Question

5 years ago Gori was thrice as old as Ganesh 10 years later Gori will be twice as old as Ganesh how old are Gauri and Ganesh​

Answer 1

$\textbf{Let age of Ganesh be x years }$

And

$\textbf{Age of Gori be 3x years.}$

5 years ago..

Age of Ganesh = (x - 5) years

Age of Gori = (3x - 5) years.

10 years later..

Age of Ganesh = (x + 10 + 5) = (x + 15) years

Age of Gori = (3x + 10 + 5) = (3x + 15) years

A.T.Q.

3x + 15 = 2(x + 15)

3x + 15 = 2x + 30

3x - 2x = 30 - 15

x = 15

So..

$\textbf{Age of Ganesh}$ = x + 5

=> 15 + 5 = $\textbf{20 years}$

$\textbf{Age of Gori}$ = 3x + 5

=> 3(15) + 5 = $\textbf{50 years.}$

$\textbf{OR}$

$\textbf{Let age of Ganesh be y years }$

And

$\textbf{Age of Gori be x years.}$

5 years ago.. (Gori was thrice as old as Ganesh)

x - 5 = 3(y - 5)

x - 5 = 3y - 15

x - 3y = - 15 + 5

$\textbf{x - 3y = - 10}$ ....(1)

10 years later.. (Gori will be twice as old as Ganesh)

x + 10 = 2(y + 10)

x + 10 = 2y + 20

x - 2y = 20 - 10

x - 2y = 10

$\textbf{x = 10 + 2y}$ ...(2)

Put value of x in (1)

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

10 + 2y - 3y = - 10

10 - y = - 10

- y = - 10 - 10

- y = - 20

y = 20

Put value of y in (2)

x = 10 + 2(20)

x = 10 + 40

x = 50

$\textbf{Age of Ganesh}$ = y years

= $\textbf{20 years}$

$\textbf{Age of Gori}$ = x years

= $\textbf{50 years.}$

Answer 2

» A.T.Q.

• 5 years later (before means substraction) Gori was trice as old as Ganesh.

In this question we have to find the age of Gori and Ganesh.

Let age of Gori be M and Ganesh be A.

=> M - 5 = 3(A - 5)

=> M - 5 = 3A - 15

=> M = 3A - 15 + 5

=> M = 3A - 10 __(eq. 1)

_________________________________

• 10 years later (addition) Gori will be twice as old as Ganesh.

=> M + 10 = 2(A + 10)

=> M + 10 = 2A + 20

=> M = 2A + 20 - 10

=> M = 2A + 10

=> 3A - 10 = 2A + 10 [From eq. (1)]

=> 3A - 2A = 10 + 10

=> A = 20

Put value of A in eq. (1)

=> M = 3(20) - 10

=> M = 60 - 10

=> M = 50

__________________________________

So, Age of Gori = M = 50 years

And

Age of Ganesh = A = 20 years.

____________________[ANSWER]