Question

16. The three digit number XYZ when divided by 8. gives as quotient the two digt mmber zx
remainder Y. The number XYZ is​

Answer 1

Answer:

The number is 435

Step-by-step explanation:

The number XYZ is

100X+10Y+Z

On dividing this no. by 8, the quotient = 10Z+X

By Euclid's Division Lemma

$100X+10Y+Z=8(10Z+X)+Y$

$\implies 92X+9Y-79Z=0$

$\implies Y=\frac{79Z-92X}{9}$

$\implies Y=\frac{72Z+7Z-90X-2X}{9}$

$\implies Y=\frac{72Z-90X}{9}+\frac{7Z-2X}{9}$

$\implies Y=\frac{9(8Z-10X)}{9}+\frac{7Z-2X}{9}$

Since XYZ are digits from 1 to 9

Therefore 7Z-2X should be multiple of 9

This is possible only when Z = 5 and X = 4

Therefore, Y = 3

Thus, the number becomes 435

Hope this answer is helpful.

Answer 2

Answer:  

The number is 435  

Step-by-step explanation:  

The number XYZ is  

100X+10Y+Z  

On dividing this no. by 8, the quotient = 10Z+X  

By Euclid's Division Lemma

$100X+9Y+Z=8(10Z+X)+Y$

⇒  $Y=\frac{79Z-92X}{9}$

⇒  $Y=\frac{72Z+7Z-90X-2X}{9}$

⇒  $Y=\frac{72Z+90X}{9} +\frac{7Z-2X}{9}$

⇒  $Y=\frac{9(8Z-10X)}{9} +\frac{7Z+2X}{9}$

Since XYZ are digits from 1 to 9  

Therefore 7Z-2X should be multiple of 9  

This is possible only when Z = 5 and X = 4  

Therefore, Y = 3

Thus, the number becomes 435

Hope this answer is helpful.