Question

Four years ago, Raju’s father’s age was 8 times of Raju’s age. After 6 years, his age will be 3 times Raju’s age. Find their present ages.
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Answer 1

Step-by-step explanation:

father. raju

8. 1

aft-6 3. 1

____________________

6×2/5

raju' father =8×12/5=96/5=19.2 years

.

raju age-- 1×12/5=2.4 years

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Answer 2

Answer:

$\boxed{\sf The\; present\; age\; of\; Raju \; is \; 8 \; years \;and\; the\; present\; age \;of \;his \;father is\; 36\;years.}$

Step-by-step explanation:

Let the present age of Raju be 'x'.

Let the present age of Raju's father be 'y' .

Four years ago, Raju’s father’s age was 8 times of Raju’s age

Four years ago Raju's age was , x-4.

Four years ago age of  Raju's father was , y-4.

So, From the question

8(x-4)  = y-4

8x - 32 = y -4

8x - 32+ 4 = y

8x - y - 28 = 0 $\longrightarrow$ (1)

∵ After 6 years, his age will be 3 times Raju’s age.

After six years Raju's age will be  , x+6

Age of Raju's father will be , y+6

So, From the question

After 6 years, his age will be 3 times Raju’s age  , i.e

y+6 = 3(x+6)

y+6 = 3x + 18

3x - y+ 18 - 6 = 0

3x - y +12 =0 $\longrightarrow$ (2)

On solving (1) and (2) ,by elimination method

3x -  y + 12 =0

-8x + y +28 = 0    

-5x + 40 =0

So,

-5x = -40

5x = 40

x = 40/5 = 8

Substituting the value of x in (2),

3 × 8 - y + 12 = 0

24 - y + 12 = 0

36 -y = 0

36 = y