# maths

A number on being divided by 10 and 11 successively leaves the remainders 5 and 7. Find the number.
ie, x/10 = remainder 5 and
x/11 = remainder 7.

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1. If the number is x, then
x = 10t+5
so,

10t+5 = 7(mod 11)
10t = 2(mod 11)
so, which multiple of 10 leaves a remainder of 2 when divided by 11? How about 90 = 88+2?
So, t=9

95 = 10*9+5 = 11*8+7

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