A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? A.310 m B.350 m C.600 m D.490 m E.None of these
Answer
Answer – B (350 m) Explanation – when it cross a pole actually it is crossing itself
so, S = 300/18
let length of platform be “p”
relative speed = total lengths/time
speed of train = [300 + p ]/39
(300/18)x39=300 +p
650 -300=p
p=350 m
Note : in this type of question one thing is pole,man and other is of considerable length like platform ,bridge.
when train crosses pole,man it crosses itself
2.Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is: A.1 : 3 B.3 : 4 C.3 : 2 D.Data inadequate E.None of these
Answer
Answer – C (3 : 2) Explanation – Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
and length of the second train = 17y metres.
relative speed = total lengths/time
y – x = [27x + 17 y ]/23
23y -23x = 27x + 17 y
27x+23x= 23 y-17y
4x=6y
x/y=6/4=3/2= 3:2
3.Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is: A. 1: 2 B. 4 : 3 C. 7 : 8 D. 3 : 4 E. none of these
Answer
Answer- B (4:3) Explanation:
Let us name the trains as A and B. Then,
trick formula
(A’s speed) : (B’s speed) = square root of b : square-root of a =square-root of 16 : square-root of 9 = 4 : 3.
Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds? A.9 : 28 B.11 : 9 C.11 : 8 D.9 : 22 E.None of these
Solution
Answer – B (11 : 9) Explanation – In the same time, they cover 110 km and 90 km respectively.Ratio of their speeds = 110 : 90 = 11 : 9
2. A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9.30 a.m.? A.15 B.8 C.7 D.10 E.None of these
Solution
Answer – C (7) Explanation – Relative speed = (2 + 3) = 5 rounds per hourSo, they cross each other 5 times in an hour and 2 times in half an hourHence, they cross each other 7 times before 9.30 a.m.
3.The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet? A.10:30 am B.10:45 am C.11 am D.11:25 am E.None of these
Solution
Answer – C (11 am) Explanation – Suppose they meet x hrs after 8 a.m.
Then, (Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs] = 330
60x + 75(x – 1) = 330
x = 3
So, they meet at (8 + 3), i.e. 11 a.m
4.The speed of a car increases by 2 kms after every one hour. If the distance travelled in the first one hour was 35 kms, what was the total distance traveled in 12 hours? A.456 kms B.482 kms C.552 kms D.556 kms E.None of these
Solution
Answer – C (552 kms) Explanation – Total distance travelled in 12 hours = (35 + 37 + 39 + …… upto 12 terms) This is an A.P. with first term,
a = 35, number of terms, n = 12, common difference, d =2.
Required distance =12/2 (2 x 35 + (12 – 1) x 2) = 6(70 + 22) = 552 kms
5.A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes? A.100 m B.150 m C.190 m D.200 m E.None of these
Solution
Answer- A(100m) Explanation:
Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr
Distance covered in 6 minutes =[(1/60)*6] km = (1/10)km = 100 m.
Distance between the thief and policeman = (200 – 100) m = 100 m.
1.A starts business with Rs. 7000 and after 5 months, B joins with A as his partner. After 1 year, the profit is divided in the ratio 2 : 3. What is B’s contribution in the capital? A)Rs 13000 B)Rs 12000 C)Rs 15000 D)Rs 18000 None of these Answer – D (Rs 18000) Explanation – Let B’s capital be Rs. x. Then. (7000 x 12) / 7x = 2/3 [ capital ratio= profit ratio] 14x = 252000 x = 18000 2.shikha started a business investing Rs. 50,000 in 1999, In 2000, she invested an additional amount of Rs. 20,000 and Raju joined him with an amount of Rs. 70,000. In 2001, Shikha invested another additional amount of Rs. 20,000 and Jolly joined them with an amount of Rs. 70,000. What will be Raju’s share in the profit of Rs. 300,000 earned at the end of 3 years from the start of the business in 1999? A)Rs Rs. 250,000. B)Rs Rs. 120,000. C)Rs Rs. 100,000. D)Rs Rs. 150,000. E)None of these Answer – C (Rs. 100,000) Explanation – Shikha : Raju : Jolly = (50000 x 12 + 70000 x 12 + 90000 x 12) : (70000 x 24) : (70000 x 12) = 2520000 : 1680000 : 840000 = 3 : 2 : 1 Raju’s share = Rs.300,000 x 2/6 = Rs. 100,000. 3.A, B and C started a business. They invest Rs. 80,000, Rs. 160,000 and Rs. 2,40,000 respectively. At the end of the first year, B withdraws Rs. 80,000, while at the end of the second year, C withdraws Rs. 160,000. In what ratio will the profit be shared at the end of 3 years? A)2:3:4 B)3:4:7 C)3:2:5 D)3:1:4 E)None of these Answer – D (3:4:7) Explanation – A : B : C = (80000 x 36) : (160000 x 12 + 80000 x 24) (240000 x 24 + 80000 x 12) =144 : 192 : 336 = 3: 4 : 7
