MPSC Rajyaseva 2020 CSAT — Question 62

झिनाने एका स्तंभात चार नैसर्गिक संख्या लिहिल्या. प्रत्येक वेळी यातल्या तीन सर्वांना बेरजेच्या समान संधी मिळतील अशा प्रकारे निवडून तिने त्या त्रिकुटांची बेरीज केली आणि तिला 186, 206, 215 आणि 194 या बेरजा मिळाल्या. झिनाने लिहिलेली सर्वात मोठी संख्या निवडा. Zina has written down four natural numbers in column. She chose three of these numbers at a time such that all numbers had equal chances of getting added. Each triple she came up with sums 186, 206, 215 and 194. Select the largest number that Zina has written.

Let the four numbers be a, b, c, d. The given sums of triples represent combinations of three numbers out of four. Solving the simultaneous equations derived from these sums gives the values of the numbers, identifying 81 as the largest number.