Question 1

X covers 1 km in 8 min 40 s while Y covers the same distance in 10 min. By what distance does X defeat Y?

Accepted Answer

Clearly, X beats Y by 8 s. Distance covered by Y in 600 s = 1000 m (∵ 10 min = 600 s) Distance covered by Y 80 s. = (1000/600) x 80 = 400/3 m = 1331/3 m

Question 2

L can run 1 km in 10 min while M can run it in 12 min. How many metres start can L give M in a km race, so that the race may end in a dead heat?

Accepted Answer

Time taken by L to run 1 km = 600 s Time taken by M to run 1 km = 720 s ∴ L can give M a start of (720 - 600) = 120 s ∵ In 720 s, M runs 1000 m. In 120 s M runs = (1000/720) x 120 = 500/3 m = 1662/3 m Hence, L can give a start of 1662/3 m

Question 3

Yogesh can run 1km in 6 min 20 s and Vijay can cover the same distance in 6 min 40 s . By what distance can Yogesh beat Vijay?

Accepted Answer

Clearly, Yogesh beats vijay by 20 s. Distance covered by vijay in 400 s = 1000 m [∵ 6 min 40 s = 400 s] Distance covered by Vijay in 20 s = (1000/400) x 20 m = 50 m ∴ Yogesh beats Vijay by 50 m.

Question 4

In a game of 160 points, A can give 10 points to B and 30 points to C. How many points B can give C in a game of 60?

Accepted Answer

A : B = 160 : 150, A : C =160 : 130 B/C = (B/A) x (A/C) = (150/160) x (160/130) = 15/13 = 60 : 52 ∴ In a game of 60, B can give C = (60 - 52)= 8 points

Question 5

In a 200 m race, A can beat B by 50 m and B can beat C by 8 m. In the same race , A can beat C by what distance?

Accepted Answer

According to the question, A : B = 200 : 150 and B : C = 200 : 192 ∴ A : C = (A/B) x (B/C) = (200/150) x (200/192) = 200/144 So, A beats C by (200 - 177) = 56 m

Question 6

In a game of 200 points, A can give 40 points to B and 56 points to C. How many points can B give to C?

Accepted Answer

A : B = 200 : 160 A : C = 200 : 144 ∴ B/C = (B/A) x (A/C) = (160/200) x (200/144) = 160/144 = 10/9 = 200/180 Hence, B can give C 20 points

Question 7

A can run 100 metres in 27 seconds and B in 30 seconds. A will beat B by

Accepted Answer

Distance covered by B in 27 seconds = 100 x 27 / 30 = 90 m Hence, A will beat B by (100 – 90) = 10 m.

Question 8

A can run 440 m in 51 seconds and B in 55 seconds. By how many seconds will B win if he has 40 m start?

Accepted Answer

To reach the winning post B will have to cover the distance (440 – 40) = 400 m. Hence, time taken by B to cover 440 meter = 55 time taken by B to cover 1 meter = 55 / 440 time taken by B to cover 400 meter = 400 x 55 / 440 = 40 x 55/44 =10 x 55/11 = 10 x 5 time taken by B to cover 400 meter = 50 Sec. Since, A reaches the winning post in 51 sec. while B in 50 sec. So, B will win by 1 second.

Question 9

In a km race A can give B 50 m start and B can give C 40 m start. What start can A give C in a 2 km race?

Accepted Answer

∵ B runs 1000 m while C 960 m ∴ B runs 995 m while C 960 * 995 / 1000 = 912 m Now, A runs 1000 m while C 960 m ∴ A runs 2000 m while C 2000 * 912 / 1000 = 1824 m Hence, A can give C (2000 – 1824) = 176 m start.

Question 10

A can give B 40 m and C 82 m in a 880 m race while B can give C 9 seconds over the post, find the time C takes to run 880 m.

Accepted Answer

If A runs 880 meter then B runs 840 meters and C runs 798 meters. ∵ B runs 840 m while C 798 m ∴ B runs 880 m while C 798 * 880 / 840 = 836 m Now, 880 – 836 = 44 m Hence, C runs 44 m in 9 seconds ∴ C runs 880 m in 9 * 880 / 44 = 180 sec. = 3 min.

Question 11

A can give B 15 points, A can give C 22 points and B can give C 10 points. How many points make the game?

Accepted Answer

Let assume the game has P points. Then A has P points , B has (P – 15) and C has (P – 22) points and also if B has P points then C has (P – 10) points. Applying chain rule, P x P ( P – 22 ) = P ( P – 15) ( P – 10) ⇒ P2 – 22P = P2 – 25P + 150 ⇒ 3P = 150 ∴ P = 50

Question 12

In a game of 80 points, A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60?

