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.
Similar Questions
Find the smallest number that can be subtracted from 148109326 so that it becomes divisible by 8.
The largest 5 - digit number exactly divisible by 88 is:
During a division, Pranjal mistakenly took as the dividend a number that was 10% more than the original dividend. He also mistakenly took as the divisor a number that was 25% more than the original divisor. If the correct quotient of the original division problem was 25 and the remainder was 0, what was the quotient that Pranjal obtained, assuming his calculations had no error?
Which of the following numbers is divisible by 36 ?
Which number among 98984, 98992, 98998 and 99008 is NOT divisible by 8?
When m is divided by 7, the remainder is 5. When 3m is divided by 7, the remainder is:
How many of the following numbers are divisible by 3 but NOT by 9?
5826, 5964, 6039, 6336, 6489, 6564, 6867 and 6960
Which number among 11368, 11638, 11863 and 12638 is divisible by 11?
What is the remainder when 8127 is divided by 8?
The difference of two numbers is 1564. After dividing the larger number by the smaller, we get 6 as quotient and 19 as remainder. What is the smaller number?
Important Questions from Divisibility and Remainder
What is the sum of the digits of the least number which when divided by 12, 16 and 20 leaves the same remainder 6 in each case and it is divisible by 9?
As nine-digit number 89563x87y is divisible by 72. What is the value of \(\sqrt{7x-3y}\) ?
The greatest number that on dividing 2675 and 2320 leaves the reminder 5 and 6 ,respectively is :
Find the greatest number that exactly divides 2880, 6525 and 8307.
If a 10 - digit number 643x1145y2 is divisible by 88, then the value of (2x - 3y) for the largest value of y is :
