Question
Download Solution PDFThe sum of two digits is 12 and the sum of their reciprocals is 4/9. Then find the larger of these digits.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Sum of two digits = 12
Sum of their reciprocals = 4/9
Formula Used:
Let the two digits be x and y.
x + y = 12
1/x + 1/y = 4/9
Calculation:
From the second condition:
⇒ (y + x) / (xy) = 4/9
Substitute x + y = 12:
⇒ 12 / (xy) = 4/9
⇒ xy = (12 × 9) / 4
⇒ xy = 108 / 4
⇒ xy = 27
Now we have two equations:
1) x + y = 12
2) xy = 27
We need to find two numbers whose sum is 12 and product is 27.
Consider the factors of 27: (1, 27), (3, 9).
The pair (3, 9) satisfies the condition x + y = 12 (3 + 9 = 12).
So, the two digits are 3 and 9.
The larger of the two digits is 9.
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