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# The difference between a two-digit number and the number obtained by interchanging the two digits of the number is 18. The sum of the two digits of the number is 12. What is the product of the digits of two-digit number?

 A) 32 B) 27 C) 35 D) Couldn't be determined

Correct Answer:
 C) 35

Description for Correct answer:

Let the unit's digit be y and ten's digit, be x.

Then, the number = 10x + y

When interchang in the number is 10y + x.

According to the question,

$$\Large \left(10x + y\right) - \left(10y + x\right) = 18$$

$$\Large 10x + y - 10y - x = 18$$

= 9x - 9y = 18

= x - y = 2 ...(i)

and x + y = 12 ...(ii)

On adding Eqs. (i) and (ii), we get

x - y = 2

x + y = 12

2x = 14

x = 7

Therefore, x = 7 and y = 5

Product= $$\Large xy = 7 \times 5 = 35$$

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