The sum of three prime numbers is 90. If one of them exceeds another by 30, then one of the numbers is:

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SSC Graduation Level Previous Paper (Held on: 5 Aug 2022 Shift 3)
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  1. 67
  2. 41
  3. 59
  4. 47

Answer (Detailed Solution Below)

Option 3 : 59
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Given:- 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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