The sum of the digits of a three digit number is 16. If the ten's digit of the number is 3 times the unit's digit and the unit's digit is one-fourth of the hundredth digit, then what is the number ?
Correct Answer: Description for Correct answer:
Let a, b and c be the digits at the hundredth, ten's and unit place respectively.
a + b + c = 16 ...(i)
b = 3c ...(ii)
and \( \Large c = \frac{1}{4}a \) ...(iii)
From Eqs. (ii) and (iii), \( \Large b = \frac{3}{4}a \) ...(iv)
From Eqs. (i), (iii) and (iv), we get
\( \Large a + \frac{3}{4}a + \frac{1}{4}a = 16 \)
=> a = 8, b = 6 and c = 2
Therefore, the three digit number is 862.
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