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Select the correct answerA number consists of two digits and the digit in the ten’s place exceeds that in the unit’s place by 5. if 5 times the sum of the digits be added from the numbers, the digits of the number are reversed. Then the sum of digits of the number is?Options79161113

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Select the correct answerA number consists of two digits and the digit in the ten’s place exceeds that in the unit’s place by 5. if 5 times the sum of the digits be added from the numbers, the digits of the number are reversed. Then the sum of digits of the number is?Options79161113

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Solution 1

Let's solve this step by step:

  1. Let's denote the digit in the tens place as T and the digit in the units place as U. According to the problem, T = U + 5.

  2. The number is then 10T + U.

  3. If 5 times the sum of the digits is added to the number, the digits are reversed. This gives us the equation 10T + U + 5(T + U) = 10U + T.

  4. Substituting T = U + 5 into the equation gives us 10(U + 5) + U + 5((U + 5) + U) = 10U + (U + 5).

  5. Simplifying this equation gives us 10U + 50 + U + 5U + 25 = 10U + U + 5.

  6. Simplifying further gives us 16U + 75 = 11U + 5.

  7. Solving for U gives us U = -14, which is not possible for a digit.

  8. Therefore, there seems to be a mistake in the problem as it does not have a valid solution.

This problem has been solved

Solution 2

Let's solve this step by step:

  1. Let's denote the digit in the tens place as T and the digit in the units place as U. According to the problem, T = U + 5.

  2. The number is then 10T + U.

  3. If 5 times the sum of the digits is added to the number, the digits are reversed. This gives us the equation 10T + U + 5(T + U) = 10U + T.

  4. Substituting T = U + 5 into the equation gives us 10(U + 5) + U + 5(U + 5 + U) = 10U + U + 5, which simplifies to 15U + 50 = 11U + 5.

  5. Solving for U gives U = -9, which is not possible for a digit.

  6. Therefore, there seems to be a mistake in the problem as it does not have a valid solution.

This problem has been solved

Solution 3

Let's solve this step by step:

  1. Let's denote the digit in the tens place as T and the digit in the units place as U. According to the problem, T = U + 5.

  2. The number is then 10T + U.

  3. If 5 times the sum of the digits is added to the number, the digits are reversed. This gives us the equation 10T + U + 5(T + U) = 10U + T.

  4. Substituting T = U + 5 into the equation gives us 10(U + 5) + U + 5((U + 5) + U) = 10U + (U + 5).

  5. Simplifying this equation gives us 15U + 50 = 11U + 5.

  6. Solving for U gives us U = 1.

  7. Substituting U = 1 into T = U + 5 gives us T = 6.

  8. Therefore, the sum of the digits of the number is T + U = 6 + 1 = 7.

So, the correct answer is 7.

This problem has been solved

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