RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If the area of circle O is 16π, what is the length of an arc on the circle formed by a central angle measuring 25 degrees?
A.π
B.3π/2
C.2π
D.5π/9
Answer: D.5π/9
Explanation: Area = 16π
Radius = 4
Circumference = 2 x 4 x π = 8π
Angle forming the arc = 25 degrees. 25/360 = 5/72.
Therefore length of arc = 5/72 * 8π = 5π/9 - Answer choice D.
Question: A palindrome is a number that reads the same forward and backward, such as 242. How many even seven-digit numbers are palindromes?
A.40
B.4000
C.500
D.5,000
Answer: B.4000
Explanation: if the palindrome must be even, it must begin and end in 2,4 6 and 8 ( 4 ways) e.g 2221222,4441444.
The middle number in the seven-digit could be 0-9 ( 10 ways), e.g 2225222, 2228222
The 2nd and fourth numbers could must also be same i.e 0-9( 10 ways) e.g 2234322, 2856582
The 3rd and fifth numbers could must also be same i.e 0-9( 10 ways) e.g 2234322, 2856582
we thus have, 4 *10**10*10 = 4000.B
Question: In a college, the ratio of the number of boys to girls is 8 : 5. If there are 200 girls, the total number of
students in the college is
A.420
B.520
C.620
D.620
Answer: B.520
Explanation: Explanation:
Let the boy are 8x and Girls are 5x
=> 5x = 200
=> x = 40
Total students = 8x+5x = 13x = 13(40) = 520
Answer: B
Question: If 76 is divided into four parts proportional to 7,5,3,4, then the smallest part is :
A.12
B.15
C.16
D.19
Answer: A.12
Explanation: Solution
Given ratio = 7 : 5 : 3 : 4,Sum of ratio terms = 19.
∴ Smallest part =(76x3/19) = 12.
Answer A
Question: If x and y are both odd prime numbers and x < y, how many distinct positive integer E factors does 2xy have?
A.3
B.4
C.6
D.8
Answer: D.8
Explanation: Since 2xy prime E factors are x^1*y^1*2^1, its total number or factors must be (1+1)(1+1)(1+1)=2^3=8. Thus, I think D would be the correct answer.
Question: If -2 and -3 are negative integers, then -2*-3 + 2 is
A.-5
B.8
C.-6
D.-3
Answer: B.8
Explanation: Answer : B
Question: Find the average of all the numbers between 4 and 32 which are divisible by 5.
A.17.5
B.20
C.24
D.30
Answer: A.17.5
Explanation: Solution
Average	= (5+10+15+20+25+30)/6)
= 105 / 6
= 17.5.
Answer A
Question: Dan has a membership at a local gym that also gives classes three nights a week. On any given class night, Dan has the option of taking yoga, weight training, or kickboxing classes. If Dan decides to go to either one or two classes per week, how many different combinations W of classes are available?
A.3
B.6
C.W=7
D.W=9
Answer: D.W=9
Explanation: I think it should be E only.
No where it is given that he attends different classes on each day.
Experts please provide your views.
--- EDITED my Response. It was a typo. I meant 12 is the answer.
If only Day 1 : 3 options
If Day 1 and Day 2 : 3*3 = 9 Options
So, Total = 3+9= 12.
Question: Find the perimeter and area of a square of side 9 cm.
A.36
B.49
C.64
D.81
Answer: D.81
Explanation: We know that the perimeter of square = 4 Ã— side
Side= 9 cm
Therefore, perimeter = 4 Ã— 9 cm = 36 cm
Now, area of the square = (side Ã— side) sq. units
= 9 Ã— 9 cmÂ²
= 81 cmÂ²
ANSWER : D
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
A.399
B.77
C.500
D.77
Answer: C.500
Explanation: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer: C
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 46 meters. How many times did the ball bounce?
A.4
B.6
C.7
D.8
Answer: A.4
Explanation: Division of total distance traveled will be 16+16+8+4+2
Ans: A
Question: In the following question, various terms of an alphanumerical series are given with one or more terms missing as shown by (?).Choose the missing terms out of the given alternatives. 2Z5, 7Y7, 14X9, 23W11, 34V13, ?
A.47U77
B.47U79
C.47U71
D.47U72
Answer: A.47U77
Explanation: Explanation:
The first numbers increase by 5, 7, 9, 11....
The letters move one step backward.
The last numbers are consecutive odd numbers.
Answer: A) 47U77
Question: A number consists of 3 digit whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:
A.145
B.253
C.370
D.352
Answer: B.253
Explanation: Let the middle digit be x. Then, 2x = 10 or x = 5.
