The sum of the digits of a two digit number is 9. On adding 27 to the number , its digits are reversed. The number is
36
45
54
72
Linear Eqns One Variable
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Question

The sum of the digits of a two digit number is 9. On adding 27 to the number , its digits are reversed. The number is 1. 36 2. 45 3. 54 4. 72

KnowledgeBoat · Accepted Answer

Let the digit in the units place be x. Since the sum of the digits is 9, the digit in the tens place must be (9 - x). A two-digit number is written as: 10 x (Tens digit) + (Units digit) Original Number = 10(9 - x) + x = 90 - 10x + x = 90 - 9x When digits are reversed, x becomes the tens digit and (9 - x) becomes the units digit. Reversed Number = 10(x) + (9 - x) = 10x + 9 - x = 9x + 9 The problem states that adding 27 to the original number results in the reversed number. Original Number + 27 = Reversed Number (90 - 9x) + 27 = 9x + 9 ⇒ 117 - 9x = 9x + 9 ⇒ 117 - 9 = 9x + 9x [Transposing -9x to RHS and +9 to LHS] ⇒ 108 = 18x ⇒ x = ⇒ x = 6 Units digit = x = 6 Tens digit = (9 - x) = (9 - 6) = 3 ∴ The original number is 36. Hence, option 1 is the correct option.

Mathematics

The sum of the digits of a two digit number is 9. On adding 27 to the number , its digits are reversed. The number is
36
45
54
72

Linear Eqns One Variable

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Mathematics

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Linear Eqns One Variable

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The sum of the digits of a two digit number is 9. On adding 27 to the number , its digits are reversed. The number is
36
45
54
72

Three times a number exceeds its one-third by 64. The number is
24
36
42
48

Two supplementary angles differ by 42°. One of these angles is
57°
69°
75°
81°

What number must be added to 54 so that the resulting number is 7 times the number added?
6
7
8
9