out that there was still space left for another 11 cans.
What is the number of cans Soham had if it is known that the number of cans were more than 15 and no can was put on top of another can?

Answer 1

44

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n- the number of cans, n>15
n=x^2+8, x- the size of square
n+11= y*(y+6), y- the width of the rectangle

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Let's try some numbers of x to find y
For x=3/4/5/6 we get n+11=28/35/44/55
By solving y^2+6y-(n+11)=0 for each value of n+11 above we only get one integer solution (for n+11=55 only), therefore the solution is n=44, where 44=6^2+8 and 44=5*11-11