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Six Digit Transformation Problem (Posted on 2025-03-24)

The first digit of the six digit number 1abcde is 1.

If the first digit is moved to the last place, we get a new number abcde1.

Given that, abcde1:1abcde = 7:2, find the value of abcde.

No Solution Yet Submitted by K Sengupta

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solution

| Comment 2 of 4 |

x = the string abcde

abcde1 = 10x+1

1abcde = x + 100000

2(10x+1) = 7(x+100000)

20x + 2 = 7x + 700000

13x = 699998

x = 53846

Checking 538461/153846 = 3.5 = 7/2

Note: the repeating decimals for 7/13 and 2/13 are

0.538461 538461 538461 ...

0.153846 153846 153846 ...

Posted by Jer on 2025-03-24 11:22:53

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