Find the total length of the cloth Mr. X and Mr. Y had in the beginning

Question

Mr. X had 24 m more clothes than Mr. Y. 
Mr. X used 12.8 m of cloth whereas Mr. Y used 11.9 m of cloth everyday.
When Mr. X finished all the cloth he had, Mr. Y was still left with 6.60 m of cloth.

Find the total length of the cloth Mr. X and Mr. Y had in the beginning ?

My attempt

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Let Mr. Y had K meters of cloth in the beginning. Then Mr. X had (K+24) meters of cloth in the beginning.

Mr. Y use (K-11.9) m of cloth everyday. Mr. X use (K+24 -12.8) m of cloth everyday.

As per the question,

K-11.9 m = 6.60 m (since, Mr. Y was still left with 6.60 m of cloth)

or K = 18.50 meter

i.e. Mr.Y had 18.50 meter of cloth in the beginning.

So, Mr. X had K+24m -12.8 m = 18.5 m + 24m - 12.8m = 29.7 meter

Total length of the cloth Mr. X and Mr. Y had in the beginning = 29.7 meter + 18.50 meter = 48.2 meter

But the answer given is 846.4 meter.

Please help to understand what is wrong in my approach.

Answer 1

No, your approach is wrong. In the problem it has not been stated that both men finish their cloth by the end of the first day. That has to be calculated. Here's what you should do. Let Mr.Y have $x$ unit long cloth, then Mr.X has $x+24$ units. Now, let Mr.X finish his cloth on the $t^{th}$ day. Then, we have equations: $$x+24-12.8t=0$$ $$x-11.9t=6.6$$ Solve these two equations, you'll get your answer.