Question : Five years from now, the ratio of the ages of A, B and C will be 3 : 5 : 2. The sum of the squares of their present ages is 525. What is the present age of B?
Option 1: 10 years
Option 2: 15 years
Option 3: 25 years
Option 4: 20 years
Correct Answer: 20 years
Solution :
The ratio of ages of A, B and C after 5 years = 3 : 5 : 2
Let the ages of A, B and C after 5 years be $3x, 5x$ and $2x$ respectively.
Present ages of A, B and C = $(3x-5), (5x-5), (2x-5)$
The sum of squares of present ages = 525
So, $(3x-5)^2 + (5x-5)^2 + (2x-5)^2 = 525$
$⇒9x^2 - 30x + 25 + 25x^2 - 50x + 25 + 4x^2 - 20x + 25 = 525$
$⇒38x^2 - 100x + 75 = 525$
$⇒38x^2 - 100x - 450 = 0$
$⇒38x^2 - 190x + 90x - 450 = 0$
$⇒38x(x-5) + 90(x-5) = 0$
$⇒(38x + 90)(x-5) = 0$
Since age cannot be negative,
$x = 5$
Present age of B = $5x - 5= 5 × 5 - 5= 25 - 5= 20$
Hence, the correct answer is 20 years.
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