Sum of the present ages of two friends are 23 years, five years ago pr

1.	Sum of the present ages of two friends are 23 years, five years ago productof their ages was 42. Find their ages 5 years hence.
Answer» Let the ages of friends 5 years ago be X , Y ATQ: 5 years ago, X * Y = 42 ...(i) Now, X +5 + Y+5 = 23 X + Y = 13 .... (ii) X = 13-Y ...(iii) (iii) in (i) (13-Y)*Y = 42 13Y - Y² = 42 Y² - 13Y + 42 = 0 Sum = -13 && product = 42 Numbers are -6,-7 Y² - 6Y - 7Y +42 = 0 Y(Y-6) -7(Y-6) = 0 [Y-6][Y-7] = 0 Y = 6 or Y =7 When Y = 6, X = 7 Y = 7, then, X = 6 Ages 5 years ago = 6,7 tq

Sum of the present ages of two friends are 23 years, five years ago productof their ages was 42. Find their ages 5 years hence.

Answer»

Let the ages of friends 5 years ago be X , Y

ATQ:

5 years ago,

X * Y = 42 ...(i)

Now, X +5 + Y+5 = 23

X + Y = 13 .... (ii)

X = 13-Y ...(iii)

(iii) in (i)

(13-Y)*Y = 42

13Y - Y² = 42

Y² - 13Y + 42 = 0

Sum = -13 && product = 42

Numbers are -6,-7

Y² - 6Y - 7Y +42 = 0

Y(Y-6) -7(Y-6) = 0

[Y-6][Y-7] = 0

Y = 6 or Y =7

When Y = 6, X = 7

Y = 7, then, X = 6

Ages 5 years ago = 6,7