IPMAT Rohtak 2020 (QA) - The height of nineteen people of comic book is in Arithmetic progression. The average height of them is 19 feet. If the tallest is 37 feet. Then what is the height of the shortest? | PYQs + Solutions

IPMAT Rohtak 2020

Algebra

Progression & Series

Medium

The height of nineteen people of comic book is in Arithmetic progression. The average height of them is 19 feet. If the tallest is 37 feet. Then what is the height of the shortest?

Correct Option: 2

According to the question:

\frac{a+a+d+a+2d...+a+18d}{19}=19

Finding the sum of everyone's height:

S_n=\frac{n[2a+(n-1)d]}{2}

=\frac{19[2a+18d]}{2}=19[a+9d]

So:

\frac{19[a+9d]}{19}=19

a+9d=19

--> Eq. 1

The tallest is 37 feet tall, hence

a+18d=37

--> Eq. 2

Subtracting Eq. 1 from Eq. 2, and we'll get

9d=18

d=2

Put it back into Eq. 1 and we'll get:

a+9(2)=19

\newline

a=19-18=1

Hence, the shortest person is 1 ft tall.