Accepted Answer

∵ B scores 75 points while A 80 ∴ B scores 60 points while A = 80 x 60 / 75 = 64 Again, A scores 80 points while C = 65 ∴ A scores 64 points while C = 65 x 64 / 80 = 52 points Hence, in a game of 60, B can give C (60 – 52) = 8 points

Question 13

Two men A and B run a 500 m race, A having 140 m start, their speeds are as 3 : 4. Then, A wins by :

Accepted Answer

Here, A will have to cover a distance of (500 – 140) = 360 meters to reach the winning point while B 500 meters . A covers 3 while B covers 4. ∴ A covers 360 m while B covers 4 x 360/ 3 = 480 m Hence, B will be (500 – 480) = 20 m behind the winning post. ∴ A wins by 20 m.

Question 14

In a race of 600 m, A can beat B by 60 m and in a race of 500 m, B can beat C by 50 m. By how many meters will A beat C in a race of 400 m?

Accepted Answer

Clearly, if A runs 600 meters, B runs = 540 m. ∴ If A runs 400 m, B runs = 540 x 400 / 600 = 540 x 4 / 6 = 90 x 4 = 360 m Again, when B runs 500 m, C runs = 450 m ∴ When B runs 360 m, C runs = 450 x 360 / 500 = 45 x 36 / 5 = 9 x 36 = 324 m. ∴ A beats C by 400 - 324 = 76 m.

Question 15

In a race of 600 m, A can beat B by 60 m and in a race of 500 m, B can beat C by 50 m. By how many meter will A beat C in a race of 400 m?

Accepted Answer

If A runs 600 m, B runs 600 - 60 or, 540 m. If A runs 400 m, B runs = 540 x 400 / 600 = 360 m. Now, when B runs 500 m, C runs 500 - 50 = 450 m. ∴ When B runs 360 m, C runs = 450 * 360 / 500 = 324 m ∴ A beats C by 400 - 324 = 76 m.

Question 16

In a game A can give B 25 points in 75 and C 18 points in 90. How many points can C give B in a game of 120?

Accepted Answer

When A scores 75 points, B scores 50 points. When A scores 90 points, C scores (90 - 18) = 72 points. ∴ When A scores 75 points, C scores = 72 × 75 / 90 = 60 points. A : B : C = 75 : 50 : 60 C : B = 60 / 50 = 120 / 100 So, in a game of 120, C can give B (120 - 100) = 20 points.

Question 17

In a 500 m race, the ratio of speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:

Accepted Answer

To reach the winning post, A will have to cover a distance of (500 - 140). i.e, 360 m. While A covers 3 m, B covers 4 m. While A covers 360 m, B covers 4 × 360 / 3 = 480 m. So, A reaches the winning post while B remains 20 meter behind. ∴ A wins by 20 m.

Question 18

Two boys, A and B, runs at 4 1⁄ 2 and 6 Km an hour. A having 190 m start. The course being 1 Km, B wins by a distance of :

Accepted Answer

Speeds (in m/sec) of A and B are 9 / 2 * 5 / 18 = 5 / 4 and 6 * 5 / 18 = 5 / 3, respectively. A has a start of 190 m. So, A has to run 1000 - 190 = 810 m, while B 1000 m. Time taken by B to cover 1000 m = 3 5 × 1000 = 600 seconds. In this time, A covers 5 × 600 / 4 = 750 m. So, B reaches the winning post while A remains 810 - 750 = 60 m behind. ∴ B wins by 60 m.

Question 19

A and B take part in a 100 m race. A runs at 5 Km/h. A gives B a start of 8 m and still beat him by 8 sec. Speed of B is :

Accepted Answer

A's speed = (5 * 5 / 18) m/sec = 25 / 18 m/sec Time taken by A to cover 100 m = (100 * 18 / 25) sec = 72 seconds. ∴ B covers 92 m in 72 + 8 = 80 seconds. B's speed = (92 / 80 * 18 / 5) Km/h = 4.14 Km/h.

Question 20

From a point on a circular tract 5 Km long A, B and C started running in the same direction at the same time with speeds of 2 1⁄ 2 Km/h, 3 Km/h and 2 Km/h. respectively. Then on the starting point all three will meet again after :

Accepted Answer

A will reach at starting point in 5 * 2 / 5 = 2 hours ; B will reach at starting point in 5 / 3 hours ; C will reach at starting point in 5 / 2 hours ; Then, on the starting point all three will meet after the L.C.M. of 2, 5 / 3, 5 / 2, 10 / 1 = 10 hours.

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