Question

please solve this question ​

Answer 1

Answer.

Let the present age of first friend be x years.

So, according to question,

x + Age of second friend = 23

⇒ Age of second friend = 23 – x

Now,

Age of first friend 5 years ago = x – 5

and, age of second friend 5 years ago

= 23 – x – 5 = 18 – x

According to question,

(x – 5)(18 – x) = 42

⇒ 18x – x² – 90 + 5x = 42

⇒ –x² + 23x – 90 – 42 = 0

⇒ –x² + 23x – 132 = 0

⇒ x² – 23x + 132 = 0

⇒ x² – 11x – 12x + 132 = 0

⇒ x(x – 11) –12(x – 11) =0

⇒ (x – 11)(x – 12) = 0

⇒ x – 11 = 0 or x – 12 = 0

⇒ x = 11 or x = 12

CASE 1. When x = 11

Age of first friend 5 years ago = 11 – 5

= 6 years

Age of second friend 5 years ago

= 23 – 11 – 5 = 23 – 16 = 7 years

CASE 2. When x = 12

Age of first friend 5 years ago = 12 – 5

= 7 years

Age of second friend 5 years ago

= 23 – 12 – 5 = 23 – 17 = 6 years

Hence, in either case, the ages of two friends 5 years ago were 5 and 6 years.

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