Question

5 years ago Shikha was thrice as old as honey 10 years later Shikha will be twice as old as honey how old are they now ?

Answer 1

Hi !

Let the present ages of Shikha and Honey be "x" and "y" respectively.
Shikha's age 5 years before is  "x - 5"
Honey's age 5 years before is "y - 5"

x - 5 = 3(y - 5)

x - 5 = 3y -15

x - 3y  = -10            ------------> (1)

Also,

Their ages 10 years later is "x +10" and "y+10" respectively.

x + 10 = 2(y + 10)

x +10 = 2y + 20

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

Subtracting equation (2) from(1) , 

x - 3y = -10

x - 2y = 10
-------------------------
-y = -20

y = 20

x - 2y = 10
x - 40 = 10

x = 40 + 10 = 50

Present age of Shikha = x  = 50 years
Present age of Honey = y = 20 years 

Answer 2

Let the present age of Shikha and Rani be x and y respectively.

∴ Given that five years ago, Shikha was thrice as old as Rani.

⇒(x−5)=3(y−5)

⇒x−5=3y−15

⇒3y−x=10⟶(i)

Also given that 10 years later, Shikha will be twice as old as Rani.  

∴(x+10)=2(y+10)

⇒x+10=2y+20

⇒x=2y+10

Substituting the value of x in eq  

n

(i), we have

3y−(2y+10)=10

⇒3y−2y−10=10

⇒y=20

∵x=2y+10

⇒x=2×20+10

⇒x=50

Hence, present age of Shikha and Rani are 50 and 20 respectively.