10 years ago, the age of Sunita was thrice the age of her daughter Tanya. 10 years hence, the age of Sunita will be twice the age of Tanya. What is the ratio of their present ages?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 7 : 3
Let's define the present ages of Sunita and Tanya as:
Sunita's age = S years
Tanya's age = T years
Sunita's age 10 years ago = S - 10
Tanya's age 10 years ago = T - 10
Given that Sunita's age was three times Tanya's age,
so
⇒ S − 10 = 3(T − 10)
⇒ S − 10 = 3T − 30
⇒ S − 3T = −20 (Equation 1)
Sunita's age 10 years later = S + 10
Tanya's age 10 years later = T + 10
Given that Sunita's age will be twice Tanya's age,
so S + 10 = 2(T + 10)
⇒ S + 10 = 2T + 20
⇒ S − 2T = 10 (Equation 2)
Subtract Equation 1 from Equation 2:
⇒ (S − 2T) − (S − 3T) = 10 − (−20)
⇒ S − 2T − S + 3T = 30
Now, substitute T = 30 into Equation 2:
⇒ S − 2(30) = 10
⇒ S − 60 = 10
⇒ S = 70