**Find solutions for all the questions at the end of each set:**

### Set A

1. A person travels 285 km in 6 hr. In the first part of the journey, he travels at 40 km/hr by bus. In the second part, he travels at 55 km/hr by train. The distance traveled by train is

(a) 156 km

(b) 165 km

(c) 615 km

(d) 561 km

2. A car covers four successive 6 km stretches at speeds of 25 kmph, 50 kmph, 75 kmph and 150 kmph respectively. Its average speed over this distance is

(a) 55 kmph

(b) 50 kmph

(c) 75 kmph

(d) 150 kmph

3. The speeds of three cars are in the ratio 3 : 4 : 5. The time taken by each of the them to travel the same distance is in the ratio;

(a) 12 : 15 : 20

(b) 3 : 4 : 5

(c) 20 : 15 : 12

(d) 5 : 4 : 3

4. A certain distance is covered by a cyclist at a certain speed. If a jogger covers half the distance in double the time, the ratio of the speed of the jogger to that of the cyclist

(a) 1 : 2

(b) 2 : 1

(c) 1: 4

(d) 4 : 1

5. Walking at 5 km/hr a student reaches his school from his house 15 minutes early and walking at 3 km/hr is late by 9 minutes. What is the distance between his school and his house?

(a) 5 km

(b) 8 km

(c) 3 km

(d) 2 km

6. A man has to be at a certain place at a certain time. He finds that he shall be 20 minutes late if he walks at 3 km/h speed and 10 minutes earlier if he walks at a speed of 4 km/h. The distance he has to walk is

(a) 24 km

(b) 12. 5 km

(c) 10 km

(d) 6 km

7. Shri X goes to his office by scooter at a speed of 30 km/h and reached 6 minutes earlier. If he goes at a speed of 24 km/h, he reaches 5 minutes late. The distance to his office is

(a) 20 km

(b) 21 km

(c) 22 km

(d) 24 km

8. If a man walks 3 km/hour, he is late to his office by 20 minutes. If he increases his speed to 6 km/hour, he reaches the office 30 minutes early. The distance of his office from the starting place is

(a) 6 km

(b) 5 km

(c) 5.5 km

(d) 4 km

9. A and B walk on a circular path whose circumference is 35 km. They start walking from the same place in the same direction at the same time. Speed of A is 4 km/hr and speed of B is 5 km/hr. They will meet earliest again after.

(a) 15 hours

(b) 21 hours

(c) 35 hours

(d) 42 hours

10. Four runners started running simultaneously from a point on a circular track. They took 200 sec, 300 sec, 360 sec and 450 sec to complete one round. After how much time to they meet at the starting point for the first time?

(a) 1800 Seconds

(b) 3600 Seconds

(c) 2400 Seconds

(d) 4800 Seconds

Answers and solutions:

1. (b)

Let distance traveled by train be x km

so (285-x)/40 + x/55 = 6

=> x = 165 km

2. (b)

Total distance = 4*6 = 24 km

Total time = 6/25 + 6/50 + 6/75 + 6/150 = 72/150 hr.

so The average speed = total distance /total time = 24/(72/150) = (24*150)/72 = 50 km/hr.

3. (c)

4. (d)

If the time taken by cyclist to cirtain distance is t

then jogger covers half distance in 2t time

then jogger covers total distance in 4t time

then the ratio between their time = t:4t = 1:4

so The ratio between their speeds = 4:1

5. (c)

Distance = Product of speed/Difference of speeds * time difference

= (5*3)/2 * 24/60 = 3 km

6. (d)

7. (c)

The distance= Product of speed/Difference of speeds * time difference

= (30*24)/6 * 11/60 = 22 km

8. (b)

9. (c)

The time taken by A in 1 round = 35/4 hrs.

The time taken by B in 1 round = 35/5 hrs.

so L.C.M. of 35/4 and 35/5 = 35

they will meet earlist again after 35 hours.

10.(a)

**Find solutions for all the questions at the end of each set:**

### Set B

1. A and B together can complete a piece of work in 18 days, B and C in 24 days and A and C in 36 days. In how many days, will all of them together complete the work?

