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Question
A two digit number is 3 more than 4 times the sum of its digits. If 18 is added to this number, the sum is equal to the number obtained by interchanging the digits. Find the number.
Solution
Let the two digit number be 10x + y.
A two digit number is 3 more than 4 times the sum of its digits.
10x + y = 4 (x + y) + 3
⇒ 10x + y = 4x + 4y + 3
⇒ 2x - y = 1 ...(I)
If 18 is added to this number, the sum is equal to the number obtained by interchanging the digits.
10x + y + 18 = 10y + x
⇒ 9x - 9y = - 18
⇒ x - y = - 2 ...(II)
(I) - (II)
2x - y = 1
x - y = - 2
- + +
x = 3
Put x = 3 in equation (II)
∴ x - y = - 2
∴ 3 - y = - 2
∴ 3 + 2 = y
∴ y = 5
∴ The required number = 10x + y
= 10 × 3 + 5
= 30 + 5
= 35
Thus, the number obtained is 35.
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