ARITHMETIC ABILITY 3

Thursday, April 29, 2010

Read the questions carefully and pick the correct answer.


1.
"A game of 50" means a game in which the player scoring 50 points first is the winner. In a game of 50, A can give B 10 points. This means that when A scores 50, B scores 40 points. In a game of 50, A can give B 10 points, but B can give C 20 points. With the same efficiency how many points can A give C?
A.
30

B.
25
C.
40
D.
50
Answer & Explanation
Answer: Option A
Explanation:
A = 50pts., B = 40pts.B = 50pts., C = 30pts.l.c.m. of 50 and 40 is 200If B gets 200, A gets 250, C gets 150pts.If A gets 50, C gets 50*150/250 = 30pts.

2.
2 pipes X and Y fill a tub in 10 min and 15 min resp. Both are opened and at the end of 5 minutes X is turned off. How much time will the tub take to fill?
A.
3/2 min
B.
1/2 min
C.
4/3 min
D.
5/2 min

Answer & Explanation
Answer: Option D
Explanation:
Work done by x and y in 5 min = 5(10+15/150) = 5/6Remaining work = 1/6for doing 1/15 work, q takes 1 min.for doing 1/6 work,?1/6*1*15 = 5/2 min

3.
Walking at 2/3 of his usual speed a man is 2 hrs.late. Find his actual travel time.
A.
8 hours
B.
4 hours

C.
3 hours
D.
None of these
Answer & Explanation
Answer: Option B
Explanation:
Let time be t and speed be s.Distance travelled = st = 2/3 s*(t+2)t = 2/3 (t+2)t = 4hrs.

4.
A train after travelling 30 km from X meets with an accident and proceeds at 3/4 of the former speed and reaches by 45 min. late. Had the accident happened 10 kms further one, it would have arrived 15 min sooner. Find the original speed and distance.
A.
60 km

B.
30 km
C.
50 km
D.
20 km
Answer & Explanation
Answer: Option A
Explanation:
Let the speed be x.When speed becomes 3/4th of the usual time, time becomes 4/3 i.e. 1/3rd more of the usual time.1/3rd of usual time = 45min.1/3rd of usual time taken to travel by = 45-151/3rd of usual time taken to travel AB = 10kms = 15min.Usual time taken to travel 10km = 45 minusual speed = 10*60/45 = 40/3 km/hrUsual time taken to travel Ay = 45*3 =135 min = 2 hrs.15min.Distance = 40/3*135/60 = 90/3 = 30 kmTotal distance = 30+30 = 60km

5.
A cat sees a rat 50 metres away from her and moves in the opposite direction at a speed of 12 km/hr. A minute later the rat sees her and gives chase at a speed of 15 km/hr. How soon will the rat overtake her?
A.
5 min

B.
6 min
C.
2 min
D.
12 min
Answer & Explanation
Answer: Option A
Explanation:
12km/hr = 12*100/60 = 200 metres/minDistance of the cat from the rat = 50+200 = 250 metresSince both are moving in same direction, the rat gains 15-12 = 3km/hr i.e. 50 metres/minTime required to overtake = 250/50 = 5 min

6.
3 pipes can fill a reservoirin 10,15 and 20 hrs. resp. The first was opened at 5 a.m. , the second at 6 a.m., third at 7 a.m. When will the reservoir the filled?
A.
5:20 AM
B.
6:30 AM
C.
10:20 AM

D.
4:00 PM
Answer & Explanation
Answer: Option C
Explanation:
Let time be t hrs after 5a.m.6.5t-5 = 306.5t = 35t = 5 1/3 hrs.The resoirvoir will fill at 5a.m.+5 hrs20min = 10.20a.m.

