Given:
The ratio of the present ages of Manthan and his mother is 3 ∶ 7 respectively
The ratio of the present ages of Manthan and his father is 5 ∶ and 14 respectively.
Calculation:
Let's denote Manthan's age as Ma, his mother's age as Mo, and his father's age as F.
According to the question,
Manthan's age to his mother's age forms a ratio of 3 : 7.
⇒ MoMa=73
Manthan's age to his father's age forms a ratio of 5 : 14.
⇒ FMa=145
From these two equations, we can express the Mother's age and the Father's age in terms of Manthan's age:
⇒ Mo = 37 × Ma
⇒ F = 514 × Ma
Now we need to find the ratio of the Mother's age to the Father's age:
⇒ FMo= (37× Ma)/(514 × Ma)
⇒ FMo= (37)/(514) = (7 × 5)/(14 × 3) = 4235 = 65
∴ The ratio between the present ages of Manthan's mother and his father is 5:6.