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QUESTION

CSAT

Easy

Maths

Prelims 2026

A toy TT jumps forward or backward. In each forward jump, it moves 5′5' forward whereas in each backward jump, it moves 2′2' backward. If in 3131 jumps, TT moves exactly 15′15' forward, then what is the difference of the number of forward and backward jumps?

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Explanation

Answer: D — 9

Let ff = forward jumps, bb = backward jumps.

Set up.

  • Total jumps: f+b=31f + b = 31
  • Net displacement: 5f−2b=155f - 2b = 15

Solve.

Substitute b=31−fb = 31 - f:

5f−2(31−f)=15  ⇒  7f−62=15  ⇒  f=115f - 2(31 - f) = 15 \;\Rightarrow\; 7f - 62 = 15 \;\Rightarrow\; f = 11

So b=20b = 20. The difference is ∣f−b∣=∣11−20∣=9|f - b| = |11 - 20| = 9.

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