7.
Rowing at a steady rate, a man travels downstream for an hour and covers 5 km. If he takes 1hr.20min. For the return journey. Find the speed of the current?
A.
0.625 km/hr

B.
0.325 km/hr
C.
0.75 km/hr
D.
None of these
Answer & Explanation
Answer: Option A
Explanation:
speed down the river = 5km/hrspeed up the river = 5/(1 1/3) = 3.75 km/hrspeed of the current = 1/2(5-3.75) = 0.625 km/hr

8.
If 15 men and 10 boys can do in 1 day as much work as 12 men and 20 boys. How much should a man be paid a day if a boy is to get Rs.10 a day?
A.
Rs. 30
B.
Rs. 33.33

C.
Rs. 40
D.
Rs. 45
Answer & Explanation
Answer: Option B
Explanation:
15m + 10b = 12m+20b3m = 10bmoney earned by 10 boys = Rs.100Rs.100 = money earned by 3 men.1 man should be paid 100/3 = Rs.33.33

9.
A cop after a robber who has 100m start. The cop runs 2 km in 8mins. And the thief 2 km in 12 mins. How far the thief has gone before he overtaken?
A.
200

B.
210
C.
250
D.
300
Answer & Explanation
Answer: Option A
Explanation:
The cop gains 1/8-1/12 = 1/24 km/min = 41 2/3 m/minTo gain 100m, time, 100/(41 2/3) = 2.4 minThe thief has gone ahead by 2.4*1/12*1000 = 200m

10.
The sides of a triangle are 5:6:7 and its area is 800 sqft. Find its sides?
A.
sqrt[800/sqrt(225)]
B.
sqrt[800/sqrt(216)]

C.
sqrt[800/sqrt(210)]
D.
sqrt[760/sqrt(220)]
Answer & Explanation
Answer: Option B
Explanation:
If the sides are 5x, 6x and 7xs = 18x/2 = 9xArea = sqrt[s(s-a)(s-b)(s-c)] = 800= sqrt[9x(9x-5x)(9x-6x)(9x-7x)] = 800x = sqrt[800/sqrt(216)]

11.
Find the area of the cyclic quadrilateral whose sides are 15,12,10 and 13 cms.
A.
30*sqrt(26)

B.
30*sqrt(20)
C.
10*sqrt(6)
D.
10*sqrt(2)
Answer & Explanation
Answer: Option A
Explanation:
s = a+b+c+d/2 = 50/2 = 25Area of the quadrilateral = sqrt(10*13*15*12) = 30*sqrt(26)cm2

12.
Cost of painting the 4 walls of a room 40ft.*15ft. At Rs.5 per square feet is Rs.7500. Find the height of the room?
A.
14 feet.
B.
13.63 feet

C.
15.72 feet
D.
21.2 feet
Answer & Explanation
Answer: Option B
Explanation:
Area of 4 walls = perimeter * height= 2(40+15)*h= 110*hArea = 7500/5 = 15001500 = 110hh = 13.63

13.
The areas of a trapezium of height 20 cm. Is 800 cm2. One parallel side is 10 cm. Longer than the other. Find the parallel side?
A.
35,45

B.
30,40
C.
45,35
D.
60,70
Answer & Explanation
Answer: Option A
Explanation:
Area = 1/2(sum of parallel sides * height)= 1/2 * sum of sides *20800 = 10*sum of parallel sides80 = sum of parallel sidesx + (x+10) = 80x = 35other side = 45

14.
Volume of a right circular cylinder is 450 cm3 and its curved surfaces area is 200 cm2. Find its radius?
A.
2.5 cm
B.
1.5 cm
C.
5 cm
D.
4.5 cm

Answer & Explanation
Answer: Option D
Explanation:
450/200200r = 900r = 4.5 cm

15.
Iron weighs 8 times the weight of steel . Find the diameter of an iron ball whose weight is equal to that of a ball of steel 16 inches diameter?
A.
6
B.
7.5
C.
9
D.
8

Answer & Explanation
Answer: Option D
Explanation:
density of steel is 1 i.e. iron is 8weight of iron ball = weight of steelvolume of iron * 8 = volume of steel * 1r3 * 8 = 512r3= 512/8 = 64r = 4diameter = 8

16.
A rectangle 5cm*3cm is rotated about its smaller edge as axis. Find the curved surface area and volume of solid generated?
A.
85,60
B.
35,40
C.
75,30
D.
30,75

Answer & Explanation
Answer: Option D
Explanation:
sc = 2*22/7*r*h = 2*22/7*5*3 = 30*22/7 cm2 volume = 22/7*r*r*h = 75*22/7 cm2

17.
A well 20m in diameter is dug 15m deep and earth is spread all around a width of 5m to form an embankment. Find the height of the embankment.
A.
69
B.
82

