Question

There are four men of different heights. The fourth man is the tallest and the first man is the shortest. If the difference in heights among the first three men was $2$ inches and the difference between the third and the fourth man was $6$ inches and the average height was $74$ inches, how tall was the fourth man?

Answer 1

Let the height of $1^{st}$ men be $a$, $2^{nd}$ be $b$, $3^{rd}$ be $c$ & $4^{th}$ be $d$.

It is given that the difference in heights among the first three men was $2$ inches and the difference between the third and the fourth man was $6$ inches, therefore, we have:

$a=a$

$b=a+2$

$c=b+2=a+2+2=a+4$

$d=c+6=a+2+2+6=a+10$

It is also given that the average height was $74$ inches, which means that

$74=\frac{a+b+c+d}{4}\Rightarrow 74=\frac{a+a+2+a+4+a+10}{4}\Rightarrow 74=\frac{4a+16}{4}\Rightarrow 74=\frac{4(a+4)}{4}$

$\Rightarrow 74=a+4\Rightarrow a=74-4\Rightarrow a=70$

Thus,

$b=a+2=70+2=72$

$c=a+2+2=70+2+2=74$

$d=a+2+2+6=70+2+2+6=80$

Hence, the height of the fourth man is $80$ inches.