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Races and Games

Theory and Formula


Question


Q1. In a 1000 m race A can beat B by 100 m and C by 200 m . In the same race, B can beat C by _________ m .

(a) 111.1 m

(b) 100 m

(c) 141.2 m

(d) 136.89 m

Solution. a
As per question , A:B:C = 1000:900:800

= 10:9:8

In the race means distance of 1000 m . Now convert ratio of B and C with respect to 1000 m .

B:C = 900:800

B/C
=
900/800
=
900 x
1000/900
/800 x
1000/900
=
1000/888.9


Clearly B beats C by 111.1 m .
Solution

Q2. In a race of 100 m , A beat B by 10 m and C by 15 m . In a race of 200 m A beats C by _____ m .

(a) 20

(b) 30

(c) 15

(d) 10

Solution. b
As per question A:B:C = 100:90:85

clearly in 100m race A beats B by 15 m .

So in 200 m Race A beats C by 30 m .
Solution

Q3. In a race of 100 m , A runs at 5m/s . A gives a start of 10 m and still beats him by 5 sec. Find the speed of B ?

(a) 16km/h

(b) 14 km/h

(c) 12.96 km/h

(d) 13.4 km/h

Solution.
A will take
100/5
= 20 sec to cover 100 m race

As per question B will cover 90 m in 25 sec

So B's speed is
90/25
m/s =
90/25
x
18/5
km/h

=
1620/125
km/h

= 12.96 km/h
Solution

Q4. In a game of 100 points , A can give B 25 points and C 30 points . then how many points can A gives B .

(a) 25

(b) 30

(c) 20

(d) 35

Solution. a
A:B:C = 100:75:70

A gives B 25 points in 100 points .
Solution

Q5. In a game of billiards , A can gives B 3 points in 10 points and A can give C 5 points in 20 points . How many points can C give B in a game of 150 points .

(a) 140

(b) 150

(c) 130

(d) 120

Solution.b
As per question A:B = 10:7 = 20:14

A:C = 20:15

A:B:C = 20:14:15

C:B = 15:14

C:B = 15 x 10:14 x 10

C:B = 150:140

Clearly C gives B 10 points in 150 points .
Solution