mathewhe/aqua_rat huggingface dataset:
Question: A person walking at 4 Kmph reaches his office 6 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?
(A) 4 1/5 Km
(B) 4 1/7 Km
(C) 3 1/5 Km
(D) 3 1/7 Km
(E) 2 4/5 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 14/6
= 24/2 * 14/60
= 7 * 2/5
= 14/5 = 2 4/5 Km
E)
Answer: (E) 2 4/5 Km
Question: Jessica can text 95 words per minute, while Maurice can text 10 words per minute. An abridged English translation of Tolstoy’s War and Peace contains 410,400 words. Working together, how many days will it take Jessica and Maurice to text the entire abridged translation of War and Peace?
(A) 2.7
(B) 1.3
(C) 3
(D) 9
(E) 11.3
Rationale: Since the answer choices are reasonably spaced out, we can approximate and save time
Combined words per day = 105*60*24 which should be something close to 151200
410400/151200 will be closest to only 2.7,
So, Answer should be A
Answer: (A) 2.7
Question: What is the least number to be added to 661 to make it a perfect square?
(A) 13
(B) 15
(C) 20
(D) 16
(E) 45
Rationale: The numbers greater than 661 and are square of number is 676.
The least number that should be added 661 to make it perfect square = 676 - 661 = 15.
ANSWER:B
Answer: (B) 15
Question: A person travels from P to Q at a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips ?
(A) 43
(B) 25
(C) 48
(D) 50
(E) 62
Rationale: Speed = 40 km/hr
Return= 150% of 40 = 60 km/hr
avg = 2xy/x+y
=2*40*60/40+60 = 4800/100
== 48 km/hr
ANSWER C
Answer: (C) 48
Question: If a farmer sells 10 of his chickens, his stock of feed will last for 4 more days than planned, but if he buys 15 more chickens, he will run out of feed 3 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?
(A) 12
(B) 24
(C) 48
(D) 35
(E) 60
Rationale: Say farmer has n chicken and he is good for d days.:-
We have 3 equations given in question:-
(n-10) * d+4 =(n+15) *(d-3) = n * d
Solving these: (You can solve 1st and 3rd and 2nd and 3rd together)
We get:
15d-3n=45
4n-10d =40
=> n=35
Ans D it is!
Answer: (D) 35
Question: A certain collage has total of 400 seniors each majoring in exactly one of six subjects. A minimum of 25 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?
(A) 100
(B) 80
(C) 75
(D) 60
(E) 50
Rationale: Answer is B.
Six majors are as follows: a + b + c + d + e + f
Each has at least 20 seniors: 25 + 25 + 25 + 25 + 25 + 25
4 of the majors have 300 seniors: a + b + c +d = 300
There are a total of 400 seniors.
So e + f = 100. One of the subjects has to be 25 for the other to be maximized. If e = 25, then f = 75
C.
Answer: (C) 75
Question: Jack, Jill, and Sandy each have one try to make a basket from half court. If their individual probabilities of making the basket are 1/6, 1/7, and 1/8 respectively, what is the probability that Jack and Sandy will make a basket but Jill will miss?
(A) 1/8
(B) 3/8
(C) 3/28
(D) 5/28
(E) 1/56
Rationale: The probability that Jack and Sandy will make a basket but Jill will miss is 1/6*6/7*1/8=1/56.
The answer is E.
Answer: (E) 1/56
Question: Tammy climbed a mountain in two days. She spent a total of 14 hours climbing the mountain. On the second day, she walked at an average speed that was half a kilometer per hour faster, but 2 hours less than what she walked on the first day. If the total distance she climbed during the two days is 52 kilometers, how many E kilometers per hour did Tammy walk on the second day?
