A five-digit number abcde is such that the number abcde1 is the product of 1abcde and 3. The sum of the digits of abcde is

25

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26

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27

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28

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Solution

The correct option is B $26$
abcde is a $5$ digit no.
$∴ a b c d e = 10000 a + 1000 b + 100 c + 10 d + e$ (1)
because, $a b c d e 1 = 3 \times 1 a b c d e$
So, $=> 100000 a + 10000 b + 1000 c + 100 d + 10 e + 1 = 3 \times (100000 + 10000 a + 1000 b + 100 c + 10 d + e)$
$=> 100000 a + 10000 b + 1000 c + 100 d + 10 e + 1 = 300000 + 30000 a + 3000 b + 300 c + 30 d + 3 e$
$=> 100000 a + 10000 b + 1000 c + 100 d + 10 e - 30000 a - 3000 b - 300 c - 30 d - 3 e = 300000 - 1$
$=> 70000 a + 7000 b + 700 c + 70 d + 7 e = 299999$
$=> 7 (10000 a + 1000 b + 100 c + 10 d + e) = 7 (42857)$
$=> 10000 a + 1000 b + 100 c + 10 d + e = 42857$
Putting value from $1$ we get
$a b c d e = 42857$
sum of digits = $4 + 2 + 8 + 5 + 7$
$= 26$

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