In the sum ⊗ + 1⊗ + 5⊗ + ⊗⊗ + ⊗1 = 1⊗⊗ for which digit does the symbol ⊗ stand?

(a) 2
(b) 3 ✓ UPSC's answer
(c) 4
(d) 5

Why the answer is (b)

• Let the digit represented by ⊗ be $x$. The equation is $x + (10 + x) + (50 + x) + (10x + x) + (10x + 1) = 100 + 10x + x$.

• Simplify the left-hand side: $x + 10 + x + 50 + x + 11x + 10x + 1 = 24x + 61$.

• Simplify the right-hand side: $100 + 11x$.

• Equate both sides: $24x + 61 = 100 + 11x$.

• Solve for $x$: $13x = 39$, which gives $x = 3$.

• Therefore, the symbol ⊗ stands for the digit 3, corresponding to option (b).

Why the other options are wrong

(a) 2: Substituting 2 gives $2 + 12 + 52 + 22 + 21 = 109$, but the right side is $122$, so the equation does not hold.
(c) 4: Substituting 4 gives $4 + 14 + 54 + 44 + 41 = 157$, but the right side is $144$, so the equation does not hold.
(d) 5: Substituting 5 gives $5 + 15 + 55 + 55 + 51 = 181$, but the right side is $155$, so the equation does not hold.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.