Model 5 Problems with Races Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (c)

According to the question,

Since, When B runs 200 m metres, A runs 190 metres

When B runs 180 metres, A runs

= $190/200 × 180$ = 171 metres

When C runs 200m, B runs 180 metres.

Hence, C will give a start to A by

= 200 - 171 = 29 metres

Answer: (d)

According to the question,

When A runs 800 metres, B runs 760 metres

When A runs 200 metres, B runs

= $760/800 × 200$ = 190 metres

Again, when B runs 500 metres, C runs 495 metres.

When B runs 190 metres, C runs

= $495/500 × 190$ = 188.1 metres

∴ Hence, A will beat C by

200 - 188.1 = 11.9 metres in a race of 200 metres.

Answer: (a)

Let the time taken to complete the race by A,B, and C be x minutes.

Speed of A = $1000/x$,

B = ${1000 - 50}/x = 950/x$

C = ${1000 - 69}/x = 931/x$

Now, time taken to complete the race by

B = $1000/{950/x} = {1000 × x}/950$

and distance travelled by C in

${1000x}/950$ min = ${1000x}/950 × 931/x$ = 980 km.

B can allow C

= 1000 - 980 = 20 m

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

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

Answer: (a)

Required time

= LCM of 40 and 50 seconds

= 200 seconds