The sum of the digits of a two-digit number is 1/7 of the number. The units digit is 4 less than the tens digit. If the number obtained on reversing its digits is divided by 7, the remainder will be:
6
Let the tens digit be \(t\) and units digit be \(u\); number \(=10t+u\).
Condition 1: \(t+u=\tfrac{1}{7}(10t+u)\Rightarrow 7t+7u=10t+u\Rightarrow 6u=3t\Rightarrow t=2u\).
Condition 2: \(u=t-4\). Substituting: \(u=2u-4\Rightarrow u=4,\;t=8\). The number is 84; reversed it is 48.
\(48=7\times 6+6\), so the remainder is 6.
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select the correct answer using the code given below:
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