Question

The sum of the present age of rani and her father's is 43 years .Six years hence ,father will be 4 times old as his daughter .Find their present ages.

Answer 1

Step-by-step explanation:

Let present age of father be x years

Let present age of Rani be y years

ATQ ,Sum of present ages of Rani and her father is 43 years

So x + y = 43 --------------(1)

Now , After six years father's age= x + 6

After six years Rani's age = y + 6

ATQ

After six years father's age = 4 (After six

year's Rani's age )

=> x + 6 = 4 ( y + 6 )

=> x + 6 = 4y + 24

=> x = 4 y + 24 - 6

=> x = 4y + 18 ------------------- (2)

Now we have two equations and we have to solve them

putting value of x from second equation to euation one

=> 4 y + 18 + y = 43

=> 5y = 43 - 18

=> 5y = 25

=> y = 25 / 5

=> y = 5

Now putting y = 5 in equation (2)

=> x = 4 y + 18

=> x = 4( 5 ) + 18

=> x = 20 + 18

=> x = 38

Present age of father = x

= 38 years

Present age of Rani = y

= 5 years

Answer 2

Given:

Sum of present ages of Rani and her

father is 43 years and after 6 years age

of father will be 4 times as old his

daughter

To find:

Present ages of Rani and her father

Explanation:

let the present age of Rani=x

let the present age of her father =y

According to the given information,

$\longrightarrow \: x + y = 43..........(1)$

After 6 years,

$\longrightarrow \: y + 6 = 4(x + 6) \\ \\ \longrightarrow \: y + 6 = 4x + 24 \\ \\ \longrightarrow4x - y = -18...........(2)$

Solving both the equations

Add (1)+(2)

$\longrightarrow \: x + y + 4x - y = -18 + 43$

$\longrightarrow 5x=25$

$\boxed{\sf x=5\: years}$

Age of Rani=5 years

substituting in eq (1)

$\longrightarrow y+5=43 \\ \\ \longrightarrow y=43-5$

$\boxed{\sf y=38\: years}$

Age of father=38 years