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

### Set A

1. A man travels first 50 km at 25 kmph, next 40 km at 20 kmph and then 90 km at 15 kmph. His average speed for the whole journey (in kmph) is:

(a) 25

(b) 20

(c) 18

(d) 40

2. A man walks at the rate of 5 km/hr for 6 hours and at 4km/hr for 12 hours. The average speed of the man (inkm/hr) is:

(a) 4

(b) 4(1/3)

(c) 4(1/2)

(d) 4(2/3)

3. A boy goes to the school with the speed of 3 kmph and returns with the speed of 2 kmph. If he takes 5 hours in all, then the distance (in kms) between the village and the school is:

(a) 6

(b) 7

(c) 8

(d) 9

4. A is twice as fast as B and B is thrice as fast as C is. The journey covered by C in 42 minutes will be covered by A in:

(a) 14 min.

(b) 7 min.

(c) 28 min.

(d) 54 min.

5. A certain distance is covered at a certain speed. If half of this distance is covered in double the time, the ratio of the two speeds is:

(a) 4 : 1

(b) 1 : 4

(c) 2 : 1

(d) 1 : 2

6. A train takes 18 seconds to pass completely through a station 162 m long and 15 seconds through another station 120 m long. The length of the train (in metres) is:

(a) 70

(b) 80

(c) 90

(d) 100

7. Two trains whose lengths are 180 m and 220 m respectively are running in directions opposite to one another with respective speeds of 40 km/hr and 50 km/hr. Time taken by them in crossing one another will be:

(a) 16 sec

(b) 17 sec

(c) 18 sec

(d) 22 sec

8. A man standing on a railway platform observes that a train going in one direction takes 4 seconds to pass him. Another train of same length going in the opposite direction takes 5 seconds to pass him. The time taken (in seconds) by the two trains to cross each other will be:

(a) 31/9

(b) 40/9

(c) 49/9

(d) 50/9

9. A man rows upstream 11 km and downstream 26 km taking 5 hours each time. The velocity of the current is:

(a) 1 km/hr

(b) 1.5 km/hr

(c) 2.5 km/hr

(d) 7.5 km/hr

10. A motor boat takes 2 hours to travel a distance of 9 km down the current and it takes 6 hours to travel the same distance against the current. The speed of the boat in still water and that of the current (in km/hr) respectively are:

(a) 3, 1.5

(b) 3, 2

(c) 3.5, 2.5

(d) 3, 1

Answers and Solution:

1. Total distance covered=(50+40+90)km=180 km.

Total time taken=(50/25+40/20+90/15)hrs=10 hrs.

∴ Average speed for the whole journey=(180/10)=18 kmph

2. Total distance covered=(5×6+4×12)km=78 km.

Total time taken=(6+12)hrs=18 hr.

∴Average speed=(78/18) km/hr=4(1/3) km/hr.

3. Let required distance be x km. Then,

x/3+x/2=5 → x=6 km.

4.Let C’s speed=x kmph, B’s speed=3x kmph & A’s speed = 6x kmph

∴ Ratio of speeds of A, B, C = 6x∶3x∶x = 6∶3∶1

Ratio of times taken=1/6 ∶ 1/3:1 = 1∶2∶6 .

If C takes 6 min, A takes 1 min.

If C takes 42 min, A takes (1/6×42) min = 7 min.

5.Let x km be covered in y hours. The,

1st speed=(x/y)kmph,2nd speed=(x/2 *1/2y)=(x/4y) kmph

∴ Ratio of speeds=x/y ∶ x/4y=1∶1/4=4∶1

6.Let the length of the train be x metres.

(x+162)/18 = (x+120)/15→15(x+162)=18(x+120)→x=90

7.Relative speed=(40+50)kmph=(90×5/18)m/sec =25 m/sec

Required time=Time taken to cover (180+220) m at 25 m/sec. =(400/25)=16 sec.

8.Let the length of each train be x metres.

The, speed of first=(x/4)m/sec, speed of 2nd=(x/5)m/sec

Relative speed=(x/4+x/5)m/sec=(9x/20)m/sec

Time taken to cross each other

=time taken to cover 2x metres at (5x/12)m/sec

=(2x*20/9x)sec=(40/9)sec.

9.Rate upstream=(11/5)kmph=2.2 kmph

Rate downstream=(26/5)kmph=5.2 kmph.

∴ Velocity of current=1/2(5.2-2.2)kmph=1.5 kmph.

10. Rate downstream=(9/2)kmph = 4.5 kmph

Rate upstream=(9/6)kmph=1.5 kmph

∴ Rate in still water=1/2(4.5+1.5)kmph=3 kmph

Rate in current=1/2(4.5-1.5)kmph=1.5 kmph

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

### Set B

1. In what ratio must 25% of alcohol be mixed with 50% of alcohol to get a mixture of 40% strength alcohol?

1) 1:2

2) 2:1

3) 2:3

4) 3:2

2. Find two mean proportionals between 2 and 54.

1) 6 and 18

2) 6 and 12

3) 12 and 18

4) 6 and 9

3. A man had 7 children, when their average age was 12 years, a child aged 6 years died. The average age of remaining six children is

1) 13 years

2) 10 years

3) 11 years

4) 14 years

4. The average marks obtained by 22 candidates in an examination are 45. The average marks of the first 10 candidates are 55 and those of the last eleven are 40. The number of marks obtained by the eleventh candidate is

1) 45

2) 0

3) 50

4) 47.5

5. A shop-keeper sold a sewing machine for Rs. 1,080 at a loss of 10%. At what price should he have sold it so as to gain 10% on it? (Rs.)

1) 1,069

2) 1,200

3) 1,230

4) 1,320

6. A man invested Rs.27,000 in 121/2% stock at 108, then his yield percentage is

1) 183/4%

2) 1131/54%

3) 15%

4) 81/2%

7. Sarita and Julie start walking from the same place in the opposite directions. If Julie walks at a speed of 21/2 km/hr and Sarita at a speed of 2km/hr, in how much time will they be 18 km apart?

1) 4.0 hrs

2) 4.5 hrs

3) 5.0 hrs

4) 4.8 hrs

8. Two trains 125 metres and 115 metres in length, are running towards each other on parallel lines, one at the rate of 33km/hr and the other at 39km/hr. How much time (in seconds) will they take to pass each other from the moment they meet?

1) 8

2) 10

3) 12

4) 15

9. A sum of money at compound interest will amount to Rs.650 at the end of the second year. The amount of money is

1) Rs.1,300

2) Rs.650

3) Rs.1,250 4) Rs.625

10. If two angles of a triangle are 210 and 380 , then the triangle is

1) Right-angled triangle

2) Acute-angled triangle

3) Obtuse-angled triangle

4) Isosceles triangle

Answers Key

1.(3)

2.(1)

3.(1)

4.(2)

5.(4)

6.(2)

7.(1)

8.(3)

9.(4)

10.(3)

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