(A) 3
(B) 3.5
(C) 4
(D) 4.5
(E) 6
Rationale: Ans: C
Total time = 14 hrs
Let time traveled during 1st day = x
Let time traveled during 2nd day = x-2
Total time =14
x+x-2 = 14
x=8
speed * time = distance
s*8 + (s+0.5)(8-2) = 52
solving s = 4.5
now speed for 2nd day is 0.5 less than the 1st day which is 4.5
Thus speed for 2nd day = 4
Its simple algebra for s*8 + (s+0.5)(8-2) = 52 but for some reason Im getting 3.5 and not 4.5.
8s+6s+3=52
14s=49
s=3.5
Answer: (C) 4
Question: Running at the same constant rate, 16 identical machines can produce a total of 32 shirt per minute. At this rate, how many shirt could 8 such machines produce in 10 minutes?
(A)  911
(B)  100
(C)  101
(D)  160
(E)  785
Rationale: Let's take the approach that uses the answer choices to eliminate wasted time.
32/16 = 2 shirt per minute per machine. 8 machines = 16 per minute. 10 minutes worth = 160 shirt.
Looking at the answers it is clear...we can only choose (D)
THE CORRECT ANSWER IS D.
Answer: (D)  160
Question: A began business with 10000 and is joined afterwards by B with 20000. When did B join, if the profits at the end of the year are divided equally?
(A) 8 months
(B) 9 months
(C) 6 months
(D) 7 months
(E) None of these
Rationale: Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.
∴ Profit ratio is 12 × 10000 : (12 – x) × 20000
or 12 : 2(12 – x)
Since profit is equally divided so
12 = 2(12 – x) or x = 6. Thus B joined after 8 months.
Answer C
Answer: (C) 6 months
Question: There are 40 doors marked with numbers 1 to 40. There are 40 individuals marked 1 to 40.
An operation on a door is defined as changing the status of the door from open to closed or vice versa. All the doors are closed to start with. One at a time, one randomly chosen individual goes and operates the doors. The individual however operates only those doors which are a multiple of the number he/she is carrying. For example, the individual marked with number 5 operates the doors marked with 5, 10, 15, 20, 25, 30, 35, and 40. If every individual in the group gets one turn, then how many doors are open at the end?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: If a door is closed at the start, it requires an odd number of people to operate to be open at the end. Only the perfect squares have an odd number of factors.
The doors which are open at the end are: 1, 4, 9, 16, 25, 36 for a total of 6 doors.
The answer is D.
Answer: (D) 6
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good?
(A) 20/65
(B) 20/63
(C) 20/45
(D) 20/29
(E) 20/20
Rationale: Required probability = (5C3 . 4C1)/9C4
= (10 * 4)/126
= 20/63
Answer:B
Answer: (B) 20/63
Question: If q is a positive integer and q^2 is divisible by 12, then the largest positive integer that must divide q ^3 is
(A)  2^3
(B)  2^6
(C)  3^3
(D)  6^3
(E)  12^2
Rationale: Since q is an integer so q cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making q^2 as a multiple of 12))
q^2 is divisible by 12 (12 = 2*2*3), So, q should have at least one 2 and one 3 so that q^2 has a 2^2 and two 3
So, q will have a 2 and a 3. Or q will be a multiple of 6
So, largest possible integer than should divide q^3 is 6^3
So, Answer will be D
Answer: (D)  6^3
Question: A farmer spent $34 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 20% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined?
(A) $37.40
(B) $38.50
(C) $39.20
(D) $39.50
(E) $40.60
Rationale: A farmer spent 40% money on chicken feed, so he spent 0.4*$34=$13.6 on chicken feed, thus he spent the remaining 34-13.6=$20.4 on goat feed.
Now, since he bought chicken feed at a 20% discount then the original price of it was x*0.8=$13.6 --> x=$17.
Therefore if the farmer had paid full price for both the chicken feed and the goat feed, then he would he have spent 17+20.4=$37.4.
Answer:A.
Answer: (A) $37.40
Question: If 2^z is a factor of 23!, which of the following could be the value of z?
I. 22
II. 23
III. 24
(A) I ​only
(B) II only
(C) I​ and II
(D) I, II, and III
(E) None
Rationale: 23! contains all numbers from 1 to 23. To find the factor with the highest power of 2, we count the number of multiples of 2, 4, 8 and 16.
