In a two-digit positive number, the unit digit is equal to the square of ten's digit. The difference between the original number and the number formed by interchanging the digits is 54. What is 40% of the original number?

A) 15.6

B) 73

C) 84

D) None of the above

Correct Answer:
A) 15.6

Description for Correct answer:

Let ten's digit be x and unit's digit be x2.

Original number = \( \Large 10x + x^{2} \)

New number = \( \Large 10x^{2} + x \)

According to the question,

=\( \Large 10x^{2} + x - 10x - x^{2} = 54 \)

= \( \Large 9x^{2} - 9x = 54 \)

= \( \Large 9 \left(x^{2} - x\right) = 54 \)

= \( \Large x^{2} - x - 6 = 0 \)

= \( \Large x^{2} - 3x + 2x - 6 = 0 \)

= \( \Large x \left(x - 3\right) + 2 \left(x - 3\right) = 0 \)

= \( \Large \left(x - 3\right) \left(x + 2\right) = 0 \)

Therefore, x = 3, -2

Therefore, Ten's digit = x = 3

Unit's digit = \( \Large x^{2} = 3^{2} = 9 \)

Original number = 39

Required number = \( \Large 39 \times \frac{40}{100} = 15.6 \)

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