1.Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour? A.10 min B.12 min C.18 min D.15 min E.None of these Answer – A (10 min) Explanation – Due to stoppages, it covers 9 km less.Time taken to cover 9 km = (9/54 x 60) min = 10 min 2.A motor car starts with the speed of 70 km/hr with its speed increasing every two hours by 10 kmph. In how many hours will it cover 345 kms? A.4 hrs B.4 hrs 5 mins C.4 1/2 hrs D.2 hrs E.None of these Answer – C (4 1/2 hrs) Explanation – Distance covered in first 2 hours = (70 x 2) km = 140 km Distance covered in next 2 hours = (80 x 2) km = 160 km Remaining distance = 345 – (140 + 160) = 45 km. Speed in the fifth hour = 90 km/hr Time taken to cover 45 km = as speed is 90km/hr means it covers 90 km in 1 hour so,if 90km………..1 hr 45km……….? ?=45/90hr=1/2hr Total time taken = 2 + 2 +1/2=4 (1/2)hrs 3.A person travels from P to Q at a speed of 40 kmph and returns by increasing his speed by 50%. What is his average speed for the both the trips? A.35 kmph B.4o kmph C.48 kmph D.55 kmph E.None of these Answer – C (48 kmph) Explanation – Speed on return trip = 150% of 40 = 60 kmph Average speed = [2 x 40 x 60] / [40 + 6]km/hr =4800/100km/hr = 48 km/hr. 4.Three trains are running from a place A to another place B. Their speeds are in the ratio of 4 : 3 : 5. The time ratio to reach B by trains will be A. 4 : 3 : 5 B. 5 : 3 : 4 C. 15 : 9 : 20 D. 15 : 20 : 12 Answer: D(15 : 20 : 12) Explanation: Ratio of speeds = 4 : 3 : 5 Therefore Ratio of times taken [t=d/s or t indirectly proportional to s when distance is same]= (1/4) : (1/3) : (1/5) = 15 : 20 : 12 5.A man in a train notices that he can count 21 telephone posts in one minute. If they are known to be 50 meters apart, then at what speed is the train travelling? A.50 kmph B.54 kmph C.60 kmph D.62 kmph E.None of these Answer – C (60 kmph) Explanation – Number of gaps between 21 telephone posts = 20 Distance traveled in 1 minute = (50 x 20) m = 1000 m = 1 km Speed = 60 km/hr
A boat takes 4hours for traveling downstream from point P to point Q and coming back to point P upstream. If the velocity of the stream is 2km ph and the speed of the boat in still water is 4kmph, what is the distance between P and Q?A.9 km B.7 km C.5 km D.6km
Answer
Answer- D Basic Formula:
Speed of stream = ½ (a-b) km/hr
Speed of still water = ½ (a+b) km/hr Explanation:
Time taken by boat to travel upstream and downstream = 4 hours
Velocity of the stream, ½ (a-b) = 2km/hr
a-b = 4km/hr ……………….( 1)
velocity of the boat in still water = ½ (a+b) = 4km/hr
a+b = 8 km/hr ………………(2)
1 +2 we get a = 6 km/hr ,b = 2km/hr
let the distance between A and B be x km
x / 2 + x / 6 = 4
3x + x / 6 = 4 4x = 24 so,x = 6
distance between P and Q = 6km
2.Speed of a boat in standing water is 9kmph and the speed of the stream is 1.5kmph. A man rows to a place at a distance of 10.5 km and comes back to the starting point. Find the total time taken by him.A.24 hours B.16 hours C.20 hours D.15 hours
Answer
Answer- A Basic Formula:
i. speed = distance traveled / time taken
ii. speed of the stream = ½ (a-b) km/hr
iii. speed in still water = ½ (a+b) km/hr Explanation:
Speed in still water= ½ (a+b) = 9km ph
= a+b = 18 …………….1
speed of the stream = ½ (a-b) = 1.5 kmph
= a-b = 3 kmph…………2
solving 1 and 2 gives a = 10.5km/hr ; b=7.5 kmphr
Total time taken by him = 105/10.5 + 105/7.5 = 24 hours
3.A man rows to a place 48km distant and back in 14 hours. He finds that he can row 4km with the stream in the same time as 3km against the stream. Find the rate of the stream.A.2 km/hr B.1.1km/hr C.3 km/hr D.3.5km/hr
Answer
Answer- B Basic Formula:
Speed of the stream = ½ (a-b) km / hr
Speed = distance traveled / time taken Explanation:
Suppose he moves 4km downstream in x hours
Then, downstream a= 4 / x km/hr
Speed upstream b = 3/ x km/hr
48 / 4 /x + 48 / 3/x = 14
x/4 + x/3 = 14/48 = 1/4
3x + 4x / 12 = 1/4
7x x 4 = 12 so,x = 3/7
a=28/3 km/hr ,b = 7km/hr
rate of stream = ½ (28/3 – 7 )
= 7/6 = 1.1 km/hr
1.A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time when the clock indicates 1 p.m. on the following day?
