1. In a 600 m race A beats B by 60 m and in a race of 500 m B beats C by 25 m. By how many metres will A beat C in a 400 m race.
Sol:
2. In a 100 m race, A runs 2.5 m/sec. If A gives B a start of 10 m and still beats him by 5 sec. Find the speed of B.
Sol:
time taken by A to completer the race = \(\frac{{10}}{{2.5}}\) = 40 sec
B is beaten by 5 sec ⟹ time taken by B to completer race = 40 + 5 = 45 sec
& distance covered by B = 100 – 10 = 90 m
∴ speed of B = \(\frac{{90}}{{45}}\) = 2m/sec Answer
3. A runs 100 m in 15 seconds and B runs the same distance in 20 seconds. By what distance will A beat b in 100 m race.
Sol:
Speed of B = \(\frac{{1000}}{{20}}\) = 5 m/sec
A reaches end point in 15 sec. At that time B will cover a distance of 15 × 5 = 75 m
∴ A will beat B by 100 – 75 = 25m Answer
4. In a linear race of 1000m, A beats B by 50m or 5 sec. What is the difference between the speeds of A and B ?
Sol:
∴ Speed of B = \(\frac{{50}}{5}\) = 10 m/sec
time taken by B = \(\frac{{1000}}{9}\) = 100 sec
Since A beats B by 5 sec ⟹ A takes 5 sec less than B
∴ time taken by A = 100 – 5 = 95 sec
speed of A = \(\frac{{1000}}{{95}}\) = \(\frac{{200}}{19}\)
∴ required difference = speed of A – speed of B = \(\frac{{200}}{{19}}\) – 10 = \(\frac{{10}}{{19}}\) sec Answer
5. In a 2100 m race A reaches finish point in 55 sec, while B reaches the finish point in 77 sec. By how much distance A beats B ?
Sol:
Speed of B = \(\frac{{2100}}{{77}}\) m/sec
Since A reaches end point first in 55 sec ⟹ In this time B will run distance = \(\frac{{2100}}{{77}} \times 55\) = 1500 m
∴ A beats B by 2100 – 1500 = 600 m Answer
6. In a race of 100 m, A beats B by 20 m and B beats C by 20 m. By how much distance does A beat C ?
Sol:
7. In a 1800 m race A beats B by 300 m and B beats C by 1000 m. By how much distance does A beat C ?
Sol:
8. In a 1200 m race, bike A beats bike B by 100 m. Bike B beats bike C by 100 m in a 600 m race. If bike A beats bike C by 30 sec in a 720 m race then what is the speed of bike C ?
Sol:
∴ C is beaten by 170 m or 30 sec
∴ Speed of C = \(\frac{{170}}{{30}}\) = \(\frac{{17}}{3}\) m/sec Answer
9. In a linear race of 400 m, A can beat B by 100 m and in a race of 500 m, B cacn beat C by 100 m. By how much metres will A beat C in a race of 200 m ?
Sol:
10. In a 150 m race, if A gets a 5 m headstart, then he would beat B by 35 m. If B gets a 25 m headstart in a 100 m race then who will win the race and by how many metres ?
Sol:
In t time distance covered by A = 150 – 5 = 145 m
In t time distance covered by B = 150 – 35 = 115 m
this means in the same time if A travells 29m, B will travell 23 m.
B will travel 75 m in \(\frac{{75}}{{23}}\) time & in this time A will travel = \(\frac{{75}}{{23}}\)×29 = 94.56 m i.e. < 100
So B will finish the race first.
∴ B will win the race by 100 – 94.56 = 5.44 m Answer