(a) 16 cm

(b) 15 cm

(c) 12 cm

(d) 10 cm

2. A and B can do a piece of work in 72 days, B and C can do it in 120 days, and A and C can do it in 90 days. When A, B and C work together, how much work is finished by them in 3 days.

(a) 1/40

(b) 1/30

(c) 1/20

(d) 1/10

3. A can complete 2/3 of a work in 4 days and B can complete 3/5 of the work in 6 days. In how many days can both A and B together complete the work?

(a) 3

(b) 2

(c) 3 ¾

(d) 2 7/8

4. A, B and C can do a piece of work in 15, 20 and 24 days respectively. If they get R. 76 as the total wages, find the share of C.

(a) Rs.30

(b) Rs. 40

(c) Rs. 20

(d) Rs. 24

5. A alone can complete a work in 18 days and B alone in 15 days. B alone worked at it for 10 days and then left the work. In how many more days, will A alone complete the remaining work?

(a) 5

(b) 5 ½

(c) 6

(d) 8

6. A takes twice as much time as B and thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. The number of days required by B to do the work alone is

(a) 4

(b) 6

(c) 8

(d) 12

7. Working efficiency of P and Q for completing a piece of work are in the ratio 3 : 4. The number of days to be taken by them to complete the work will be in ratio:

(a) 3 : 2

(b) 2 : 3

(c) 3 : 4

(d) 4 : 3

8. A is 50% as efficient as B, C does half of the work done by A and B together. If C alone does the work in 20 days, then A, B and C together can do work in

(a) 5 2/3 days

(b) 6 2/3 days

(c) 6 days

(d) 7 days

9. If 10 men or 18 boys can do a work in 15 days, then the number of days required by 15 men and 33 boys to do twice the work is

(a) 9

(b) 36

(c) 4 ½

(d) 8

10. If 12 men or 18 women can reap a field in 14 days, then working at the same rate, 8 men and 16 women can reap the same field in:

(a) 9 days

(b) 5 days

(c) 7 days

(d) 8 days

Answers and Solution:

1. (a)

Workdone by A and B in 1 day = 1/18

Workdone by B and C in 1 day = 1/24

Workdone by C and A in 1 day = 1/36

so Workdone by 2(A, B and C) in 1 day = 1/18 + 1/24 + 1/36 = 9/72

so Workdone by A, B and C in 1 day = 9/(72*2) = 9/144 = 1/16

so all of them together complete the work in 16 days.

2. (c)

Workdone by (A + B) in 1 day = 1/72

Workdone by (B + C) in 1 day = 1/120

Workdone by (C + A) in 1 day = 1/90

so Workdone by 2(A + B + C) in 1 day = 1/72 + 1/120 + 1/90 = 1/30

so Workdone by (A + B + C) in 1 day = 1/(30*2) = 1/60

so Workdone by (A + B + C) in 3 day = = 1/60 *3 = 1/20

3. (c)

A can complete 2/3 of a work in 4 days

A can complete the whole of a work in (4*3)/2 = 6 days

similarly B can complete the whole of a work in (6*5)/3 = 10 days

so Workdone by A and B in 1 day = 1/6 + 1/10 = 4/15

so Days taken by A and B to complete the whole work = 15/4 = 3(3/4)

4. (c)

Ratio of share of A,B c = ratio of 1 day’s work

= 1/15 : 1/20 : 1/24

= 120*1/15:120*1/20 : 120*1/24 = 8:6:5

so sum of ratio turms = 8+6+5 = 19

so The share of C = 76*5/19 = Rs.20

5. (c)

6. (b)

Let B take x day to finish the work.

so A take 2x days and C takes 2x/3 days

so 1/2x + 1/x + 1/(2x/3) = 1/2

so x = 6

so The number of days required by B = 6 days

7. (d)

8. (b)

9. (a)

10 men = 18 boys => 5 men = 9 boys => 15 men = 27 boys

15 men and 33 boys = 27 boys + 33 boys = 60 boys

so 18 boys can do a work in 15 days……I

Let 60 boys can do twice work in x days…..II

so (18*15)/1 = (60*x)/2 => x = 9 days

10. (a)