Correct Option (3)
Let the common value of the given expression be k.
p−2016=q+2017=r−2018=s+2019=k
From this, each variable can be expressed in terms of k:
- p=k+2016
- q=k−2017
- r=k+2018
- s=k−2019
To identify the largest natural number, we compare the constant terms associated with k. The constants are +2016, −2017, +2018, and −2019. The largest among these constants is +2018. Consequently, r=k+2018 represents the largest natural number.
Incorrect Options:
Based on the expressions derived:
- p=k+2016
- q=k−2017
- s=k−2019
Comparing these with r=k+2018:
- Since 2016<2018, p is less than r.
- Since −2017<2018, q is less than r.
- Since −2019<2018, s is less than r.
The complete order from smallest to largest is s<q<p<r. Therefore, p,q, and s are not the largest natural numbers.