Last year the age of R was three times that of V. At present, the age

Last year the age of R was three times that of V. At present, the age of R is double that of V. How old is R ?

8 years
6 years
5 years
4 years
This question was previously asked in
UPSC CISF-AC-EXE – 2020
Let R’s age at present be $R_P$ and V’s age at present be $V_P$.
According to the problem, at present, the age of R is double that of V:
$R_P = 2 V_P$ (Equation 1)

Let R’s age last year be $R_L$ and V’s age last year be $V_L$.
Last year’s age is one year less than the present age:
$R_L = R_P – 1$
$V_L = V_P – 1$

According to the problem, last year the age of R was three times that of V:
$R_L = 3 V_L$ (Equation 2)

Substitute the expressions for $R_L$ and $V_L$ from the ages at present into Equation 2:
$(R_P – 1) = 3 (V_P – 1)$
$R_P – 1 = 3V_P – 3$

Now substitute the expression for $R_P$ from Equation 1 into the above equation:
$(2 V_P) – 1 = 3V_P – 3$
$2 V_P – 1 = 3V_P – 3$

Rearrange the terms to solve for $V_P$:
$3 – 1 = 3V_P – 2V_P$
$2 = V_P$

So, V’s age at present is 2 years.
Now find R’s age at present using Equation 1:
$R_P = 2 V_P = 2 \times 2 = 4$.

R’s age at present is 4 years.
Let’s check this:
Present ages: R=4, V=2. R is double V (4 = 2*2). Correct.
Last year’s ages: R=3, V=1. R was three times V (3 = 3*1). Correct.

The question asks: How old is R? This refers to R’s age at present.
R is 4 years old.

– Set up equations based on the given information for different time periods (last year and present).
– Use the relationship between age in consecutive years (age last year = present age – 1).
– Solve the system of equations.
This is a typical age-based word problem solvable using linear equations. Careful definition of variables for each person and time period is key.