48 min. past 12.
46 min. past 12.
45 min. past 12.
47 min. past 12.
2.The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero ?
0
-1
1
None of these
3.If each side of a square is increased by 25%, find the percentage change in its area?
65.25
56.25
65
56
4.A grocer has a sale of Rs 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs, 6500 ?
4991
5467
5987
6453
5.The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was :
10000
12000
14000
16000
1.Today is Monday. After 61 days, it will be :
Tuesday
Monday
Sunday
Saturday
2.Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100 kg of fresh fruits ?
20
40
30
50
3.A bag contains 50 P, 25 P and 10 P coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of each type respectively.
360, 160, 200
160, 360, 200
200, 360,160
200,160,300
4.Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?
10:5
15:2
20:2
25:2
5.The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:
15
16
18
25
1.A, B and C jointly start a business venture with a agreement that A would invest Rs. 13,000 for 6 months, B, Rs. 16,800 for 5 months and C, Rs. 20,000 for 3 months. A wants to be the working member for which he was to receive 5% of the profits. The profit earned was Rs. 14800 Calculate the share of B in the profit?
Rs 6000
Rs 5320
Rs 7800
Rs 5840
Explanation –
For managing, A receives = 5% of Rs. 14800 = Rs. 740.
Balance = Rs. (14800 – 740) = Rs. 14060
Ratio of their investments = (13000 x 6) : (16,800 x 5) : (20000 x 3)
= 78000 : 84000 : 60000 = 13 : 14 : 10
B’s share = Rs.14060 x 14/37 = 5320
2.Anuj, kamlesh and Vinni invested Rs. 16000, Rs. 8000 and Rs. 16000 respectively to open a business. Anuj left after 6 months. If after 8 months, there was a gain of Rs. 8010, then What will be the share of kamalesh?
1780
1635
1680
1800
Explanation –
Anuj : Kamalesh : Vinni = (16000 x 6) : (8000 x 8) : (16000 x 8) = 48 : 32 : 64 = 3 : 2 : 4.
Kamal’s share = Rs.8010 x 2/9
= Rs. 1780.
3.A and B start a business with investments of Rs. 10000 and Rs. 9000 respectively. After 4 months, A takes out 1/2 of his capital. After 2 more months, B takes out 1/3 of his capital while C joins them with a capital of Rs. 14000. At the end of a year, they earn a profit of Rs. 10160. Find the share of each member in the profit?
Rs A – Rs. 3300, B – Rs. 3500, C – Rs. 3360
Rs A – Rs. 3200, B – Rs. 3600, C – Rs. 3360
Rs A – Rs. 3200, B – Rs. 3700, C – Rs. 3260
Rs A – Rs. 3200, B – Rs. 3500, C – Rs. 3460
Explanation –
A : B : C = (10,000 x 4 + 5000 x 8) : (9000 x 6 + 6000 x 6) : (14000 x 6)
= 80000 : 90000 : 84000 = 40 : 45 : 42
A’s share = Rs. 10160 x 40/127 = Rs. 3200;
B’s share = Rs. 10160 x 45/127 = Rs. 3600;
C’s share = Rs. 10160 x 42/127 = Rs. 3360.
