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Question

In a multiplication sum the multiplicand is 999 and the last three digits of the product are 193 . Other figures are missing . Complete the multiplication by supplying the missing figures .

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Solution

Dear student,

Let the multiplier be the 3-digit number XYZ.

We know 999 times XYZ is a number with last three digits 193:
XYZ×999 = ???193

999 times XYZ is 1000 times XYZ, minus 1 times XYZ:


1000×XYZ-XYZ = ???193

1000 times XYZ is a number that ends with 3 zeros. The 3-digit number XYZ, subtracted from a number that ends with 3 zeros, equals a number with last 3 digits 193. That gives us only one possible value for XYZ:
XYZ000-XYZ = ???193
???193+XYZ = XYZ000
XYZ = 807

Hence the multiplication becomes 807×999=806193


N.B- The multiplier is any integer with last 3 digits 807

Regards

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