Time & Work, Speed & Distance — Practice

Question 1

A does a job in 10 days, B in 15. Working together they finish in:
(a) 5 days  (b) 6 days  (c) 7.5 days  (d) 8 days

Accepted Answer

LCM 30; rates 3+2=5/day ⇒ 30/5 = 6.

Answer: (b) 6 days.

Question 2

A is 50% more efficient than B and finishes a job in 12 days. B alone takes:
(a) 8 days  (b) 15 days  (c) 18 days  (d) 24 days

Accepted Answer

Efficiency A:B = 3:2 ⇒ times inverse 2:3. A=12 ⇒ B = 12×3/2 = 18.

Answer: (c) 18 days.

Question 3

A man covers a distance in 6 hours at 40 km/h. To cover it in 4 hours his speed must be:
(a) 50  (b) 55  (c) 60  (d) 65 km/h

Accepted Answer

Distance = 240 km; speed = 240/4 = 60 (or 40 × 6/4).

Answer: (c) 60 km/h.

Question 4

A 150 m train at 54 km/h crosses a 250 m platform in:
(a) 24 s  (b) 26.67 s  (c) 20 s  (d) 30 s

Accepted Answer

54 km/h = 15 m/s; distance = 400 m ⇒ 400/15 = 26.67 s.

Answer: (b) 26.67 s.

Question 5

Two trains 120 m and 180 m long move in opposite directions at 40 and 50 km/h. Time to cross each other:
(a) 10 s  (b) 12 s  (c) 15 s  (d) 8 s

Accepted Answer

Relative speed = 90 km/h = 25 m/s; total length = 300 m ⇒ 300/25 = 12 s.

Answer: (b) 12 s.

Question 6

A boat's downstream speed is 20 km/h and upstream 12 km/h. Speed of boat in still water and stream:
(a) 16, 4  (b) 14, 6  (c) 18, 2  (d) 15, 5

Accepted Answer

b = (20+12)/2 = 16; s = (20−12)/2 = 4.

Answer: (a) 16, 4.

Practice — Time & Work, Speed & Distance