Question

The ratio of the ages of Kim, Jim, and Tim is 4: 7: 5. The ratio of the ages of Tim, Dan, and Linda is 3 : 11 : 9. What is the ratio of ages of all the friends in the same order?

• A. 4:7:5:11:9
• B. 4:7:5:9:11
• C. 12:21:15:45:55
• D. 12:21:15:55:45

Answer 1

The correct option is D 12:21:15:55:45

The ratio of the ages of Kim, Jim, and Tim is $4:7:5$.
Let their ages be:
Kim $=4x$
Jim $=7x$
Tim $=5x$

The ratio of the ages of Tim, Dan, and Linda is $3:11:9$.
Let their ages be:
Tim $=3y$
Dan $=11y$
Linda $=9y$

Age of Tim $=5x=3y$
$3y=5xy=\frac{5x}{3}$

Let's substitute the value of $y$.
The ages of:
Tim $=5x$
Dan $=11\times \frac{5x}{3}=\frac{55x}{3}$
Linda $=9\times \frac{5x}{3}=15x$

Hence, the ratio of the ages of Kim, Jim, Tim, Dan, and Linda is:
$4x:7x:5x:\frac{55x}{3}:15x$

Multiply each of them by $3$ to remove the denominator.

$3(4x:7x:5x:\frac{55x}{3}:15x)$
$12x:21x:15x:55x:45x$

On canceling out all $x$, we get:

$12:21:15:55:45$