Question
Download Solution PDFThe sum of the ages of A and B (in years) is 22. The product of their ages two years back was 77. Which one of the following is the value of the difference of their current ages?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe Correct answer is Option 3.
Key PointsLet's denote the current ages of A and B as x and y respectively. According to the problem:
⇒ x+y=22
⇒ The product of their ages two years ago was 77, so
⇒ (x−2)(y−2)=77.
Expanding the second equation:
⇒ (x−2)(y−2)=xy−2x−2y+4=77
Substitute
⇒ x+y=22 into the equation:
⇒ xy = 117
So, we have:
⇒ x+y=22
⇒ xy=117
⇒ The quadratic equation whose roots are
x and y is:
⇒ 𝑡2 −(x+y)t+xy=0
⇒ 𝑡2 −22t+117=0
⇒ Solve this quadratic equation using the quadratic formula t
⇒ So, the ages of A and B are 13 years and 9 years.
⇒ The difference between their current ages is: 13−9=4
Thus, the correct answer is: 3) 4
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