Multiples of 2 = 11
Multiples of 4 = 5
Multiples of 8 = 2
Multiples of 16 = 1
Total count = 19
The answer is E.
Answer: (E) None
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 150 m
(B) 200 m
(C) 240 m
(D) 400 m
(E) 150 m
Rationale: Answer: Option C
Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m.
Answer: (C) 240 m
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
(A) 1 kmph.
(B) 2 kmph.
(C) 3 kmph.
(D) 4 kmph.
(E) 5 kmph.
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A
Answer: (A) 1 kmph.
Question: The sale price at which a store sells an article is 25% more than its cost price. If the sale price is an integer, which of the following cannot be the cost price?
(A) $23
(B) $28
(C) $36
(D) $44
(E) $72
Rationale: Sale Price = (5/4)*(Cost Price)
If the sale price is an integer, then the cost price must be divisible by 4.
The answer is A.
Answer: (A) $23
Question: From a vessel on the first day, 1/3rd of the liquid evaporates. On the second day 3/4th of the remaining liquid evaporates. what fraction of the volume is present at the end of the 2 day
(A) 1/3
(B) 1/4
(C) 1/5
(D) 1/6
(E) 1/7
Rationale: let x be the volume...
after 1st day volume remaining=(x-x/3)=2x/3
after 2st day volume remaining=(2x/3)-((2x/3)*(3/4))
=(2x/3)(1-3/4)=(2x/3)*(1/4)=x/6
ANSWER:D
Answer: (D) 1/6
Question: Four barrels of water have an average capacity of 8 gallons. What is the maximum possible capacity of the smallest barrel W if the median is 10 gallons?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Suppose 4 barrels are B1, B2, B3, B4 in ascending capacity.
(B1+B2+B3+B4)/4 = 8
B1+B2+B3+B4=32
median is 10 ....... as the no. of terms are even i.e 4, median = (B2+B3)/2
==> B2+B3 = 20
now we have B1+B4 = 32-20 =12
Only the following possible cases can be there :
1,9,11,11
1,10,10,11
2,10,10,10
Max value of smallest barrel W= 2
Answer: (B) 2
Question: A sum of money at simple interest amounts to Rs. 800 in 3 years and to Rs. 854 in 4 years. The sum is:
(A) Rs. 438.
(B) Rs. 488.
(C) Rs. 518.
(D) Rs. 638.
(E) Rs. 664.
Rationale: S.I. for 1 year = Rs. (854 - 800) = Rs. 54
S.I. for 3 years = Rs.(54 x 3) = Rs. 162.
Principal = Rs. (800 - 162) = Rs. 638.
ANSWER : D
Answer: (D) Rs. 638.
Question: Of the 14 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man?
(A) 22
(B) 35
(C) 56
(D) 70
(E) 90
Rationale: another approach :
one scenario : [WWWM]
now we have 5 ways for the first women , 4 ways for the 2nd women and , 3 ways for the third women.
and 9 ways to select one man
so 5*4*3*9 = 540
now the three women are same so combinations with win them are irrelevant the 3 women can we arranged in 3! ways
hence 540/3!= 540/6= 90
E
Answer: (E) 90
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 37150. What percentage of profit did he make?
(A) 22
(B) 27
(C) 40
(D) 26
(E) 67
Rationale: The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 37150
Profit(%) = (37150 - 22250)/22250 * 100 = 67%.Answer:E
Answer: (E) 67
Question: If 1/a + 2/a + 3/a is an integer, which of the following must also be an integer?
(A) 12/a
(B) 3/a
(C) 6/a
(D) 9/a
(E) 15/a
Rationale: 1/a + 2/a + 3/a
=6/a
Answer C
Answer: (C) 6/a
Question: A group of medical interns at Bohemus Medical School want to go on dates. There are 5 girls and 5 guys. Assuming girls go on dates with guys, how many possible ways can these 10 medical interns date each other?
