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Train speed and distance calculation

CAT 2024 Slot 3 · Quantitative Ability · Easy · Arithmetic

This is an easy Quantitative Ability question from the CAT 2024 Slot 3 paper. It tests Arithmetic. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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A train travelled a certain distance at a uniform speed. Had the speed been 6 km per hour more, it would have needed 4 hours less. Had the speed been 6 km per hour less, it would have needed 6 hours more. The distance, in km, travelled by the train is

  1. A.

    780

  2. B.

    720

  3. C.

    640

  4. D.

    800

Answer

B

Explanation

Let uniform speed =s= s km/h, original time =t= t hours, distance D=s⋅tD = s \cdot t.

From condition 1: (s+6)(t−4)=st  ⟹  3t−2s=12(s + 6)(t - 4) = st \implies 3t - 2s = 12

From condition 2: (s−6)(t+6)=st  ⟹  s−t=6  ⟹  s=t+6(s - 6)(t + 6) = st \implies s - t = 6 \implies s = t + 6

Substituting s=t+6s = t + 6 into 3t−2s=123t - 2s = 12: 3t−2(t+6)=12  ⟹  t=24 hours3t - 2(t + 6) = 12 \implies t = 24 \text{ hours} s=30 km/hs = 30 \text{ km/h}

Distance D=30×24=720D = 30 \times 24 = 720 km.

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