Question : On dividing a number by 56, we get 29 as the remainder. On dividing the same number by 8, what will be the remainder?
Option 1: 6
Option 2: 7
Option 3: 5
Option 4: 3
Correct Answer: 5
Solution :
Divisor = 56, Remainder = 29
Let D = Dividend, R = Remainder, Q = Quotient
$(56\times Q)+29 = D$ ---(1)
$R=\frac{D}{8}$ ---(2)
Solving equation (1) and equation (2), we get
$R=\frac{(56\times Q)+29 }{8}$
⇒ $R=\frac{(56\times Q)}{8}+ \frac{29}{8}$
⇒ $R=7Q+ \frac{24+5}{8}$
⇒ $R=(7Q+3)+ \frac{5}{8}$ (Dividing by 8 gives 5 as a reminder)
Thus, the remainder is 5.
Hence, the correct answer is 5.
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