4. 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:
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Let the digits of the number be x, y, z.
x+y+z = 10
y = x+z
x+y+z = 2y
2y = 10
y = 5
x+z= 5
The number that is formed by x, y, z digits is
100x + 10y + z
let this be a
so 100x + 10y + z = a
according to question
100z + 10y + x = a + 99
100z + 10y + x = 100x + 10y + z + 99
99z - 99x = 99
z - x = 1
z + x = 5
2z = 6
z = 3
z - x = 1
3 - x = 1
x = 2
The number is 243
x+y+z = 10
y = x+z
x+y+z = 2y
2y = 10
y = 5
x+z= 5
The number that is formed by x, y, z digits is
100x + 10y + z
let this be a
so 100x + 10y + z = a
according to question
100z + 10y + x = a + 99
100z + 10y + x = 100x + 10y + z + 99
99z - 99x = 99
z - x = 1
z + x = 5
2z = 6
z = 3
z - x = 1
3 - x = 1
x = 2
The number is 243
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