Question

paul is the elder brother of lisa. paul's age seven years ago is equal to lisa's age three years ago. the ratio between lisa's age eight years hence and paul's age two years ago is 8:5

Answer 1

Solution:

Let Present age of Lisa = x years

Present Age of Paul = y years

The statement for which we have make equation is

Paul's age seven years ago is equal to Lisa's age three years ago.

The ratio between Lisa's age eight years hence and Paul's age two years ago is 8:5.

1. y - 7=  x- 3 → x - y = -7 + 3 → x -y = -4

2. $\frac{x+8}{y-2}=\frac{8}{5}\\\\ 5 x + 40= 8 y - 16 \\\\ 5 x - 8 y= -56$

Multiply equation 1 by 5

1. 5 x - 5 y = -20

Equation 2 - Equation 1

- 3 y =- 36

Dividing both sides by 3, we get

y = 12

Putting the value of y in equation 1

x -12= -4

x= 12 -4

x=8

Age of Lisa = 8 years

Age of Paul = 12 years