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 ?<\/p>\n
[amp_mcq option1=”8 years” option2=”6 years” option3=”5 years” option4=”4 years” correct=”option4″]<\/p>\n
Let R’s age last year be $R_L$ and V’s age last year be $V_L$.
\nLast year’s age is one year less than the present age:
\n$R_L = R_P – 1$
\n$V_L = V_P – 1$<\/p>\n
According to the problem, last year the age of R was three times that of V:
\n$R_L = 3 V_L$ (Equation 2)<\/p>\n
Substitute the expressions for $R_L$ and $V_L$ from the ages at present into Equation 2:
\n$(R_P – 1) = 3 (V_P – 1)$
\n$R_P – 1 = 3V_P – 3$<\/p>\n
Now substitute the expression for $R_P$ from Equation 1 into the above equation:
\n$(2 V_P) – 1 = 3V_P – 3$
\n$2 V_P – 1 = 3V_P – 3$<\/p>\n
Rearrange the terms to solve for $V_P$:
\n$3 – 1 = 3V_P – 2V_P$
\n$2 = V_P$<\/p>\n
So, V’s age at present is 2 years.
\nNow find R’s age at present using Equation 1:
\n$R_P = 2 V_P = 2 \\times 2 = 4$.<\/p>\n
R’s age at present is 4 years.
\nLet’s check this:
\nPresent ages: R=4, V=2. R is double V (4 = 2*2). Correct.
\nLast year’s ages: R=3, V=1. R was three times V (3 = 3*1). Correct.<\/p>\n