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Two times a two digit number is 9 times the number obtained by reversing the digits and the sum of the digits is 9. The number is.
- a)72
- b)54
- c)63
- d)81
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Two times a two digit number is 9 times the number obtained by reversi...
On checking the options we find that option (d) satisfies all the conditions i.e., 2 x 81 = 9 x 18. Also sum of the digits of 81 is 9.
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Two times a two digit number is 9 times the number obtained by reversi...
To solve this question, we will use algebraic equations to represent the given conditions.
Let's assume the two-digit number to be xy, where x represents the tens digit and y represents the units digit.
According to the first condition, "two times a two-digit number is 9 times the number obtained by reversing the digits," we can write the equation:
2 * (10x + y) = 9 * (10y + x)
Simplifying this equation, we get:
20x + 2y = 90y + 9x
19x = 88y
Dividing both sides by 19, we have:
x = (88/19)y
Since x and y represent digits, x must be a whole number. Therefore, (88/19)y must be a whole number as well.
The only value of y that satisfies this condition is 19 because 19 is the only factor of 19 that divides 88 evenly.
Therefore, y = 19.
Substituting the value of y back into the equation, we can find the value of x:
x = (88/19)(19)
x = 88
Thus, the two-digit number is 88.
Now, let's check if the second condition, "the sum of the digits is 9," is satisfied by the number 88.
Sum of the digits of 88 = 8 + 8 = 16 ≠ 9
Since the sum of the digits is not 9, the number 88 does not satisfy all the given conditions.
Therefore, the correct answer is not among the given options.
Let's assume the two-digit number to be xy, where x represents the tens digit and y represents the units digit.
According to the first condition, "two times a two-digit number is 9 times the number obtained by reversing the digits," we can write the equation:
2 * (10x + y) = 9 * (10y + x)
Simplifying this equation, we get:
20x + 2y = 90y + 9x
19x = 88y
Dividing both sides by 19, we have:
x = (88/19)y
Since x and y represent digits, x must be a whole number. Therefore, (88/19)y must be a whole number as well.
The only value of y that satisfies this condition is 19 because 19 is the only factor of 19 that divides 88 evenly.
Therefore, y = 19.
Substituting the value of y back into the equation, we can find the value of x:
x = (88/19)(19)
x = 88
Thus, the two-digit number is 88.
Now, let's check if the second condition, "the sum of the digits is 9," is satisfied by the number 88.
Sum of the digits of 88 = 8 + 8 = 16 ≠ 9
Since the sum of the digits is not 9, the number 88 does not satisfy all the given conditions.
Therefore, the correct answer is not among the given options.
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Two times a two digit number is 9 times the number obtained by reversing the digits and the sum of the digits is 9. The number is.a)72b)54c)63d)81Correct answer is option 'D'. Can you explain this answer?
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