If the present age of X is half that of Y and | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the present ages of $X$ and $Y$ be $x$ and $y$ respectively.According to the problem,$x = \frac{1}{2}y$,which implies $y = 2x$ (Equation $1$).

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(A) Let the present ages of $X$ and $Y$ be $x$ and $y$ respectively.According to the problem,$x = \frac{1}{2}y$,which implies $y = 2x$ (Equation $1$).After $20$ years,the age of $X$ will be $(x + 20)$ and the age of $Y$ will be $(y + 20)$.The problem states that after $20$ years,$Y$'s age will be $1 \frac{1}{2}$ (or $\frac{3}{2}$) times $X$'s age:$y + 20 = \frac{3}{2}(x + 20)$ (Equation $2$).Substitute $y = 2x$ from Equation $1$ into Equation $2$:$2x + 20 = \frac{3}{2}(x + 20)$.Multiply both sides by $2$ to clear the fraction:$4x + 40 = 3(x + 20)$.$4x + 40 = 3x + 60$.$4x - 3x = 60 - 40$.$x = 20$.Therefore,the present age of $X$ is $20$ years.

If the present age of $X$ is half that of $Y$ and after $20$ years the age of $Y$ will be $1 \frac{1}{2}$ times that of $X$,what is the present age of $X$?

Similar Questions

Present ages of Sameer and Anand are in the ratio $5:4$. Three years hence,the ratio of their ages will become $11:9$. What is Anand's present age in years?

The present age of Romila is $\frac{1}{4}$ that of her father. After $6\, \text{years}$, her father's age will be twice the age of Kapil. If Kapil celebrated his fifth birthday $8\, \text{years}$ ago, what is Romila's present age? (in $\text{years}$)

$A$ man's age is $125 \%$ of what it was $10 \, \text{years}$ ago, but $83 \frac{1}{3} \%$ of what it will be after $10 \, \text{years}$. What is his present age? (in $\text{years}$)

One $year$ ago the ratio between Samir and Ashok's age was $4: 3$. One year hence the ratio of their ages will be $5: 4$. What is the sum of their present ages in $years$?

In a family,a couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of his mother. The wife is $9$ years younger than her husband and the brother is $7$ years older than his sister. What is the age of the mother? (in years)

Vedclass Test Series

Exam Paper Generator

Online Exam Module