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?
Answer & explanation
Answer: (d) 9
Let f forward and b backward jumps: f + b = 31 and 5f − 2b = 15. This gives f = 11 and b = 20, so the difference is 9.
- f + b = 31 and 5f − 2b = 15.
- Substitute b = 31 − f: 5f − 62 + 2f = 15, so 7f = 77 and f = 11.
- b = 31 − 11 = 20.
- Difference = 20 − 11 = 9 (more backward jumps than forward).
- Check: 11 × 5 − 20 × 2 = 55 − 40 = 15′ forward.
Remember · Two unknowns, two facts (count and net result): write both equations and eliminate one variable.
Question and answer: UPSC's provisional GS Paper II (2026, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·