(A) 10
(B) 25
(C) 60
(D) 90
(E) 120
Rationale: 1st girl can go with 5 guys
2nd girl can go with remaining 4
3rd girl can go with remaining 3 and so on
so the total ways are 5!= 120
E should be the answer
Answer: (E) 120
Question: Average of five numbers is 16. If one number is excluded the average becomes 15. The excluded number is
(A) 20
(B) 40
(C) 55
(D) 65
(E) 67
Rationale: Explanation:
Number is (5*16) - (4*15) = 80-60= 20
Answer: Option A
Answer: (A) 20
Question: A straight one-mile stretch of highway is 40 feet wide. You ride your bike on a
path composed of semicircles as shown. If you ride at 5 miles per hour, how many hours will
it take you to cover the one-mile stretch?
Note: 1 mile = 5280 feet
(A) π/11 hours
(B) π/10 hours
(C) π/5 hours
(D) 2π/5 hours
(E) 2π/3 hours
Rationale: We wish to solve for t in the equation s = v t, where s is the distance covered in
feet, and v = 5 5280 feet an hour.
Note that each semicircle has a radius of 20 feet (half the width of the road). This means
that you must complete 5280=40 semicircles to cover the one-mile stretch. Each of thosesemicircles measures 20 feet. You ride then a grand total of
5280/40*20π=5280/2π
feet. We have then :
5280/2π=5*5280*t which gives t =π/10 hours
correct answer B
Answer: (B) π/10 hours
Question: Five medical experts, working together at the same constant rate, can write an anatomy textbook in 32 days. How many additional experts, working together at this same constant rate, are needed to write the textbook in 10 days?
(A) 7
(B) 9
(C) 11
(D) 13
(E) 15
Rationale: Each expert can write 1/160 of the book per day.
To complete the book in 10 days, we need 160/10 = 16 experts, thus 13 more experts are needed.
The answer is D.
Answer: (D) 13
Question: Govind, Bipul and Shaik has won Rs. 6000, Rs. 4000 and Rs. 8000 respectively in a Jockpat. The next time, Bipul has won Rs. 3000. The difference between the additional winnings of Govind and Shaik is?
(A) 400
(B) 1500
(C) 986
(D) 600
(E) 670
Rationale: Ratio of the Jockpat won by Govind, Bipul and Shaik is 6000 : 4000 : 8000 = 3 : 2 : 4
And also given that, additional winning of Bipul is Rs. 3000
=> 2 parts out of 9 parts is Rs. 3000
Now, required difference is 4 - 3 = 1 part
Required difference = 1/2 (3000) = Rs. 1500.Answer: B
Answer: (B) 1500
Question: In 2003 there are 28 days in February and 365 days in a year in 2004 there are 29 days in February and 366 days in the year. If the date march 11 2003 is Tuesday, then which one of the following would the date march 11 2004 would be?
(A) 27
(B) 35
(C) 56
(D) 2
(E) 11
Rationale: If 11-3-2003 is Tuesday, Then 11-3 - 2004 is Thursday
The number of odd days between the two dates are [3667]Rem[3667]Rem= 2.
Answer:D
Answer: (D) 2
Question: The average (arithmetic mean) of 4 different integers is 74. If the largest integer is 90, what is the least possible value of the smallest integer?
(A) 1
(B) 19
(C) 29
(D) 30
(E) 33
Rationale: Total of Integers=74*4=296
Lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer.
But all integers are distinct. So if the largest integer is 90, then the middle 2 will be 88 and 89
Lowest of least possible integer = 296-(90+89+88)=296-267=29
Answer: C
Answer: (C) 29
Question: Solve the equation for x : 2(x + 2y + 3) = -x + y
(A) 1
(B) 2
(C) 3
(D) -1
(E) -2
Rationale: E
-2
2(x + 2y + 3) = -x + 4y
2x + 4y + 6 = -x + 4y
3x + 6 = 0
3x = -6
=> x = -2
Answer: (E) -2
Question: The Weirdo Holiday Resort follows a particular system of holidays for its employees. People are given holidays on the days where the first letter of the day of the week is the same as the first letter of their names. All employees work at the same rate.