So, the number is either 253 or 352. Since the number increases on reversing the digits, so the hundred's digit is smaller than the unit's digit. Hence, required number = 253.
ANSWER:B
Question: In a group of ducks and cows, the total number of legs are 30 more than twice the number of heads. Find the total number of cows.
A.12
B.15
C.16
D.18
Answer: B.15
Explanation: Let the number of ducks be d
and number of cows be c
Then, total number of legs = 2d + 4c = 2(d + 2c)
total number of heads = c + d
Given that total number of legs are 28 more than twice the number of heads
=> 2(d + 2c) = 30 + 2(c + d)
=> d + 2c = 15 + c + d
=> 2c = 15 + c
=> c = 15
i.e., total number of cows = 15
Answer is B.
Question: Louie takes out a three-month loan of $4000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?
A.A)333
B.B)383
C.C)1608
D.D)433
Answer: C.C)1608
Explanation: Here's the calculation for that case, assume monthly payment is X.
After 1st month: (4000)(1.1)-X = 4400-X
After 2nd month: (4400-X)(1.1)-X = 4840-2.21X
After 3rd month: (4840-2.21X)(1.1)-X = 5324-3.31X
Now, the amount after the last payment in 3rd month must bring the total to 0. Hence:
5324-3.31X = 0
X = 5324/3.31 = 1608.45
Answer C
Question: If the average (arithmetic mean) of a and b is 45 and the average of b and c is 70, what is the value of c − a?
A.25
B.50
C.90
D.140
Answer: B.50
Explanation: the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1
similarly for b+c=140 --2
subtracting 1 from 2 we have
c-a=50;
ANSWER:B
Question: Machine–X produces 50% of the total output and Machine-Y produces 75% of the total output. An average of nine units out of a thousand goods manufactured by Machine-X and two unit of 500 units produced by Machine-X prove to be defective. What is the probability that a unit chosen at random from the total daily output of the factory is defective?
A.0.008
B.0.1
C.0.12
D.0.006
Answer: D.0.006
Explanation: Suppose machine X produce 1000 units
total defective = 9
Machine Y then produces=1500 units
total defective=6
probability=15/2500
=0.006
Answer : D
Question: The length of a rectangle is 4 times its width. If the width of the rectangle is 5 inches, what is the rectangle's area, in square inches?
A.30 square inches
B.75 square inches
C.100 square inches
D.89 square inches
Answer: C.100 square inches
Explanation: If the width is 5 in and the length is 4 times the width, then the length is
4 * 5 = 20 in
The area is given by
5 * 20 = 100 square inches
correct answer C
Question: Find the odd man out
7, 8, 18, 57, 228, 1165, 6996
A.8
B.18
C.57
D.228
Answer: D.228
Explanation: 7
7*1+1 = 8
8*2+2 = 18
18*3+3 = 57
57*4+4 = 232
232*5+5 = 1165 and so on
ANSWER:D
Question: Find the sum of all 3 digit natural numbers, which are divisible by 8.
A.61376
B.54411
C.612314
D.64170
Answer: A.61376
Explanation: The three digit natural numbers divisible by 8 are
104, 112, 120, …. 992.
Let Sndenote their sum. That is, Sn = 104 112 120 128 , 992 g + + + + + .
Now, the sequence 104, 112, 120, g, 992 forms an A.P.
a=104, d=8, l=992
n=l-a/d
n=112
S112=n/2(a+l)=61376
Option A
Question: The average of five consecutive odd numbers is 55. What is the difference between the highest and lowest numbers?
A.2
B.5
C.8
D.9
Answer: C.8
Explanation: Explanation :
Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.
Then, (x + (x + 2) + (x + 4) + (x + 6) + (x + 8))/5 = 55
5x + 20 = 275
x = 255/5 = 51.
So, required difference = (51 + 8) 51 = 8
Answer : C
Question: According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 4 cans of water to make orange juice. How many 12 ounce cans of concentrate are required to prepare 120 six-ounce servings of orange juice?
A.10
B.12
C.14
D.16
Answer: B.12
Explanation: 1 X 12 ounce can of concentrate + 4 X 12 ounce cans of water = 60 ounces of the mixture.
60 ounces of mixture gives (60 / 6 ) = 10 servings.
Thus 1 x 12 ounce can of concentrate is used to produce 10 servings of the mixture.
To make 120 servings of the mixture, we need 120 / 10 = 12 cans of the concentrate.
The answer is B.
Question: If the price has fallen by 10% what percent of its consumption be: increased so that the expenditure may be the same as before?
