The speed of a train is 110 kmph. Find the distance covered by the train in 100 seconds.

Correct — B. The time is in seconds, so convert the speed to metres per second first.

1 km/h = 1000 m ÷ 3600 s = 5⁄18 m/s
110 km/h = 110 × 5⁄18 = 550⁄18 ≈ 30.56 m/s

Distance = speed × time = 550⁄18 × 100
= 55,000⁄18 = 3055.55… ≈ 3055.56 m → option (b)

Why the others are wrong

• (a)
  3051 m — 3051 m in 100 s is 30.51 m/s, and 30.51 × 18⁄5 ≈ 109.84 km/h, not 110. It is 4.56 m short of the exact figure.
• (c)
  3011.56 m — 3011.56 m in 100 s is about 30.12 m/s, or about 108.4 km/h. A train at 110 km/h covers 44 m more in the same 100 s.
• (d)
  3000.56 m — 3000.56 m in 100 s is about 30.01 m/s, roughly 108 km/h. That is 55 m short of what a 110 km/h train covers.

Distance = speed × time works only when the units agree. Speed here is in km/h and time in seconds, so one of them must change.

Multiply km/h by 5⁄18 to get m/s, and m/s by 18⁄5 to get km/h. The factor is 1000 m ÷ 3600 s = 5⁄18.

Keep 550⁄18 as a fraction until the last step, because the options differ only in the decimals.

Key facts

• km/h × 5⁄18 = m/s, and m/s × 18⁄5 = km/h.
• 36 km/h = 10 m/s and 72 km/h = 20 m/s.
• 110 km/h = 550⁄18 ≈ 30.56 m/s.

Common traps

• Multiplying by 18⁄5 instead of 5⁄18. That gives 396 m/s and a distance of 39,600 m, far above every option.
• Rounding the speed first. 30.56 m/s × 100 gives 3056 m, not 3055.56 m, so keep 550⁄18 exact until the end.

No directly related past PYQ was found.