Question

A Sumo Wrestler wants to gain weight. He eats 5 Eggs on day 1. He increases the number by 3 on day 2. He repeats the same thing for 'n' number of days. If the total number of Eggs consumed by him in 'n' days is 185, find 'n'.

• A. 45
• B. 20
• C. 10
• D. 35

Answer 1

The correct option is C

10

He eats 5 Eggs on day 1.
5 + 3 Eggs on day 2
5 + 3 + 3 Eggs on day 3
5, 8, 11, 14,..

The sequence of Number of Eggs consumed on each day forms an A.P with initial term equal to 5 and common difference equal to 3.

Given that total number of Eggs consumed in 'n' days is 185.
$\therefore$ Sum of n terms is also 185

$S_n=\frac{n}{2}(2a+(n-1\left)d\right)$
$185=\frac{n}{2}\left(2\right(5)+(n-1\left)3\right)$
$370=n(10+(n-1\left)3\right)$
$370=n(10+3n-3)$
$370=n(7+3n)$
$370=(7n+3n^2)$
$(3n^2+7n-370=0)$
$(3n^2-30n+37n-370=0)$
$\left(3n\right(n-10)+37(n-10)=0)$
$\left(\right(n-10\left)\right(3n+37)=0)$

$n=10$ or $n=-\frac{37}{3}$
Since the number of days can't be negative,

Number of days = 10.