The ratio of a two digit number to the number obtained by reversing its digits is 4:7. If the sum of its digit is 9
find the number
Answers
Given:
The ratio of a two-digit number to the number obtained by reversing its digits is 4:7.
To find:
The number.
Solution:
1) Let the one digit of the number be x then the other will be 9-x.
2) As per the condition
The number is
- 10x+9-x
- 9x+9
Number by reversing the digits
- 10(9-x)+x
- 90-10x+x
- 90-9x
2) The ratio given in the question is:
- 9x+9/90-9x = 4/7
- x+1/10-x = 4/7
- 7x+7 = 40-4x
- 11x = 33
- x=3
so the other digit is 6
The number is 36.
Step-by-step explanation:
The ratio of a two digit number to the number obtained by reversing its digits is 4:7. If the sum of its digit is 9, what is the number?
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Let a = first digit; 9 - a = second digit (because the two digits add up to 9).
This tells us that the actual number is expressed by:
10a + (9 - a), which simplifies to 9a + 9.
And the reversed number must be:
10(9-a) + a, which simplifies to 90 - 9a.
We can now express the ratio of the number and its reversal:
(9a + 9) / (90 - 9a) = 4 / 7 (because that is what we are given.)
Cross-multiply each denominator:
7(9a + 9) = 4(90 - 9a)
Simplify and solve for a:
63a + 63 = 360 - 36a
99a = 297
a = 3
Therefore the first number must be 36 and the second number is 63.