4.Anaya, Bela and Cendrella enter into a partnership Bussiness with Anaya’s contribution Rs. 20,000. If out of a total profit of Rs. 2000, Anaya gets Rs.100 and Bela gets Rs. 600, cendrella gets rs 400 then Cendrella’s capital is:
Rs 8000
Rs 8500
Rs 7000
Rs 6500
Explanation –
A : B : C = 1000 : 600 : 400 = 5 : 3 : 2.
Let their capitals be 5x, 3x, 2x respectively.
Then, 5x = 20000 x = 4000.
C’s capital = 2x = Rs. 8000.
5.Riya and sima invested in a partnership business. Riya invests Rs. 70,000 for 8months and sima invests Rs. 84,000 for 10 months. Out of a profit of Rs. 63140, Riya’s share is:
Rs 25000
Rs 25256
Rs 24500
Rs 25270
Explanation –
Ratio of their shares = (70000 x 8) : (84000 x 10) = 2 : 3.
Reena’s share = Rs.63140 x 2/5 = Rs. 25256
1.A cricketer has completed 10 innings and his average is 21.5 runs. How many runs must he make in his next innings so as to raise his average to 24?
44
45
49
48
Explanation – Total of 10 innings = 21.5 x 10 = 215
Suppose he needs a score of a in 11th innings; then average in 11 innings =
(215 + a) / 11= 24
or, a = 264-215 = 49
2.1/3 rd of certain journey is covered at the rate of 25 km/hr, 1/4 th at the rate of 30 km/hr and rest at 50 km/hr. Find the averae speed for the whole journey?
31 1/3 km/hr
30 1/3 km/hr
33 1/3 km/hr
34 1/3 km/hr
Explanation – Let the journey by a km. Then a/3 km at the speed of 25 km/hr and a/4 km at 30 km/hr and the rest distance ( a- a/3 –a/4 ) = 5/12 x a at the speed of 50 km/hr.
Total time taken during the journey of a km
3.The average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers?
4.2
4.6
5.1
5.6
Explanation – Sum of the remaining two numbers = (3.95 x 6) – [(3.4 x 2) + (3.85 x 2)] = 23.70 – (6.8 + 7.7) = 23.70 – 14.5 = 9.20
Average = 9.2/2 = 4.6
4.The average salary of the entire staff in a office is Rs 120 per month. The average salary of officers is Rs 460 and that of non officer is Rs 110. If the number of officer is 15, then find the number of non-officer in the office?
450
550
510
520
Explanation – Let the required number of non-officers = a
Then, 110a + 460 x 15 = 120 (15 + a)
or, 120a – 110a = 450 x 15 – 120 x 15 = 15 (460 – 120)
or, 10a = 15 x 340; a = 15 x 34 = 510
5.Find the average of first 20 multiple of 7?
71.5
73.5
75.2
76.6
Explanation –
Average = 7 (1+2+3+…….+20)/ 20= 7 x 20 x 21/ 20×2= 73.5
In the following questions each question is followed by three statements I, II and III. Read the question and the statements carefully and choose your answer according to which set of statement(s) is/are sufficient to answer the question.
1.What is the distance between city P and city Q?
I.Two persons A and B started simultaneously from P to Q, with their speeds in the ratio 4 : 5
II.B reached P one hour earlier than A to Q.
III.The difference between speeds of A and B is 20 kmph
I and III only
II and III only
I and II only
All I, II and III together
2.What is the rate of interest on a certain sum?
I.The interest earned on the sum at the same rate of simple interest after 3 years is Rs.4500.
II.If the rate of interest is 2.5% more, the simple interest earned will be Rs.900 more.
III.The amount received on the sum at the end of the 2 years at simple interest is Rs.15,000
I and II only
II and III only
All I, II and III together
Any two statements together
3.What is the area of the rectangle?
I.The ratio of length to breadth of the rectangle is 35 : 12.
II.The perimeter of the rectangle is 188 cm.
III.The length of diagonal of the rectangle is 74 cm
I and II only
I and III only
(I and II) or (II and III)
Any two of the three
4.How many boys are there in the class?
I.The number of boys is 15 more than the number of girls.
II.The average weight of boys is 41 kg and that of girls is 32 kg.
III.The average weight of all the students of the class is 37 kg
I and II only
II and III only
All I, II and III
(I and II) or (II and III)
5.What is the profit percentage if a discount of 10% is offered on an article?
I.Had there been no discount offered, the profit earned on the sale the article would be 40%.
II.The discount offered on the article is 14% of the cost price.