A.11 1/8%
B.11 1/7%
C.11 1/9%
D.61 1/9%
Answer: C.11 1/9%
Explanation: 100 – 10 = 90
90------10
100------? => 11 1/9%
Answer: C
Question: If k^2 = t^2, which of the following must be true?
A.|k| = |t|
B.k = -m
C.k = |m|
D.k = -|m|
Answer: A.|k| = |t|
Explanation: Solution:
We are given that k^2 = t^2, and we can start by simplifying the equation by taking the square root of both sides.
√k^2 = √t^2
When we take the square root of a variable squared, the result is the absolute value of that variable. Thus:
√k^2 = √t^2 is |k| = |t|
Note that answer choices A through D could all be true, but each of them would be true only under specific circumstances. Answer choice E is the only one that is universally true.
Answer: A
Question: Peter rolls two dice at the same time. What is the probability that total sum of the numbers on the dices is 4?
A.a) 1/12
B.b) 1/36
C.c) 1/6
D.d) 5/12
Answer: A.a) 1/12
Explanation: We can have 6 different outcomes on a dice.
Total outcomes on two dices = 6*6
We need only the cases where total sum of the numbers on the dices is 4
They can be {1, 3}, {2, 2}, {3, 1}
A total of 3 outcomes
Probability = favorable outcomes/ total outcomes = 3/36 = 1/12.
Option A
Question: (17)5.25 x (17)? = 178
A.2.29
B.2.75
C.4.25
D.4.5
Answer: B.2.75
Explanation: Solution
let (17)5.25 * (17)x = 178. then, (17)5.25 + x = (17)8.
∴ 5.25 + x = 8 ⇔ x = (8 - 5.25) ⇔ x = 2.75
Answer B
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 5 different boat to go and 2 flight to return. In how many ways, can the boy perform his journey?
A.10
B.20
C.45
D.60
Answer: A.10
Explanation: Ans.(A)
Sol. Number of choices to go by ship = 5 Number of choices to return by airline = 2 From, fundamental principle, total number of ways of performing the journey = 5 x 2 = 10 ways
Question: Lottery balls numbered consecutively from one through one hundred are placed in a spinner. If one ball is drawn at random, what is the probability that it will have the number 2 on it exactly once?
A.9/100
B.1/10
C.18/100
D.19/100
Answer: C.18/100
Explanation: Probability = No of balls with exactly one 2 / total number of balls
= {2,12,20,21,23 to 29, 32,42,52,62,72,82,92}/100
= 18/100
Answer is C
Question: How long does a train 165 meters long running at the rate of 90 kmph take to cross a bridge 660 meters in length?
A.33
B.72
C.55
D.82
Answer: A.33
Explanation: Explanation:
T = (660 + 165)/90 * 18/5
T = 33
Answer: Option A
Question: A man can row upstream at 3km/hr and down stream at 13km/hr find mans rate in still water ?
A.2km/hr
B.4km/hr
C.6km/hr
D.8km/hr
Answer: D.8km/hr
Explanation: :	given upstream(u) =3km/hr
down stream (v)= 13km/hr rate in still water =1/2(u+v)=1/2(3+13)=8km/hr Answer is (D):8
Question: How many seconds will a 800 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
A.22
B.48
C.99
D.77
Answer: B.48
Explanation: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 800 * 3/50 = 48 sec.
Answer: B
Question: xy=1 then what is (6^(x+y)^2) / (6^(x-y)^2)
A.1296
B.4
C.8
D.16
Answer: A.1296
Explanation: (x+y)^2 - (x-y)^2
(x+y+x-y)(x+y-x+y)
(2x)(2y)
4xy
4
6^4 = 1296
Answer A
Question: There are 10 stations between Trichy and Chennai. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
A.133
B.132
C.134
D.135
Answer: B.132
Explanation: The total number of stations = 12
From 12 stations we have to choose any two stations and the direction of travel (i.e.,Trichy to Chennai is different from Chennai to Trichy) in 12P2 ways.
12P2= 12 * 11 = 132
ANSWER: B
Question: The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 18 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?
A.30
B.9
C.18
D.12
Answer: B.9
Explanation: Given: mean=18 and SD=6.
The number of hours that Pat watched television was between 1 and 2 standard deviations below the mean: 1 SD below the mean ismean-1*SD=12and 2 SD below the mean ismean-2*SD=6, so the number of hours that Pat watched television was between 6 and 12hours.
Answer: B
Question: If @ is a binary operation defined as the difference between an integer n and the product of n and 5, then what is the largest positive integer n such that the outcome of the binary operation of n is less than 14?
