For a 4-digit number, the sum of its digits in the thousands, hundreds and tens places is 14, the sum of its digits in the hundreds, tens and units places is 15, and the tens place digit is 4 more than the units place digit. Then the highest possible 4-digit number satisfying the above conditions is
Explanation:
Let the thousands, hundreds, tens and units digits be a, b, c and d.
Given, sum of its digits in the thousands, hundreds and tens places is 14 a + b + c = 14 …(1) The sum of its digits in the hundreds, tens and units places is 15 b + c + d = 15 …(2)
(2) – (1) ⇒ a = d – 1 …(3)
The tens place digit is 4 more than the units place digit ⇒ c = d + 4 …(4)
For the number to be highest possible d should also be highest possible.
Highest possible of d is 5 (from (4)). ∴ highest possible value of c = 9 and that of a = 4
From (1), b = 14 – a – c = 1
∴ The highest such number is 4195
Hence, 4195.
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