III.The cost price of the article is Rs.1000
I only
Either I or II
All I, II & III together
Each statement alone is sufficient
1. If Nishu can swim downstream at 6kmph and upstream at 2kmph.What is his speed in still water ?
5 km/hr
4 km/hr
8 km/hr
7 km/hr
If the speed downloadstream is a km/ hr and the speed upstream is b km/ hr
then Speed in still water is = ½ (a+b) km / hr [memory tool last 2 L cross and make +] Explanation:
Given : speed downstream a = 6 km ph
Speed upstream b = 2kmph
Speed in still water = ½ (a+b) kmph
= ½ (6+2)
= 8/2 = 4kmph
speed in still water = 4kmph
2.Ashok can row upstream at 8kmph and downstream at 12kmph.What is the speed of the stream ?
6 km/hr
3 km/hr
2 km/hr
4 km/hr
Basic Formula:
If the speed downstream is a kmph and the speed upstream is b kmph
then
Speed of the stream = ½ (a-b) kmph
Explanation:
Speed downstream a = 12kmph
Speed upstream b = 8 kmph
Speed of the stream = ½ (a-b) = ½ (12-8)
= 4/2 = 2 kmph
speed of the stream = 2kmph
3.A man rows 750m in 775 seconds against the stream and returns in 7 1/2 minutes. What is rowing speed in still water ?
4.7km/hr
4 km/hr
3.5km/hr
6 km/hr
Basic Formula:
i) Speed in still water = ½ (a+b) kmph where ‘a’ is speed
downstream and ‘b’ is speed upstream
ii) a km / hr = a x 5/18 m /s
iii) a m/sec = a x 18/5 km/hr
Explanation:
Speed upstream ‘b’ = 750m / 775 sec = 30/31 m/sec
Speed downstream ‘a’ = 750 m/ (15/2)minutes [ 1min=60 sec] a = 750m/450 sec =5/3 m/sec
speed in still water = ½ (a+b)
= ½ (750/450 + 750/675 ) m /sec
= ½ (750/450 + 750/675 ) x 18/5 km/hr
= ½ (5/3 + 30/31) x 18/5 km/hr
= 4.7 km/hr
4.A man can row 9 (1/3) kmph in still water and finds that it takes him thrice as much time to row up than as to row down the same distance in the river. What is speed of the current ?
5km/hr
3(1/2) km/hr
4 (2/3) km/hr
8 (3/2)km/hr
Basic Formula:
Speed of current = ½ (a-b) km/hr
Explanation:
Let man’s rate upstream be x km/hr. Then his rate downstream is 3 x km/hr
Given:
Speed in still water = 9 (1/3) = 28/3 km/hr
i.e, ½ (a+b) = 28/3 km/hr
½ (x+3x) = 28/3
2x = 28/3 x = 28/ 2 x 3 = 14/3 km/hr
rate upstream b = 14/3 km/hr and
rate downstream a = 14/3 x 3 = 14 km/hr
speed of the current = ½ (a-b) = ½ (14 – 14/3)
= ½ (42-14/3) = 28/6 = 4 (2/3) km/hr
5.Sham can row a boat at 10kmph in still water. IF the speed of the stream is 6kmph, the time taken to row a distance of 80km down the stream is
4 hours
5 hours
3 hours
2 hours
Basic Formula:
Speed of stream = ½ (a-b) km/hr
Speed in still water = ½ (a+b) km/hr
Explanation:
Given:
Speed in still water, ½ (a+b) = 10 km/hr
a+b = 20 km/hr…………….(1)
speed of the stream, ½ (a-b) = 6km/hr
a-b = 12 km/hr …………….(2)
(1)+(2 ) we get 2a = 32
a = 16 km/hr
speed downstream =distance traveled / time taken
time taken = 80/16 = 5 hours
1.A trader buys two articles at the same price. He sold one article at 20% profit and sold the other at 10% loss . Find his overall profit/loss percentage
10% loss
10% profit
5% loss
5% Profit
2.If a book is sold at 20% more than its usual price, an extra profit of Rs.120 would be made on it. find its usual selling price.
Rs.500
Rs.600
Rs.750
Rs.800
3.The loss made by selling 20 m of a cloth equals the cost price of 5 m of that cloth. Find the loss percentage
33 1/3%
25%
20%
40%
4.The profit made by selling 30 m of a cloth equals the cost price of 6 m of that cloth. find the profit percentage
25%
20%
16 2/3%
30%
5.The profit made by selling 25 m of a cloth equals the selling price of 5 m of that cloth. find the profit percentage?
