Model 5 Problems with Races Practice Questions Answers Test with Solutions & More Shortcuts

Question : 6 [SSC CGL Tier-I 2016]

A is faster than B. A and B each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 14 hours. Then A's speed is equal to:

a) 4 km/hr.

b) 7 km/hr.

c) 5 km/hr.

d) 3 km/hr.

Answer: (a)

Let, A's speed = x kmph.

B's speed = (7 - x) kmph

Time = $\text"Distance"/ \text"Speed"$

According to the question,

$24/x + 24/{7 - x} = 14$

$24({7 - x + x}/{x(7 - x)})$ = 14

${24 × 7}/{x(7 - x)}$ = 14

x (7 - x) = 12 = 4 × 3 or 3 × 4

x (7 - x) = 4 (7 - 4) or 3 (7 - 3)

x = 4 or 3

A's speed = 4 kmph.

Question : 7 [SSC SO 2007]

In a race of 1000 m, A can beat B by 100m. In a race of 400 m, B beats C by 40m. In a race of 500m. A will beat C by

a) 50 m

b) 60 m

c) 45 m

d) 95 m

Answer: (d)

When A runs 1000m, B runs 900m.

When A runs 500m, B runs 450 m.

Again, when B runs 400m, C runs 360 m.

When B runs 450m, C runs

= $360/400 × 450$ = 405 metres

Required distance

= 500 - 405 = 95 metres

Question : 8 [SSC CGL Tier-I 2016]

A and B start running at the same time and from the same point around a circle. If A can complete one round in 40 seconds and B in 50 seconds, how many seconds will they take to reach the starting point simultaneously ?

a) 200

b) 2000

c) 90

d) 10

Answer: (a)

Required time

= LCM of 40 and 50 seconds

= 200 seconds

Question : 9 [SSC CGL Tier-II 2015]

A is twice as fast as B, and B is thrice as fast as C is. The journey covered by C in 1$1/2$ hours will be covered by A in

a) 30 minutes

b) 10 minutes

c) 1 hour

d) 15 minutes

Answer: (d)

Time taken by C = t hours

Time taken by B = $t/3$ hours

and time taken by A = $t/6$ hours

Here, t = $3/2$ hours

∴ Required time taken by A

= $3/{2/6}$ hour = $1/4$ hour

= $(1/4 × 60)$ minutes = 15 minutes

Question : 10 [SSC CPO S.I.2007]

A runs twice as fast as B and B runs thrice as fast as C. The distance covered by C in 72 minutes, will be covered by A in :

a) 24 minutes

b) 12 minutes

c) 16 minutes

d) 18 minutes

Answer: (b)

Ratio of the speed of A, B and C = 6 : 3 : 1

Ratio of the time taken

= $1/6 : 1/3$ : 1 = 1 : 2 : 6

Time taken by A

= $72/6$ =12 minutes

IMPORTANT quantitative aptitude EXERCISES

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