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The sum of the digits of a two digit number is 10, when the number is reversed, the number increases by 72.Find the number.
- a)64
- b)82
- c)19
- d)37
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The sum of the digits of a two digit number is 10, when the number is ...
By checking options
91-19=72
Or
Let the number be xy
So 10x + y = 10 ..... (i)
When the number is reversed the new number is yx
So (10y + 10 ) - ( 10x +y ) = 72 ....(ii)
From Eqs. (i) & (ii)
x = 1 and y =9
∴number = 19
91-19=72
Or
Let the number be xy
So 10x + y = 10 ..... (i)
When the number is reversed the new number is yx
So (10y + 10 ) - ( 10x +y ) = 72 ....(ii)
From Eqs. (i) & (ii)
x = 1 and y =9
∴number = 19
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Community Answer
The sum of the digits of a two digit number is 10, when the number is ...
Analysis:
The sum of the digits of a two-digit number is 10, which means that the digits can be represented as (10 - x) and x, where x is the digit in the tens place.
When the number is reversed, the new number increases by 72. This means that the difference between the original number and the reversed number is 72.
Solution:
Let the original number be 10x + y, where x is the digit in the tens place and y is the digit in the units place.
According to the given conditions:
x + y = 10 (sum of the digits is 10)
10y + x - (10x + y) = 72 (difference between the reversed number and the original number is 72)
Solving the above equations simultaneously:
y = 10 - x (from x + y = 10)
9y - 9x = 72
9(10 - x) - 9x = 72
90 - 9x - 9x = 72
90 - 18x = 72
18x = 18
x = 1
Substitute x = 1 into y = 10 - x:
y = 10 - 1
y = 9
Therefore, the original number is 10x + y = 10(1) + 9 = 19.
Hence, the correct answer is option C) 19.
The sum of the digits of a two-digit number is 10, which means that the digits can be represented as (10 - x) and x, where x is the digit in the tens place.
When the number is reversed, the new number increases by 72. This means that the difference between the original number and the reversed number is 72.
Solution:
Let the original number be 10x + y, where x is the digit in the tens place and y is the digit in the units place.
According to the given conditions:
x + y = 10 (sum of the digits is 10)
10y + x - (10x + y) = 72 (difference between the reversed number and the original number is 72)
Solving the above equations simultaneously:
y = 10 - x (from x + y = 10)
9y - 9x = 72
9(10 - x) - 9x = 72
90 - 9x - 9x = 72
90 - 18x = 72
18x = 18
x = 1
Substitute x = 1 into y = 10 - x:
y = 10 - 1
y = 9
Therefore, the original number is 10x + y = 10(1) + 9 = 19.
Hence, the correct answer is option C) 19.
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