Question

Sunita is twice as old as Ashima. If six years is subtracted from Ashima’s age and four years added to Sunita’s age, then Sunita will be four times that of Ashima’s age. Find the sum of their ages 2 years ago.
(A) 40
(B) 42
(C) 36
(D) 38

Answer 1

Hint: If we are assuming the current age to be x, then the age after (t) years will be (x+t) years. Similarly, If we are assuming the current age to be x, then the age (t) years back will be (x-t) years.

Complete step-by-step answer:
Let present age of Ashima = x years
Then present age of Sunita will be 2x years
According to question;
\[
   = 4(x - 6) = (2x + 4) \\
   = 4(x - 6) = 2(x + 2) \\
   = 2(x - 6) = x + 2 \\
   = 2x - 12 = x + 2 \\
   = 2x - 12 = x + 2 \\
   \Rightarrow x = 14 \\
\]
Present age of Ashima=14 years.
Present age of Sunita=2(14) years=28 years.
2 years ago,
Ashima’s age=14 years-2 years=12 years
Sunita’s age=28 years-2 years=26 years
Sum of their ages, 2 years ago=26 years+12 years=38 years.
Option (D) is correct.

Note: There can be at most three situations based questions which all students have to keep in mind:
1.Present age
2.Years ago age : Subtract the given years from the present age.
3.Hence years age : Add the given years from the present age.