25%
20%
16 2/3%
30%
1. Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:
58 sec
50 sec
48 sec
56 sec
A 270 m long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
180
230
245
235
Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:
40
50
65
55
A train 125 m long passes a man, running at 5 kmph in the same direction in which the train is going, in 10 seconds. The speed of the train is:
35 km/hr
55 km/hr
48 km/hr
50 km/hr
A train travelling at a speed of 75 mph enters a tunnel 7/2 miles long. The train is 1/4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
1 min
3 min
5 min
6 min
1.Nishu is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the speed of the train? A.35 kmph B.54 kmph C.62 kmph D.70 kmph E.None of these Answer – B (54 kmph) Explanation – Let the length of the train be x metres. Then, the train covers x metres in 8 seconds (train is actually covering itself because length of man is very less compartable to train)and (x + 180) metres in 20 seconds. equate speed in both case,s=d/t ∴ x/8 =( x + 180) / 20 ⇔ 20x = 8(x + 180) ⇔ x = 120. ∴ Length of the train = 120 m. Speed of the train = [120/8]m/sec (convert to km/hr i.e x 18/5) =[120/8] x 18/5kmph = 54 kmph. 2.Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train? A.27 7/9 m B.28 m C.29 m D.30 2/7 m E.None of these Answer – A (27 7/9 m) Explanation – When SAME direction- MINUS Relative speed = (40-20) km/hr = [20 x 5/18] m/sec = [50/9] m/sec. Length of faster train = sxt=[50/9 x 5] m = 250/9 m = 27 7/9 m. 3.Two train travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 8 seconds. Then length of the faster train is: A.120 m B.140 m C.160 m D.180 m E.None of these Answer – D (180 m) Explanation – When OPP. direction-PLUS Relative speed = (36 + 45) km/hr = [81 x 5/18] m/sec = [45/2] m/sec. Length of train = [45/2 x 8] m = 180 m.
1.P and Q together can complete a work in 6 days. Q and R together can complete the same work in 15 days. P and R together can complete the work in 20/3 days. What is the ratio of number of days that Q alone takes to complete the work to the number of days that R alone takes to complete the work? 1 : 3 : 5 2 : 1 : 4 3 : 2 : 5 4 : 2 : 3 5 : None of these 2.A and B together can complete a piece of work in 15 days, B and C together can complete the work in 20 days. A and C together can complete the work in 30 days. What is the ratio of number of days A alone takes to do the work to the number of days C alone takes to do the work? 1 : 1 : 6 2 : 1 : 3 3 : 2 : 3 4 : 3 : 2 5 : None of these 3.Two boys can do a piece of work in ten days. Three girls can do the same work in five days. In how many days can a boy and a girl together do the work? 1 : 16 days 2 : 8(4/7) days 3 : 12 days 4 : 5 (1/2)days 5 : None of these 4.Four men can complete a work in 5 days which 20 women take 20 days to complete. How many days will 6 men and 40 women together take to complete the work? 1 : 1day 2 : 4days 3 : 2 (1/2)days 4 : 3days 5 : None of these 5.A and B can complete a work in 20 days and 30 days respectively. Both of them started doing the work and A left after six days. In how many more days can B complete the remaining work? 1 : 20 2 : 10 3 : 15 4 : 12 5 : None of these
1.The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is: A.51.4 B.52.6 C.56.1 D.55.3 E.None of these Answer – A (51.4) Explanation – Let the required mean score be a Then, 20 x 80 + 25 x 31 + 55 x a = 52 x 100 1600 + 775 + 55a = 5200 55a = 2825 a = 51.4 2.The average of a non-zero number and its square is 5 times the number. The number is: A.0 , 7 B.0 , 6 C.5 , 7 D.0 , 9 E.None of these Answer – D (0 , 9) Explanation – Let the number be x. Then, (x + x^2) / 2 = 5x x^2 – 9x = 0 x (x – 9) = 0 x = 0 or x = 9. 3.If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of a^2, b^2, c^2 is: A.3 M x M B.3 M C.9 M D.9 M x M E.None of these Answer – A (3 M x M) Explanation – We have : (a + b + c) / 3 = M or (a + b + c) = 3M. Now, (a + b + c)^2 = (3M)^2 = 9M^2 a^2 + b^2 + c^2 + 2 (ab + bc + ca) = 9M^2 a^2 + b^2 + c^2 = 9M^2 Required mean = (a^2 + b^2 + c^2)/3= 9M^2/ 3 = 3 M^ 2