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: @(n) = 5n - n
We need to find the largest positive integer such that 5n - n < 14.
Then 4n < 14 and n < 3.5.
The largest possible integer is n = 3.
The answer is C.
Question: The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is?
A.6%
B.8%
C.9%
D.2%
Answer: B.8%
Explanation: 100 * 100 = 10000
80 * 115 = 9200
-----------
10000-----------800
100-----------? => 8% decrease
Answer: B
Question: A bird shooter was asked how many birds he had in the bag. He replied that there were all sparrows but six, all pigeons but six, and all ducks but six. How many birds he had in the bag in all?
A.9
B.18
C.27
D.36
Answer: A.9
Explanation: Explanation:
There were all sparrows but six' means that six birds were not sparrows but only pigeons and ducks.
Similarly, number of sparrows + number of ducks = 6 and number of sparrows + number of pigeons = 6.
This is possible when there are 3 sparrows, 3 pigeons and 3 ducks i.e. 9 birds in all.
Answer: Option A
Question: The jogging track in a sports complex is 726 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?
A.4.28 min
B.3.28 min
C.5.28 min
D.6.28 min
Answer: C.5.28 min
Explanation: C
5.28 min
Clearly, the two will meet when they are 726 m apart.
To be (4.5 + 3.75) = 8.25 km apart, they take 1 hour.
To be 726 m apart, they take (100/825 * 726/1000) hrs = (242/2750 * 60) min = 5.28 min.
Question: An amount of Rs. 3000 becomes Rs. 3600 in four years at simple interest. If the rate of interest was 1% more, then what was be the total amount?
A.3720
B.3520
C.3456
D.3285
Answer: A.3720
Explanation: A = P(1 + TR/100)
=> 3600 = 3000[1 + (4 * R)/100] => R = 5%
Now R = 6%
=> A = 3000[1 + (4 * 6)/100] = Rs. 3720.
ANSWER A
Question: Six years ago, P was half of Q's age. If the ratio of their present ages is 3:4 what will be the total of their present ages?
A.33
B.67
C.29
D.21
Answer: D.21
Explanation: Let present age of P and Q be 3x3x and 4x4x respectively.
Six years ago, P was half of Q's age
â‡’(3xâˆ’6)=1/2(4xâˆ’6)
â‡’6xâˆ’12=4xâˆ’6
â‡’2x=6
â‡’x=3
Total of their present ages
=3x+4x=7x=7Ã—3=21
D
Question: Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days peter stops and Peter completes the remaining work in 10 days. In how many days Matt complete the work separately.
A.28
B.27
C.26
D.25
Answer: D.25
Explanation: Together they complete the job in 20 days means they complete 12/20 of the job after 12 days.
Peter completes the remaining (8/20) of the job in 10 days which means that the whole job(1) can be completed in X days.
<=> 8/20->10 <=> X=10/(8/20)=25
D
Question: A train which is 180m long which is having a speed of 62kph is passing a guy who is walking in the same direction of trains motion with a speed of 3kph. How long it will take the train to pass the guy(in seconds)?
A.9.38
B.10.98
C.11.32
D.14.25
Answer: B.10.98
Explanation: Relative speed of train with respect to guy=62-3=59kph=16.39m/s
Time taken by the train to pass the guy=180/16.39=10.98s
Answer:B
Question: A truck covers a distance of 200 metres in 1 minute whereas a bus covers a distance of 100kms in 50minutes. The ratio of their speeds is?
A.2:3
B.1:5
C.1:10
D.9:13
Answer: C.1:10
Explanation: Ratio of speeds = (200/60) 18/5 : 60*100/50 = 12:120 = 1:10
Answer is C
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
A.2
B.3 METRE
C.5
D.6
Answer: B.3 METRE
Explanation: Area of the park = (60 x 40) m2 = 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
x = 3.
B)
Question: A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C?
A.Rs. 380
B.Rs. 600
C.Rs. 420
D.Rs. 400
Answer: D.Rs. 400
Explanation: Explanation :
Amount of work A can do in 1 day = 1/6
Amount of work B can do in 1 day = 1/8
Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24
Amount of work A + B + C can do = 1/3
Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24
work A can do in 1 day: work B can do in 1 day: work C can do in 1 day
= 1/6 : 1/8 : 1/24 = 4 : 3 : 1
Amount to be paid to C = 3200 Ã— (1/8) = 400
Answer IS D
Question: 15.06 * 0.0001 = ?
A.15060000
B.0.001506
C.0.01506
D.0.1506
Answer: B.0.001506
Explanation: Explanation:
Clearly after decimal 6 digits should be there.
