Question

Sum of the present ages of 2 friends are 23 years, 5 years ago product of their ages was 42. Find their ages 5 years hence​

Answer 1

✰ Qᴜēsᴛíõñ :-

Sum of the present ages of 2 friends are 23 years, 5 years ago product of their ages was 42. Find their ages 5 years hence

✪ Söʟúᴛîøɴ :-

Let the ages of two friends are x and 23-x

Five years ago product of their ages = 42

➙ (x - 5) (23 - x - 5) = 42

➙ (x - 5) (18 - x) = 42

➙ 18x - x² - 90 + 5x = 42

➙ 23x - x² - 132 = 0

➙ x² - 23x + 132 = 0

➙ (x - 12) (x - 11) = 0

➙ x = 12, x = 11

The ages are 12 and 11

5 years hence :-

• 12 + 5 = 17
• 11 + 5 = 15

⛬ Their ages 5 years hence, 17 and 16.

Answer 2

Answer:

Answer:

16 years and 17 years

Step-by-step explanation:

☞Let the present age of friend A is = year

and, the present age of friend B is = year

☞Sum of their present age is =23 years

therefore,

☞ (x+y)=23

☞ X =23-y.......... (1)

and

Five years ago age of the friend A was = (x-5) years

Five years ago age of the friend B was =(y-5) years

According to question Five years ago product of their age were =42 years

☞

$(x - 5) \times (y - 5) = 42 \\ \\( 23 - y - 5) (y - 5) = 42 \\ \\ (18 - y)(y - 5) = 42 \\ (18y - 90 - y {}^{2} + 5y) = 42 \\ \\ (42 - 23y + 90 + {y}^{2} ) = 0 \\ \\ y(y - 12) - 11(y - 12) = 0 \\ \\ (y - 12)(y - 11) = 0 \\ therefore \: y = 11 \: or \: y = 12$

As

therefore or

If then

If then

therefore the present age of the two friends are 11 years and 12 years

therefore the age of the two friends after five years are 11+5=16years and 12+5 =17 years.

hence the required answer will be 16 and 17.