Question

John’s age is x. His father’s age is 5 less than thrice of John's age, and his son’s age is a sixth of John’s age. Find John’s age if his father’s age is more than 17 times his son’s age.

• A. $x>28$
• B. $x>32$
• C. $x>34$
• D. $x>30$

Answer 1

The correct option is D $x>30$

John’s age is x.
John’s father’s age = 3x - 5
John’s son’s age $=\frac{x}{6}$
Since the ratio of John’s father’s age to John’s son’s age is greater than 17, we have:
$\frac{3x-5}{\frac{x}{6}}>17$
$3x-5>17\times \frac{x}{6}$
$6\times (3x-5)>17\times x$
$18x-30>17x$
$18x-17x>30$
$x>30$
John’s age will be greater than 30 years.