Question

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Answer 1

Answer:

Largest number formed by them is -

100X + 10Y + Z -----–----------(1)

Smallest number formed by them is -

100Z + 10Y + X --------------–--(2)

Sum of (1) and (2).

100X + 10Y + Z + 100Z + 10Y + X = 1453.

101X + 20Y + 101Z = 1453. --------------(3)

Difference of (1) and (2).

100X + 10Y + Z -( 100Z + 10Y + X) = 297.

100X + 10Y + Z - 100Z - 10Y - X = 297.

99X - 99Z = 297. ---–-―---------(4)

Adding equation 3 and 4.

101X + 20Y + 101Z = 1453

+ 99X - 99Z = 297

_____________________

200X + 2Z + 20Y = 1750.

On dividing by 2.

100X + Z + 10Y = 875.------(5)

Now,

we can write,

875 + 100Z + 10Y + X = 1453

100Z + 10Y + X = 1453 - 875.

100Z + 10Y + X = 578. --------(6)

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Answer 2

Answer:

The sum of the digits was 10. A child selected a three-digit number, XYZ, where X, Y, and Z denote the digits of the number.