Question : If the mean of two numbers is 12, and the difference between the two numbers is 6, find the two numbers.
Option 1: 2 and 22
Option 2: 14 and 10
Option 3: 15 and 9
Option 4: 3 and 24
Correct Answer: 15 and 9
Solution :
Let the two numbers be a and b.
Given that the mean of the two numbers is 12,
⇒ $\frac{a + b}{2}$ = 12
⇒ a + b = 24 ___(1)
Given that the difference between the two numbers is 6,
⇒ a – b = 6 ___(2)
Adding the above equations,
⇒ 2a = 30
⇒ a = 15
From equation 2,
⇒ b = a – 6 = 15 – 6 = 9
Hence, the correct answer is 15 and 9.
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