Present age of Udit is three times the age of his daughter that was 3 years ago. Udit’s age that was 3 years ago was 50% of the present age of his mother. The sum of the present ages of all three of them is 107 years. What is the difference of present ages of Udit’s mother and daughter?

Present age of Udit is three times the age of his daughter that was 3 years ago. Udit’s age that was 3 years ago was 50% of the present age of his mother. The sum of the present ages of all three of them is 107 years. What is the difference of present ages of Udit’s mother and daughter? Correct Answer 46 years

Suppose present ages of Udit, his daughter and his mother are a, b and c respectively;

According to the question :

a = 3 × (b – 3)

⇒ 3b – a = 9

⇒ b = (9 + a)/3      ------ (1)

And

(a – 3) = 0.5 × c

⇒ c = (2a – 6)     ------ (2)

And

a + b + c = 107      ------ (3)

From all 3equations :

⇒ a + (9 + a)/3 + (2a – 6) = 107

⇒ a + 3 + a/3 + 2a – 6 = 107

⇒ 3a + a/3 = 107 – 3 + 6

⇒ 10a/3 = 110

⇒ a = 33

Then,

b = (9 + 33)/3 = 14

c = (66 – 6) = 60

∴ Present ages of Udit’s daughter = 14

Present ages of Udit’s mother = 60

Hence,