Question

16 years ago, my uncle was 8 times older than me. After 8 years from today, my uncle will be thrice as old as i will be at that time. Eight years ago, what was the ratio of my age and my uncle‘s age?

Answer 1

Step-by-step explanation:

let your present age x yrs

your uncles present age is y yrs

16 yrs ago your age was= x-16

your uncle's age was = y-16

ATQ 8×(x-16)=y-16

8x -128 -y +16=0

8x -y = 112 ........(i)

8 yrs from today your age will be = x+8 yrs

and your uncle's age will be = y+8 yrs

ATQ

3×(x+8)=y+8

3x +24 -y -8=0

3x-y=-16 .........(ii)

now subtract eq (ii) from eq (i)

we get

8x - y = 112

3x - y = -16

- + +

____________

5x = 128

x = 25.6 yrs

put in eq (ii)

3(25.6) -y = -16

y = 76.8 + 16

y = 92.8 yrs

Now 8 yrs ago your age was 25.6 - 8 = 17.6 yrs

your uncle's age was 92.8-8=86.8 yrs

now their ratio is

(17.6)/(86.8)

= 44:217

Answer 2

Answer:

$ans = > 11 \ratio53$

Step-by-step explanation:

$= > present \: age \: of \: your \: uncle = x \\ \\ = > your \: present \: age = y \\ \\ = > \: 16 \: years \: ago \: your \: uncle \: age = x - 16 \\ \\ = > 16 \: years \: ago \: your \: age = y - 16 \\ \\ = > 16 \: years \: ago \: uncle \: age \: was \: 8 \: times \\ \: \: \: \: \: \: \: \: \: times \: older \: than \: you \\ \\ \therefore \: x - 16 = 8(y - 16) \\ \\ \therefore \: x - 16 = 8y - 128 \\ \\ \therefore \: x - 8y = - 128 + 16 \\ \\ \therefore \: x - 8y = - 112.....equation(1) \\ \\ = > 8 \: year \: after \: your \: uncle \: age = x + 8 \\ \\ = > 8 \: years \: after \: your \: age = y + 8 \\ \\ = > after \: your \: uncle \: age \: will \: be \: 3 \: times \\ \: \: \: \: \: \: \: \: older \: than \: you \\ \\ \therefore \: x + 8 = 3(y + 8) \\ \\ \therefore \: x + 8 = 3y + 24 \\ \\ \therefore \: x - 3y = 24 - 8 \\ \\ \therefore \: x - 3y = 16....equation(2) \\ \\ = > solve \: to \: equation(1) \: and \: equation(2) \\ \\ x - 8y = - 112 \\ \\ x - 3y = \: \: \: 16 \\ - \: \: \: + \: \: \: \: \: \: \: - \\ ....................... \\ \: 0 \: - 5y = - 128 \\ \\ \therefore \: y = \frac{128}{5} = 25.6 \: year \\ \\ = > put \: value \: of \: y \: in \: equation(2) \\ \\ x - 3(25.6) = 16 \\ \\ x - 76.8 = 16 \\ \\ x = 92.8 \: year \\ \\ = > now \: find \: to \: ratio \: 8 \: years \: ago \: \\ \: \: \: \: \: \: \: \: your \: age \: and \: your \: uncle \: age \\ \\ = > \frac{25.6 - 8}{92.8 - 8} \\ \\ = > \frac{17.6}{84.8} \\ \\ = > \frac{176}{848} \\ \\ = > \frac{11 \times 16}{53 \times 16} \\ \\ = > \frac{11}{53} \\ \\ your \: ans = > 11 \ratio53$