Question
"PQR is a three-digit number such that it can be
expressed as the sum of its three two-digit components, PQ, QR, and RP, where all of them are natural numbers. We want to determine the maximum possible value of (P + 6Q + 4R) for PQR."Solution
Let PQR be (100p + 10q + r) where 'p', 'q' and 'r' are integers between (0 - 9). ATQ; 100p + 10q + r = (10p + q) + (10q + r) + (10r + p) Or, 100p + 10q + r = 11p + 11q + 11r So, 89p - q = 10r And, values of 'p', 'q' and 'r' must lie between 0 and 9. At p = 0, -q = 10r (Since, 'q' cannot be negative, this is never possible) At p = 1, 89 - q = 10c Maximum value of q = 9, So, 89 - 9 = 10r Or, r = 8 So, one possible pair of (p, q, and r) is (1, 9 and 8) Now at p = 1, the value of 10r will never be a multiple of 10, as the value of 'q' cannot exceed 9. So, only one pair would exist at p = 1. At p = 2, 178 - q = 10r Now, for any value of 'q', the value of '10r' would exceed 100, meaning the value of 'r' would exceed 9. So, 'p' cannot be more than 1. So, only pair of 'p', 'q' and 'r' that would satisfy the equation is 1, 9 and 8. So, required value = 1 + (6 × 9) + (4 × 8) = 1 + 54 + 32 = 87
What is the main benefit of the Geographical Indication (GI) tag for the Ajrakh craft from Kutch?
Border Security Force’s commemorated its ____ Raising day on 1 December 2021.
Recently Reserve Bank of India (RBI) accepted the Centre’s request for allowing non-financial institutions and non-regulated entities to own more ...
As per the Union Budget, the subsidy under the FAME scheme for fiscal 2024 is projected at _______ as compared with the revised estimate of Rs 2,897 cro...
Recently IDS has unveiled the Bharat Blockchain Network and Polyversity . IDS is based in which country?
Which fundamental right allows Indian citizens to reside and settle in any part of the country?
What is the title of the short film made by the Sports Authority of India on the athletes participating in the Asian Games?
Which day is celebrated as ‘No Smoking Day’ every year?
Which bank has launched an exclusive NR savings account scheme named NRE Eve+, specifically curated for NRI women designed to cater to the unique fina...
The "Vivadon Ka Samadhan" initiative, introduced by the Chief Minister of Haryana, aims to address issues related to which area?