A toy T jumps forward or backward. In each forward jump, it moves 5' forward whereas in each backward jump, it moves 2' backward. If in 31 jumps, T moves exactly 15' forward, then what is the difference of the number of forward and backward jumps?
- (a) 6
- (b) 7
- (c) 8
- (d) 9 ✓ UPSC's answer
Why the answer is (d)
• Let f be the forward jumps and b the backward jumps: f + b = 31.
• Net movement: 5f − 2b = 15.
• Substituting b = 31 − f: 5f − 62 + 2f = 15, so 7f = 77, f = 11 and b = 20.
• The difference is 20 − 11 = 9: (d).
Why the other options are wrong
- (a) 6
- The jumps are 11 forward and 20 backward, so the difference is 9, not 6.
- (b) 7
- The difference is 20 − 11 = 9, not 7.
- (c) 8
- The difference is 20 − 11 = 9, not 8.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.