# A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:

Assume the number is abc.

ATQ

a + b + c =10 ...(i)

b = a+c..(ii)

Put value of (a+c) in equation (i)

b +b =10

b = 5 = a+c ...(iii)

100 c + 10b + a - 100a - 10b - c = 99

99(c-a) = 99

c - a = 1 ...(iv)

Equation (iii) + Equation (iv)

a + c + c - a = 1+5

2c = 6

c = 3

a = 2

Hence the required number is 253.

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