Three years ago , Raghav's age was five times that of his daughter . Five years hence, the age of Raghav will be three times that of his daughter.. What are their present ages.
Answers
Let daughter's present age be x years.
Raghav's present age = y years
Three years ago , Daughter's age was = x - 3
Three years ago , Raghav's age was = y - 3
According to question, three years ago , raghav's age was 5 times his daughter.
Therefore ,
y - 3 = 5( x - 3 )
→ y - 3 = 5x - 15
→ y - 5x = -15 + 3
→ y - 5x = -12
→ 5x - y = 12 ----- (i)
After 5 years , Daughter's age will be = x + 5
After 5 years , Raghav's age will be = y + 5
According to question, five years hence , raghav's age will be 3 times his daughter.
Therefore ,
y + 5 = 3( x + 5)
→ y + 5 = 3x + 15
→ y - 3x = 15 - 5
→ y - 3x = 10 ----- (ii)
Now , (i) + (ii)
5x - y + y - 3x = 12 + 10
→ 5x - 3x + 0 = 22
→ 2x = 22
→ x = 22/2
→ x = 11
y - 3x = 10
→ y = 10 + 3x
= 10 + 3×11
= 10 + 33
= 43
Hence , the present ages of daughter is 11 years and her father Raghav's is 43 years.