A number consists of two digits. The sum of the digits is 10. On reversing the digits of the number, the number decreases by 36. What is the product of the two digits?

A) 21

  B) 24

C) 36

  D) 42

Correct Answer:
A) 21

Description for Correct answer:
Let the unit's digit of the number be x and ten's digit be y.

Therefore, Number = 10y + x

According to the question,

x + y = 10 ...(i)

\( \Large 10x+y = \left(10x+x\right)-36 \) ...(ii)

= 10x+y-10y-x=-36

= 9x - 9y = -36

= x - y = -4

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

x + y = 10

\( \Large \frac{x-y=-4}{2x=6} \)

Therefore, x = 3 and y = 7

Therefore, Required product of two digits = \( \Large 3 \times 7 \) = 21

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