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?

Question

Accepted Answer

Let the present age of Sunita be S and that of Tanya be T.

According to the problem:
1) 10 years ago, Sunita's age was thrice Tanya's age:
   S - 10 = 3(T - 10)
   => S - 10 = 3T - 30
   => S - 3T = -20  ...(i)

2) 10 years hence, Sunita's age will be twice Tanya's age:
   S + 10 = 2(T + 10)
   => S + 10 = 2T + 20
   => S - 2T = 10  ...(ii)

Subtract equation (ii) from (i):
(S - 3T) - (S - 2T) = -20 - 10
=> S - 3T - S + 2T = -30
=> -T = -30
=> T = 30

Substitute T = 30 in equation (ii):
S - 2(30) = 10
=> S - 60 = 10
=> S = 70

Therefore, the present ages are:
Sunita = 70, Tanya = 30

The ratio of their present ages = 70 : 30 = 7 : 3

However, this ratio 7:3 is not among the correct options based on the problem's conditions. Let's re-check the calculations.

Re-examining the equations:
From (i): S - 3T = -20
From (ii): S - 2T = 10

Subtract (ii) from (i):
(S - 3T) - (S - 2T) = -20 - 10
=> S - 3T - S + 2T = -30
=> -T = -30
=> T = 30

Substitute T=30 in (ii):
S - 60 = 10
=> S = 70

Ratio = 70:30 = 7:3

But the options given are 2:7, 7:2, 7:3, 3:7.

The ratio 7:3 matches option 3.

Hence, the correct answer is option 3: 7 : 3.

Answer

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