NDA Mathematics Question (2025) — Solution

Step-by-step solution

Given p = _ j=1 ^ n _ 10 2^j and q = _ j=1 ^ n _ 10 5^j. Simplifying p and q: p = _ j=1 ^ n j _ 10 2 = _ 10 2 _ j=1 ^ n j = n(n+1) 2 _ 10 2 q = _ j=1 ^ n j _ 10 5 = _ 10 5 _ j=1 ^ n j = n(n+1) 2 _ 10 5 Adding p and q: p + q = n(n+1) 2 ( _ 10 2 + _ 10 5) = n(n+1) 2 _ 10 (2 5) = n(n+1) 2 _ 10 10 Since _ 10 10 = 1, we get: p + q = n(n+1) 2 Given p + q = 15, we have: n(n+1) 2 = 15 Now, finding q - p: q - p = n(n+1) 2 _ 10 5 - n(n+1) 2 _ 10 2 q - p = n(n+1) 2 ( _ 10 5 - _ 10 2) q - p = 15 _ 10 ( 5 2 ) q - p = 15 _ 10 2.5