Two years ago, Raju was thrice as old as his daughter and six
years later, he will be four years older than twice her age.
How old are they now?
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Step-by-step explanation:
Let the present age of Raju be x
And present age of his daughter be y
Case 1:-
Two years ago
Age of Raju = x - 2
Age of his daughter = y - 2
Raju was thrice as old as his daughter
➝ x - 2 = 3(y - 2)
➝ x - 2 = 3y - 6
➝ x - 3y = -6 + 2
➝ x - 3y = -4......(i)
Case 2:-
Six years later
Age of Raju = x + 6
Age of his daughter = y + 6
Raju will be four years older than twice her age.
➝ x + 6 = 2(y + 6) + 4
➝ x + 6 = 2y + 12 + 4
➝ x - 2y = 16 - 6
➝ x - 2y = 10....(ii)
Equation (ii) - (i)
➝ x - 2y - (x - 3y) = 10 - ( -4 )
➝ x - 2y - x + 3y = 10 + 4
➝ y = 14
Substituting y = 14 in equation (ii)
➝ x - 2y = 10
➝ x - 2(14) = 10
➝ x = 10 + 28
➝ x = 38
We have:-
- x = 38
- y = 14
Therefore:-
Present age of Raju = 38 years
Present age of his daughter = 14 years
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