#### Ques 1.

A is 1 3/5 times quicker than B. A gives B a start of 75 metres, find the length of racecourse so that both of them reach the winning post at the same time.

**Sol.** Let the length of Racecourse be/m.

. . In a time in which A covers *i *m, B covers (I-75)m

let speed of B be x. Speed A = 8/5 x As time is same for both we have :

#### Ques 2.

In a game of snooker A can give B 16 points in 80 and A can give C 15 points in 90.How many points can C give B in a game of 50 ?

**Sol. ** When A 80 points B scores 64 points.

When A scores 90 points B scores 64/80x90 points = 72 points.

i.e. when C scores 75 points B scores 72 points.

.. When C scores 50 points B scores 72/75 x 50 points = 48 points .

Hence c give B 2 points in a game of 50.

#### Ques 3.

P can run 100 m in 20 seconds and Q in 25 seconds .P beats Q by.

(a) 10 m

(b) 20 m

(c) 25 m

(d) 12 m

**Sol. ** 20 m

**Hint: **In 20 seconds Q runs = 100/25 x 20 m

#### Ques 4.

In a 2 km race, P can give Q 200 m and R 560 m. In the same race, Q can give R

(a) 400 m

(b) 300 m

(c) 350 m

(d) 500 m

**Sol. ** 400 m

**Hint :** When Q runs ( 2000-200)m, R suns (2000-560)m.

#### Ques 5.

A runs 1.5 times as fast as B can. If A gives B a start of 50m, how far must the winning post be in order that A and B reach at the same time ?

(a) 150 m

(b) 120 m

(c) 125 m

(d) 180 m

**Sol.** 150 m

**Hint :** d-50/s = d/1.5s

#### Ques 6.

P and Q run a kilometre and P wins by 1 minute . P and R run a kilometre and P wins by 375 m. Q and R run a kilometre and Q wins by 30 seconds. Find the time taken by each runner to run a kilometre.

(a) 150 sec, 210 sec, 240 sec

(b) 120 sec, 160 sec, 200 sec

(c) 100 sec, 160 sec, 190 sec

(d) 140 sec, 200 sec, 230 sec

**Sol.** 150 sec, 210 sec, 240 sec

**Hint : **Let teh speed of P ,Q and R be p,q and r ms-1 respectively.

#### Ques 7.

A can give B 25 points,A can give C 40 points and B can give C 20 points .How many points make of the game ?

(a) 120

(b) 100

(c) 150

(d) 80

**Sol.** 100

**Hint :** Let the game be of X points.

when A scores x points, B scores x -25 points, and C scores X - 40 points.

#### Ques 8.

At a game of billiards, A can give B 12 points in a game of 40 and a can give C 10 points in a game of 50. How many points can C give B in a game of 80 ?

(a) 10

(b) 20

(c) 12

(d) 18

**Sol.** 10

**Hint:** When a scores 40 points, B scores ( 40-12) points.

When A scores 50 points , C scores ( 50-10) points.

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