माना कि p, q, r और s इस प्रकार की प्राकृतिक संख्याएँ हैं कि
p - 2016 = q + 2017 = r - 2018 = s + 2019
है। निम्न में से कौन-सी सबसे बड़ी प्राकृतिक संख्या है?
सही उत्तर: (d) s
माना कि p - 2016 = q + 2017 = r - 2018 = s + 2019 = k है। इससे हमें प्राप्त होता है: p = k + 2016, q = k - 2017, r = k + 2018, और s = k - 2019। स्पष्ट है कि r में k में सबसे बड़ी संख्या (2018) जोड़ी जा रही है, अतः r सबसे बड़ी प्राकृतिक संख्या है।
In English (Question & Model Answer)
Let p, q, r and s be natural numbers such that
p - 2016 = q + 2017 = r - 2018 = s + 2019
Which one of the following is the largest natural number?
Correct Option: (d) s
Let p - 2016 = q + 2017 = r - 2018 = s + 2019 = k (where k is a constant). Then we can express each variable in terms of k: p = k + 2016, q = k - 2017, r = k + 2018, s = k - 2019. Comparing the values for any given integer k: p is k plus 2016, q is k minus 2017, r is k plus 2018, and s is k minus 2019. Wait! Let's re-verify carefully: If p - 2016 = k, then p = k + 2016. If q + 2017 = k, then q = k - 2017. If r - 2018 = k, then r = k + 2018. If s + 2019 = k, then s = k - 2019. Clearly, r has the largest added value (+2018), making r the largest natural number. Wait, let's check option (c) which corresponds to r. Let's double check: if p - 2016 = q + 2017, then p = q + 4033, so p > q. If p - 2016 = r - 2018, then r = p + 2, so r > p. If r - 2018 = s + 2019, then r = s + 4037, so r > s. Thus r is unequivocally the largest natural number.