Question

The number of marbles with rahul , can be expressed as fourth power .if the power and base of this number are interchanged .then it will be equal to the no of marbles with kamal.they have a total no of marbles not exceeding 2000

Answer 1

Acc to the question,

No of marbles with Rahul = $x^{4}$

No of marbles with Kamal = $4^{x}$

Also, ($x^{4}$) + ($4^{x}$) $\leq$ 2000.

So, by brute force method, the maximum possible marbles with both of them can be 1649.

Logic: ($5^{4}$) + ($4^{5}$) < 2000

or, (625 +1024) < 2000

i.e. it holds true for x = 5.

let us take x = 6.

or, ($6^{4}$) + ($4^{6}$) > 2000

or, (1296 + 4096) > 2000

or, 5392 > 2000.

Therefore, it doesn't hold true for x = 6.

Therefore, Rahul had 625 marbles and Kamal had 1024 marbles.