Given the 4 digit number :
Considering the number in thousands digit is a number in the hundredth digit is b, number in tens digit is c, number in the units digit is d.
Let the number be a b c d .
Given that
a+b+c=14 ...(1)
b+c+d=15 ...(2)
c=d+4 ...(3)
In order to find the maximum number which satisfies the condition, we need to have a b c d such that a is maximum which is the digit in thousands place in order to maximize the value of the number. b, c, and d are less than 9 each as they are single-digit numbers.
Substituting (3) in (2) we have
b+d+4+d=15,b+2×d=11 ...(4)
Subtracting (2) and (1) : (2) - (1)
=d=a+1 ...(5)
Since c cannot be greater than 9 considering c to be the maximum value 9 the value of d is 5.
If
d=5, using
d=a+1,a=4 Hence the maximum value of
a=4 when
c=9,
d=5 Substituting
b+2×d=11.b=1 The highest four-digit number satisfying the condition is 4195.