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The sum of the digits of a three digit number is 11. If we subtract 594 from the number consisting of the same digits written in the reverse order.We shall get a required number.Find the three digit number if the sum of the pairwise product of the digits constituting the number is 31.

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700

731

590

635

answer is B.

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Detailed Solution

Concept- The task is to locate a three-digit number that meets the requirements. Given that the sum of the digits is 11, we have

and, following the third condition,

. We then substitute these values in equations 1 and 2 to obtain the values of z, y, and x.
Let three digit number be

A three-digit number has a digit sum of 11.

The total pairwise product of the digits in that number, when added together, is 31.

We will obtain a number with the same digits written in the reverse order if we deduct 594 from that number.

From (1) and (3)

From (2) , (3) , and (4):

, which is a quadratic equation
Splitting the middle term:

is not possible as digit of any number can't be a fraction
Hence,

From (3) and (4):

and

Required number

Thus, the required number is 731 .
Hence, the correct answer is option 2) 731

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