Chapter 9, Problem 2E

To determine

To find : The age of A.

Answer to Problem 2E

The correct option is (H).

Explanation of Solution

Given information :

The sum of K’s, A’s, and T’s ages is 40. A is 1 year more than rwice as old as T. K is 3 years older than A.

Calculation :

Let the ages of K, A and T be $k$ , $a$ and $t$ respectively.

Since, the sum of their ages is 40. Therefore

  $k+a+t=40\mathrm{......}\text{ (1)}$

A is one more than twice the age of T. Therefore,

  $a=1+2t\mathrm{......}\text{ (2)}$

Also, K is 3 years older than A. Therefore,

  $a=k-3\mathrm{......}\text{ (3)}$

Substitute the value of $a$ from equation (2) in equation (1) and solve:

  $\begin{array}{l}k+1+2t+t=40\\ k+3t=40-1\\ k+3t=39\mathrm{......}\text{ (4)}\end{array}$

Substitute the value of $a$ from equation (3) in equation (1) and solve:

  $\begin{array}{l}k+k-3+t=40\\ 2k+t=40+3\\ t=43-2k\mathrm{......}\text{ (5)}\end{array}$

Substitute the value of $t$ form equation (5) in equation (4) and solve for $k$ :

  $\begin{array}{l}k+3\left(43-2k\right)=39\\ k+129-6k=39\\ k-6k=39-129\\ -5k=-90\\ k=\frac{-90}{-5}\\ k=18\end{array}$

Substitute value of $k$ in equation (3) and solve for $a$ :

  $\begin{array}{l}a=18-3\\ a=15\end{array}$

Hence,

The correct option is (H).