Question

The sum of the age of Rajesh and his wife is 80 years. 10 years ago the ratio of the age of Rajesh to his wife was 3:2 find the present age

Answer 1

let the age of rajesh = x

age of his wife = y

x + y = 80 ------(1)

10 years ago age of rajesh = x - 10

his wife will be = y - 10

so, (x-10) / (y-10) = 3/2

2(x-10) = 3(y-10)

2x - 10 = 3y - 30

3y - 2x = 20 -------(2)

from equation 1 we get

x + y = 80

x = 80 - y -----------putting this value of x in equation 2

3y - 2(80 - y) = 20

3y - 160 + 2y = 20

5y = 180

y = 180/5

y = 36 ------ putting value of y in equation (1)

x + y = 80

x + 36 = 80

x = 80 - 36

x = 44

age of rajesh today is 44 and his wife 36

Answer 2

$r + w = 80 \\ r = 80 - w \\ ten \: year \: ago \\ \frac{r - 10}{w - 10} = \frac{3}{2} \\ 2(r - 10) = 3(w -10 ) \\ 2r - 20 = 3w - 30 \\ 3w - 2r = 30 - 20 \\ 3w - 2r = 10 \\ put \: value \: of \: r \\ 3w - 2(80 - w) = 10 \\ 3w - 160 + 2w = 10 \\ 5w = 170 \\ wife \: age = 34 \\ rajesh \: age = 80 - 34 = 46$