Question
Download Solution PDFThe sum of three prime numbers is 90. If one of them exceeds another by 30, then one of the numbers is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:- The sum of three prime number is 90
To find:- After exceeding one by 30 then find one of the number,
Concept used:-
Calculation:- Let the three prime numbers be x, y, and z
According to the question-
⇒ x + y + z = 90
According to the condition, let x = y + 30
⇒ (y + 30) + y + z = 90
⇒ 2y + z = 60
⇒ \(y=\frac{60-z}{2}\)
Since, the number y should have to be integer then the numerator (60 - z) must be an integer and should have to even so that on dividing with 2 no remainder left
⇒ least even prime is 2, so z = 2
⇒ \(y=\frac{60-2}{2}\)
⇒ y = 29
The value of x = 90 - (y + z)
⇒ x = 90 - (29 + 2)
⇒ x = 59
.·. The one of the prime number is 59
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