That problem would never appear on the GMAT because it is ambiguous and it requires more math than the GMAT would ever require. It's not helpful to make up problems.

This sum is from one of the books for GMAT itself. Its the "Mathematics for MBA" wriiten by R. S. Aggrawal published by S. Chand Publications. So How can it be possible it could not be a GMAT Question ?? Please explain it by solving it.

You just verified that it's not a GMAT question. As I said, it never has and never will appear on the test. As I also said, the question contains an ambiguity which the GMAT never will. Many people would read that question to mean that the total time the rations will last has not changed since 1/5 of the people left. That's impossible unless the original ration was zero. Assuming you get past the ambiguity, n/x = (n-10)/(4x/5). Then n/5 = 10 and x = 50. But the fact that I can solve it doesn't imply it would be on the GMAT. It is ambiguous and confusing and the test only requires math at the 10th grade level in the US. I teach students to do quant without solving anything. GMAT questions are developed in such a way that you can do whatever trivial math you need in your head and the answer choices give you big clues, frequently clue enough that you need no work. It is a test of reading comprehension and simple logic ability. By posting what appear to be challenging problems you actually do people a disservice by leading them to believe that they need to learn to solve problems instead of learning to read and answer the questions as they appear on the test.