C.
80
D.
75
Answer & Explanation
Answer: Option B
Explanation:
New volume/old volume = (22/7*49*r*r*h)/(22/7*r*r*25*h) = 49/25If old is 25, new is 49, then increase is 24increase% = 24/25*100 = 96%

18.
The radius of a circular cylinder is increased 40%. Find the % increase in volume?
A.
95
B.
96
C.
72

D.
48
Answer & Explanation
Answer: Option C
Explanation:
Length of water column = 6000/60volume of water = 100*10*200 = 2*105m3weight of water = 2*105*1000kgs= 2*105 tons

19.
A river 10m deep 200m wide flows at the rate of 6km/hr. Find the metric tones of water running into the sea per minute?
A.
30000
B.
10000
C.
2*105

D.
2*104
Answer & Explanation
Answer: Option C
Explanation:
Length of water column = 6000/60 = 100m/minvolume of water = 100*10*200 = 2*10 5m3 Weight of water = 2*10 5 *1000kgs= 2*105 tons

20.
If the diameter of a cylinder is 14cm. And height is 10cm, then total surface area (in cm2) is:
A.
748

B.
896
C.
558
D.
468
Answer & Explanation
Answer: Option A
Explanation:
Total surface area of a cylinder = 2*22/7*r*h+2*22/7*r*r= 2*22/7*7*10+2*22/7*7*7= 440 + 308= 748

21.
The radius of a cylinder is 2m. And its length is 20m. The area of an iron sheet constructed from the cylinder is:
A.
88*(22/7)
B.
80*(22/7)

C.
36*(22/7)
D.
54*(22/7)
Answer & Explanation
Answer: Option B
Explanation:
2*22/7*r*h= 2*22/7*2*20= 80*22/7

22.
The sum of the radius of the base and height of a solid cylinder is 40m. If the total surface area of the cylinder is 1760 m2 its volume is:
A.
57003
B.
54203
C.
50823

D.
56003
Answer & Explanation
Answer: Option C
Explanation:
r+h = 402*22/7*r*r+2*22/7*r*h = 2*22/7*r(r+h)2*22/7*r(r+h) = 1760r = 7h = 33volume = 22/7*r*r*h = 22/7*7*7*33 = 5082 m 3

23.
The radii of 2 cylinders are in the ratio 3:4. Their heights are in the ration 2:3. The ratio of their volumes is
A.
1:2

B.
2:1
C.
3:4
D.
2:3
Answer & Explanation
Answer: Option A
Explanation:
Let 3r,4r be the radiiLet 2h, 3h be the height.Ratio of volumes = 1/2

24.
Two cylinders of equal volume have their heights in the ratio 2:3. Ratio of their radii is
A.
1:4
B.
1:sqrt(2)
C.
sqrt(2):1

D.
2:1
Answer & Explanation
Answer: Option C
Explanation:
Let heights = h,2hLet radii be r and R22/7*r*r*h = 2*22/7*R*R*hr*r = 2(R*R)r/R = sqrt(2)/1

25.
If a train runs at 20 km/hr, it reaches its destination late by 10 min. But if it runs at 30 km/hr, it is late by 2 min. only. The correct time for the train to complete its journey is:
A.
12 min
B.
8 min
C.
14 min

D.
15 min
Answer & Explanation
Answer: Option C
Explanation:
Let correct time be x.distance travelled in (x+10) min. at 20km/hrDistance travelled in (x+2) at 30km/hr(x+10)*20/60 = (x+2))*30/60x = 14 min.

26.
Two busess travel to a place 20 kmph and 40 kmhr. If the second bus takes 6 hrs. less than the fixed for the journey the length of the journey is:
A.
262 km
B.
240 km

C.
200 km
D.
271.5 km
Answer & Explanation
Answer: Option B
Explanation:
x/20-x/40 = 62x-x/40 = 6x = 240km

27.
A car travels a distance of 360km at a uniform speed. If speed of the car is 20km/hr more then time is 3 hrs. less.The original speed of car was:
A.
40

B.
45
C.
32
D.
37
Answer & Explanation
Answer: Option A
Explanation:
Let speed be x.360/x - 360/(x+20) = 3360(x+20)-360x = 3x(x+20)(x+60)(x-40)x = 40

28.
A man covers 30km partly at 4km/hr and 6km/hr. If he covers former distance 6km/hr and later at 4 km/hr,he could cover 2km more in the some time. Time taken to cover the whole distance in the original time is:
A.
3.75
B.
6.2

C.
5.5
D.
4.7
Answer & Explanation
Answer: Option B
Explanation:
Suppose the first distance is covered in x hours and 2nd distance in y hours.4x+6y = 306x+4y = 32Solving equations,x = 3.6 hrs.,y = 2.6 hrs.Total time = 6.2 hrs.

