In the sum
⊗ + 1⊗ + 5⊗ + ⊗⊗ + ⊗1 = 1⊗⊗
for which digit does the symbol ⊗ stand?
Answer & explanation
Answer: (b) 3
Write the symbol as a digit x and expand each number by place value. The sum becomes a simple linear equation, 24x + 61 = 100 + 11x, which gives x = 3.
- Let ⊗ = x. Then ⊗ = x, 1⊗ = 10 + x, 5⊗ = 50 + x, ⊗⊗ = 11x, ⊗1 = 10x + 1, and 1⊗⊗ = 100 + 11x.
- Left side = x + (10 + x) + (50 + x) + 11x + (10x + 1) = 24x + 61.
- 24x + 61 = 100 + 11x, so 13x = 39 and x = 3.
- Check: 3 + 13 + 53 + 33 + 31 = 133 = 1⊗⊗ with ⊗ = 3.
Remember · In symbol-for-digit sums, expand every number by place value and solve the resulting equation; then check it back.
Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·