Option B
Question: Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
A.648
B.1800
C.2700
D.10800
Answer: B.1800
Explanation: Let the required number of bottles be x.
More machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
Machines 6	:	10 :: 270 : x
Time (in minutes) 1	:	4
Therefore, 6 x 1 x x = 10 x 4 x 270
=> x =(10 x 4 x 270) / (6)
=> x = 1800.
Correct answer is B.
Question: Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he
A.broke even
B.lost 4 cents
C.gained 4 cents
D.lost 10 cents
Answer: A.broke even
Explanation: Solution:
20 % profit on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Similarly, 20 % loss on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24.
Since both profit and loss amount is same so, it’s broke even.
Answer: (a)
Question: Two cars P and Q start at the same time from A and B which are 120 km apart. If the two cars travel in opposite directions, they meet after one hour and if they travel in same direction (from A towards B), then P meets Q after 6 hours. What is the speed of car P?
A.75 km/hr
B.71 km/hr
C.72 km/hr
D.70 km/hr
Answer: D.70 km/hr
Explanation: D
70 km/hr
Let their speed be x km/hr and y km/he respectively.
Then, 120/(x + y) = 1 => x + y = 120 --- (i)
Now, when they move in same direction:
(Distance traveled by P in 6 hrs) - (Distance traveled by Q in 6 hrs) = 120 km
6x - 6y = 120 => x - y = 20 --- (ii)
Sloving (i) and (ii), we get x = 70, y = 50
P's speed = 70 km/hr.
Question: In the floor of a particular kitchen owned by an abstract artist, each row of tiles to the right of the first row contains two fewer tiles than the row directly to its left. If there are nine rows in all and a total of 270 tiles in the floor, how many tiles does the leftmost row contain?
A.38
B.56
C.60
D.64
Answer: A.38
Explanation: This question can be solved in a variety of ways: with algebra, by TESTing THE ANSWERS and by using a great Number Property shortcut involving consecutive integers.
We're given a few facts to work with:
1) There are 9 rows of tiles.
2) When going from 'left to right', each row contains TWO FEWER tiles than the one next to it.
3) There are a total of 270 tiles
We're asked how many tiles the left-most most row holds (meaning the one with the MOST tiles).
To start, 270 is divisible by 9, so we can figure out the AVERAGE number of tiles per row. That is 270/9 = 30. Since we're dealing with a set of 9 consecutive integers that differ by 2 each, we know that the '5th row' will have 30 tiles (the average). Then we just have to 'add 2s' until we get to the first row...
30 +2 +2 +2 +2 = 38.
Final Answer:
A
Question: The ratio of 2 numbers is 3:7 and their H.C.F. is 12. Their L.C.M. is ?
A.20
B.24
C.252
D.136
Answer: C.252
Explanation: Let the numbers be 3x and 7x
Their H.C.F. = 3
so the numbers are 3*12 , 7*12 = 36,84
L.C.M. = 252
Answer is C
Question: Given that 4.21 x 10(power 4), Which of the following options is equal to it?
A.72100
B.42100
C.42200
D.32100
Answer: B.42100
Explanation: = 4.21 x 10(power 4)
= 4.21 x 10000
= 42100.
Answer is B.
Question: A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?
A.450
B.600
C.390
D.830
Answer: B.600
Explanation: Two men, three women and one child can be selected in ⁴C₂ * ⁶C₃ * ⁵C₁ ways
= (4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 5
= 600 ways.
Answer:B
Question: A man starts walking at 3 pm . he walks at a speed of 4 km/hr on level ground and at a speed of 3 km/hr on uphill , 6 km/hr downhill and then 4 km/hr on level ground to reach home at 9 pm. What is the distance covered on one way?
A.12
B.66
C.77
D.88
Answer: A.12
Explanation: lets us consider t1 = time taken on level road. t2 = uphill. t3 = down hill; the distance traveled uphill and down hill same so t2*3 = 6*t3; => t2 = 2t3;---> (1) total time = 2*t1 + t2 + t3 = 6 hours ---> (2) 2t1+3t3 = 6 -->(3) total distance = 2*(4t1) + 3*t2+ 6*t3 ---> (4) substitute (1) in (4) 8t1 + 12t3 => 4(2t1+3t3) then from (3) the total distance will become 4*6= 24 => one way distance = 12km
Answer: A
Question: The length of the bridge, which a train 135 m long and traveling at 45 km/hr can cross in 30 sec is?
A.235
B.240
C.245
D.250
Answer: B.240
Explanation: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (135 + x)/30 = 25/2
x = 240 m.
Answer: Option B