If the digits of a two-digit number are interchanged, the number so formed is 18 more than the original number. The sum of digits is 8. The thrice value of original number is

# If the digits of a two-digit number are interchanged, the number so formed is 18 more than the original number. The sum of digits is 8. The thrice value of original number is

1. A

159

2. B

78

3. C

105

4. D

150

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### Solution:

Let unit’s digit $=x$

Ten’s digit $=y$

$\therefore$ The original number $=1\left(x\right)+10\left(y\right)$

$=x+10y$

After inter changing the digits

The new number is $=10x+y$

As per the problem $10x+y=x+10y+18$

$9x-9y=18$

$x-y=2\cdots \cdots \left(1\right)$

Given the sum of digits

$x+y=8\cdots \cdots \left(2\right)$

By solving is (2)

$2x=10⇒x=5$

$x-y=2$

$5-y=2⇒y=3$

$\therefore$ The original number $=35$

Thrice value of original $=3×35=105$

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