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Linear Equation in One Variable

If 1 a 4x 3...

Question

If $\frac{(\frac{1 a 4}{x 3 b})}{8 c 8}$
$\frac{s 72}{t 5 d 8}$
then find the value of a, b, c, d, s and t where all of them are different digits.

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Solution

Let us consider 1 a 4 x 3 = s72
a x 3 results in a number ending in 6
As 16 and 26 is ruled out a is 2
Thus s = 3, t, 4
Now 1 a 4 x b = 8c8 ; b = 2 or 7
Again 2 is ruled out because in that case product would be much less than 800
$∴$ b = 7 Hence a = 2, b = 7, c = 6, d = 8, s = 3 and t = 4

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