Starting on February 25, 1996, if Raja had finished his job on April 2, 1996, when would T and S together likely to have completed the job, had they started on the same day as Raja?
(A) March 15, 1996
(B) March 14, 1996
(C) March 22, 1996
(D) Data Insufficient
(E) None
Rationale: Explanation :
Raja doesn't have his name's first letter common to any of the day.so he won't rest. He works for 38 days to complete the job. So, he does 1/38 work in a day. Now, S will take break on saturday, sunday and T on tuesday, thursday. So on monday, wednesday and friday, they both will work simultaneously.
Now, we'll apply Zeller's rule to determine what day was it on feb,1996. It'll come out to be a sunday.
Now, if we start a week from sunday they'll do 10/38 amount of work in aweek. So, in 3 weeks they'll complete 30/38 amount of work and within next friday to complete the rest, total 21 + 6 = 27 days is required.
Answer : C
Answer: (C) March 22, 1996
Question: A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.
(A) 1909
(B) 1900
(C) 1908
(D) 1905
(E) 1901
Rationale: 65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74 => 1900
Answer: B
Answer: (B) 1900
Question: In the storage room of a certain bakery, the ratio of sugar to flour is 5 to 2, and the ratio of flour to baking soda is 10 to 1. If there were 60 more pounds of baking soda in the room, the ratio of flour to baking soda would be 8 to 1. How many pounds of sugar are stored in the room?
(A) 600
(B) 1200
(C) 1500
(D) 3600
(E) 6000
Rationale: Sugar:Flour = 5:2 = 25:10;
Flour:Soda = 10:1 = 10:1;
Thus we have that Sugar:Flour:Soda = 25x:10x:1x.
Also given that 10x/(1x+60) = 8/1 --> x=240 --> Sugar = 25x = 6000
Answer: E.
Answer: (E) 6000
Question: Calculate the HCF of 30, 108, 660
(A) 6
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: Explanation:
Lets solve this question by factorization method.
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
The factors of 108 are: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The factors of 660 are: 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660
Then the greatest common factor is 6.
Answer: Option A
Answer: (A) 6
Question: Two numbers are in the ratio 3 : 4. If the sum of numbers is 63, find the numbers.
(A) 26,37
(B) 25,38
(C) 27,36
(D) 28,35
(E) 29,34
Rationale: Sum of the terms of the ratio = 3 + 4 = 7
Sum of numbers = 63
Therefore, first number = 3/7 × 63 = 27
Second number = 4/7 × 63 = 36
Therefore, the two numbers are 27 and 36.
Answer:C
Answer: (C) 27,36
Question: The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 26th of September 1990?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Thursday
(E) Friday
Rationale: 19th September
1987: Saturday
1988: Monday (due to leap year)
1989: Tuesday
1990: Wednesday
Hence 26th September was a Wednesday.
The answer is C.
Answer: (C) Wednesday
Question: A train 330 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 18
(B) 6
(C) 5
(D) 54
(E) 1
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 330 * 3/55 = 18 sec.
Answer: A
Answer: (A) 18
Question: What is the area inscribed by the lines y =4, x = 2, y = 6-2x on an xy-coordinate plane?
(A) a) 1
(B) b) 2
(C) c) 4
(D) d) 6
(E) e) 8
Rationale: First, let's graph the lines y = 4 and x = 2
At this point, we need to find the points where the line y = 6-2x INTERSECTS the other two lines.
For the vertical line, we know that x = 2, so we'll PLUG x = 2 into the equation y = 6-2x to get y = 6-2(2) = 2
Perfect, when x = 2, y = 2, so one point of intersection is (2,2)
For the horizontal line, we know that y = 4, so we'll PLUG y = 4 into the equation y = 6-2x to get 4 = 6-2x. Solve to get: x = 1
So, when y = 4, x = 1, so one point of intersection is (1,4)
Now add these points to our graph and sketch the line y = 6-2x
At this point, we can see that we have the following triangle.
