Sunita cuts a sheet of paper into three pieces. Length of first piece is equal to the average of the three single digit odd prime numbers. Length of the second piece is equal to that of the first plus one-third the length of the third. The third piece is as long as the other two pieces together. The length of the original sheet of paper is

(a) 13 units
(b) 15 units
(c) 16 units
(d) 30 units ✓ UPSC's answer

Why the answer is (d)

• The single-digit odd prime numbers are 3, 5, and 7.

• The length of the first piece is the average of these numbers: (3 + 5 + 7) / 3 = 15 / 3 = 5 units.

• Let the length of the third piece be $x$. The length of the second piece is given as the first piece plus one-third of the third piece: $5 + x/3$.

• The problem states the third piece is as long as the other two pieces together: $x = 5 + (5 + x/3)$.

• Solving for $x$: $x = 10 + x/3 \Rightarrow 2x/3 = 10 \Rightarrow x = 15$ units.

• The total length is the sum of all three pieces: First (5) + Second ($5 + 15/3 = 10$) + Third (15) = 30 units.

Why the other options are wrong

(a) 13 units: 13 units is incorrect because the calculated lengths of the pieces are 5, 10, and 15, which sum to 30, not 13.
(b) 15 units: 15 units is incorrect because it equals only the length of the third piece, not the total length of the original sheet.
(c) 16 units: 16 units is incorrect because it does not match the sum of the derived piece lengths (5 + 10 + 15 = 30).

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.