If P = +, Q = –, R = ×, S = ÷, then insert the proper notations between the successive numbers in the equation 60_15_3_20_4 = 20 :
- (a) SPRQ
- (b) QRPS ✓ UPSC's answer
- (c) QRSP
- (d) SPQR
Why the answer is (b)
• The equation is 60 _ 15 _ 3 _ 20 _ 4 = 20, with P=+, Q=-, R=×, S=÷.
• Option (b) QRPS translates to: 60 - 15 × 3 ÷ 20 + 4.
• Following BODMAS, first perform division: 3 ÷ 20 = 0.15.
• Next, perform multiplication: 15 × 0.15 = 2.25.
• Then, perform subtraction: 60 - 2.25 = 57.75.
• Finally, perform addition: 57.75 + 4 = 61.75. Wait, let me re-evaluate the order. BODMAS: Division/Multiplication left to right, then Addition/Subtraction left to right.
• Let's re-calculate 60 - 15 × 3 ÷ 20 + 4.
• Step 1: 15 × 3 = 45.
• Step 2: 45 ÷ 20 = 2.25.
• Step 3: 60 - 2.25 = 57.75.
• Step 4: 57.75 + 4 = 61.75. This does not equal 20.
• Let me check the other options to ensure I haven't misread the key or the question logic. Perhaps the question implies a different order or I made a calculation error.
• Let's check Option (a) SPRQ: 60 ÷ 15 × 3 - 20 + 4. (60/15)=4, 4*3=12, 12-20=-8, -8+4=-4. No.
• Let's check Option (c) QRSP: 60 - 15 × 3 ÷ 20 + 4. Same as (b). Wait, QRPS is Q, R, P, S. QRSP is Q, R, S, P.
• Option (b) is Q, R, P, S: 60 - 15 × 3 + 20 ÷ 4.
• Let's re-read the option letters carefully. (b) QRPS. Q=-, R=×, P=+, S=÷.
• Equation: 60 - 15 × 3 + 20 ÷ 4.
• Step 1: 15 × 3 = 45.
• Step 2: 20 ÷ 4 = 5.
• Step 3: 60 - 45 + 5.
• Step 4: 15 + 5 = 20.
• This matches the result 20.
Why the other options are wrong
- (a) SPRQ
- Option (a) SPRQ results in 60 ÷ 15 × 3 - 20 + 4, which equals -4, not 20.
- (c) QRSP
- Option (c) QRSP results in 60 - 15 × 3 ÷ 20 + 4, which equals 61.75, not 20.
- (d) SPQR
- Option (d) SPQR results in 60 ÷ 15 + 3 × 20 - 4, which equals 56, not 20.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.