29.
A theif steals a car at 1p.m. and drives it at 20km/hr. The theft is discovered at 2p.m. The owners sets of another car at 30 km/hr, he will overtake the thief at:
A.
3:06 PM
B.
2:52 PM
C.
4:00 PM

D.
2:20 PM
Answer & Explanation
Answer: Option C
Explanation:
Distance covered by thief in 1hr. is 20km.Now 10 km will be compensated in 1 hr.,20 km will be compensated in 2 hrs.So, he overtakes the thief at 4p.m.

30.
The ratio between the rate of walking of x and y is 2:3. If the time taken by B to cover a certain distance is 24min, to cover the same distance A will take:
A.
32
B.
48
C.
16
D.
36

Answer & Explanation
Answer: Option D
Explanation:
1/2:1/3 = 3:2If y takes 2 min., x takes 3 mins.If y takes 24 min, x takes 24*3/2 = 36 min.

31.
125, 106, 89, 76, 65, _____
A.
56
B.
53
C.
58
D.
59
Answer & Explanation
Answer: Option @
Explanation:
No answer description available for this question

32.
5, 6, 3, 4, 1, ____
A.
2
B.
4
C.
-2
D.
6
Answer & Explanation
Answer: Option @
Explanation:
No answer description available for this question.

33.
12, 30, 105, 473, 2599, ____
A.
15913
B.
16892
C.
3654
D.
3564
Answer & Explanation
Answer: Option @
Explanation:
No answer description available for this question.

34.
13,20,140,147,1029, ____
A.
1056
B.
7203
C.
1033
D.
1036
Answer & Explanation
Answer: Option @
Explanation:
No answer description available for this question.

35.
The area of a triangle with base 36 cms is equal to the area of a circle of radius 21 cms. Determine the approximate height of the triangle.
A.
77 cm

B.
75 cm
C.
52 cm
D.
46 cm
Answer & Explanation
Answer: Option A
Explanation:
No answer description available for this question

36.
Pens at 20 Rs each and books at 40 Rs each were purchased. In all these were 6, at a total cost of Rs.180. If the number of Pens and books were interchanged, how much less would have been spent ?
A.
0
B.
same amount
C.
Rs. 2.50
D.
Rs. 6
Answer & Explanation
Answer: Option @
Explanation:
No answer description available for this question.
37.
123, 211,299,156,244,____
A.
325
B.
250
C.
332
D.
None of these
Answer & Explanation
Answer: Option @
Explanation:
No answer description available for this question.

38.
855,7695,69255,623295,_____
A.
5629653
B.
5609655
C.
6609655
D.
1608652
Answer & Explanation
Answer: Option @
Explanation:
No answer description available for this question.

39.
An empty jar weighs w1 gm. The jar half filled with a liquid weights w2 gm. Find the weight of the jar. Completely filled with the same liquid.
A.
2(w2-w1)
B.
2w+w1
C.
2w2-w1

D.
2(w2+w1)
Answer & Explanation
Answer: Option C
Explanation:
Weight of jar = w1gWeight of liquid = w2-wWeight of liquid(half filled with liquid) = w2-w1Weight of liquid filled = 2(w2-w1)Weight of jar + weight of liquid = w1+2(w2-w1)= 2w2-w1

40.
A person travels the first 1/3 of distance to be covered at a speed of x km/hr, the 2nd 1/3rd at 2x km/hr and the final 1/3rd at 3x km/hr. What is the average speed for the entire journey?
A.
x km/hr
B.
1/2*x km/hr
C.
2/3*x km/hr
D.
18/11*x km/hr

Answer & Explanation
Answer: Option D
Explanation:
In finding average speed, we use Harmonic mean.H.M.= 1/{1/3[1/x+1/2x+1/3x]}= 18x/11 km/hr.