Two two-digit numbers are written one after the other to give a four digit number such that the larger two digit number is written first. If the difference of the four digit number and the sum of two two-digit numbers is 6237, then product of the digits of largest two digit number is?
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Answer:Let the 1st, 2nd, 3rd and 4th digits be a,b,c and d respectively.
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let 2 numbers are 'ab' and 'cd', such that ab>cd.
abcd-(ab-cd)=5481
100*ab+cd-ab+cd=5481
99*ab+2*cd=5481
99*ab and 5481 are multiples of 9, hence cd must be a multiple of 9.
At cd=18, we get ab=55
Sum of the two 2-digit numbers= 55+18=73
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