The base has length 1 and the height is 2
Area = (1/2)(base)(height)
= (1/2)(1)(2)
= 1
Answer:
A
Answer: (A) a) 1
Question: Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
(A) 2500 m^2
(B) 2510 m^2
(C) 2520 m^2
(D) 2600 m^2
(E) 2670 m^2
Rationale: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Answer: (C) 2520 m^2
Question: Kiran started a business investing Rs. 20,000. After 4 months, Sanket joined with a capital of Rs. 12000. At the end of the year, they earn a profit of Rs. 14,000. Find what will be the share of Sanket in the profit?
(A) Rs. 4000
(B) Rs. 4007
(C) Rs. 4001
(D) Rs. 4002
(E) Rs. 4047
Rationale: Explanation:
Kiran : Sanket = (20000 * 12) : (12000 * 8) = 5 : 2
Sanket's share = Rs. 14,000 * (2/7) = Rs. 4000
ANSWER: A
Answer: (A) Rs. 4000
Question: Rajan and Rakesh started a business and invested Rs.20000 and Rs.25000 respectively. After 4 months Rakesh left and Mukesh joined by investing Rs.15000. At the end of the year there was a profit of Rs.4600. What is the share of Mukesh?
(A) 2238
(B) 2378
(C) 1200
(D) 2877
(E) 1812
Rationale: Explanation:
Rajan is in the business for 12 months, Rakesh is for 4, and Mukesh is for 8.
Profits will be divided in ratio of (20 × 12) : (25 × 4) : (15 × 8) = 24 : 10 : 12
Share of Mukesh = 1246×4600=1200
Answer: C
Answer: (C) 1200
Question: The ratio between the speeds of two trains is 7: 8. If the second train runs 440 kms in 4 hours, then the speed of the first train is:
(A) 47.4 km/hr
(B) 57.19 km/hr
(C) 68.13 km/hr
(D) 96.25 km/hr
(E) 86.25 km/hr
Rationale: Let the speed of two trains be 7x and 8x km/hr.
Then, 8x = (440/4) = 110
x = (110/8) = 13.75
Hence, speed of first train = (7 x 13.75) km/hr = 96.25 km/hr.
Answer : D.
Answer: (D) 96.25 km/hr
Question: A circular well with a diameter of 2 metres , is dug to a depth of 14 metres. What is the volume of the earth dug out?
(A) 32 m3
(B) 36 m3
(C) 40 m3
(D) 44 m3
(E) None
Rationale: Solution
Volume	= πr2h
‹=› (22 /7 ×1×1×14)m3
‹=›44 m3.
Answer D
Answer: (D) 44 m3
Question: A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 4 hours. Working alone, the outlet pipe can empty out the tank in 4 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?
(A) 02:30 pm
(B) 03:30 pm
(C) 01:30 pm
(D) 04:30 pm
(E) 05:30 pm
Rationale: In 6 hours the inlet pipe will pump in water equal to 6*1/4 = 6/4 of the pool. So, 2/4 more than necessary, which should be compensated by the outlet pipe. To pump out 2/4 of the water the outlet pipe needs 8/4 = 2 hours.
Therefore, the outlet pipe should be opened at 9:30am + 6 hours - 2 hours = 01:30 pm.
Answer: C
Answer: (C) 01:30 pm
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
(A) 20/9
(B) 20/2
(C) 20/7
(D) 40/2
(E) 20/1
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.
The time required = d/s = 100/35 = 20/7 sec.
Answer: C
Answer: (C) 20/7
Question: A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work?
(A) 6 days
(B) 2 days
(C) 8 days
(D) 3 days
(E) 9 days
Rationale: Work done by A in 2 days = 2/5
Remaining work = 3/5
Work done by both A and B in one day = 1/5 + 1/10 = 3/10
Remaining work = 3/5 * 10/3 = 2 days.
Answer: B
Answer: (B) 2 days