MU-NLPC/Calc-aqua_rat huggingface dataset:
A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 12 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?	Choose the correct choice from the following choices:
A) 18/79
B) 1/60
C) 1/25
D) 1/50
E) 1/900

Solution: If it takes 12 minutes to inspect one vehicle, the # of vehicles that can be inspected in 3 hours (180 minutes) = 180/12= 
180/12 = 15
15. Hence, for calculating the probability that the police will find the transmitter within three hours, the favorable cases= 15. Now, we need to figure out the total # of cases.   The total # of cases = Total # of such cars possible. The details given about the car is that it starts with 79, which leaves 2 more digits, both of which can be filled by all 10 numbers (0-9). In addition, we have 3 letters, each of which can be filled by any from the set {A,B,C}. Hence the total # of such cars possible = 10*10*3*3= 
10*10*3*3 = 900
900   So, the probability that the police will find the transmitter within three hours= 15/900 = 1/60. Option 1/60
Answer: B
A man swims downstream 28 km and upstream 16 km taking 4 hours each time, what is the speed of the man in still water?  Choose the correct choice from the following.
A) 6.5
B) 8.6
C) 7.5
D) 9.2
E) 5.5

Solution: 28 --- 4 DS = 7   ? ---- 1   16 ---- 4 US = 4   ? ---- 1 M = ?   M = (7 + 4)/2= 
(7 + 4)/2 = 11/2 = around 5.5
5.5   Answer: 5.5
Answer: E
In a river flowing at 2 km/hr, a boat travels 48 km upstream and then returns downstream to the starting point. If its speed in still water be 6 km/hr, find the total journey time.
Choose the correct answer
A) 10 hours B) 12 hours C) 14 hours D) 18 hours E) None of these

Solution: Explanation :   speed of the boat = 6 km/hr   Speed downstream = (6+2)= 
(6+2) = 8
8 km/hr   Speed upstream= (6-2)= 
(6-2) = 4
4 km/hr   Distance traveled downstream= Distance traveled upstream = 48 km   Total time taken = Time taken downstream + Time taken upstream   = (48/8) + (48/4)= 
(48/8) + (48/4) = 18
18 hr. Answer : Option 18 hours
Answer: D
If x is a prime integer and y = 9x, which of the following CANNOT be a divisor of y? Choose one.
A) 18	B) 45	C) 28	D) 27	E) 99

Solution: Prime integer are as follows as 2,3,5,7,11.,   y = 9x   Go with options   if it is 18 so x must be 2 which is a prime integer   if it is 45 so x must be 5 which is a prime integer   if it is 28 so x must be 4 which is not a prime integer   so ans is 28
Answer: C
After decreasing 20% in the price of an article costs Rs.620. Find the actual cost of an article?	Answers:
A) 775	B) 620	C) 750	D) 800	E) 720

Solution: CP* (80/100) = 620   CP= 7.75 * 100 => CP = 775   775NSWER:775
Answer: A
From 5 consonants and 4 vowels, how many words can be formed using 3 consonants and 2 vowels? Pick: A) 7000 B) 7200 C) 7800 D) 7500 E) None

Solution: From 5 consonants, 3 consonants can be selected in 5C3 ways. From 4 vowels, 2 vowels can be selected in 4C2 ways. Now with every selection, number of ways of arranging 5 letters is 5P5 Total number of words =5C3*4C2*5P5= 7200   Answer 7200
Answer: B
A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.  Choose the correct choice from the following answers:
A) 220 km	B) 224 km	C) 230 km	D) 234 km	E) 255 km

Solution: (1/2)x/21 + (1/2)x/24 = 10   x/21 + x/24 = 20   15x=168x20   x=[168x20/15] = 224km   Answer is 224 km
Answer: B
A coin is tossed until sequence HTH appears (H denotes the fall of heads, T denotes the fall of tails). What is the probability E that the game will end after the fourth throw? Choose the correct choice from the following options.
A) 1/16 B) 3/32 C) 1/8 D) 3/16 E) 1/4

Solution: Another approach:   Two likely scenarios would be : HHTH or THTH   for each of the scenarios probability would be 1/16   So Probablilty E is 1/16 + 1/16 = 1/8.1/8
Answer: C
Find the odd man out
49, 51, 53, 55, 57, 62	Pick.
A) 57
B) 53
C) 49
D) 62
E) 51

Solution: 62 is the number which is not belong to the arithmetic progression where all other number are in A.P. Ans: 62
Answer: D
In how many ways can a group of 20 friends be seated round 2 tables if one of the tables can seat 12 and the other can seat 8 people?  Choose the correct choice:
A) 15C5 * 9! *4!  B) 15C3 * 8! *3!  C) 20C4 * 11! * 7!  D) 21C2 * 10! *3!  E) 25C5 * 10! *4!

Solution: 12 people can be selected from 20 people in 20C12 ways.   Remaining 8 people can be selected from 8 people in 8C8 ways.   Now, arranging 12 people on a round table = (12-1)= 
(12-1) = 11
11!   Arranging 8 people on a round table= (8-1)= 
(8-1) = 7
7!   Hence, total number of ways= 2020C4 * 11! * 7!12 * 11! * 820C4 * 11! * 7!8 * 7!   = 2020C4 * 11! * 7!4 * 11! * 7!   20C4 * 11! * 7!
Answer: C
A Man travelled a distance of 61 km in 9 hours. He travelled partly on foot at 4 km/hr and partly on bicycle at 9 km/hr. What is the distance travelled on foot?	Choose the correct choice from the following answers.
A) 33
B) 38
C) 16
D) 87
E) 127

Solution: Let the time in which he travelled on foot = x hr   Then the time in which he travelled on bicycle = (9 - x) hr   distance = speed x time   ⇒4x+9(9−x)=61⇒4x+81−9x=61⇒5x=20⇒x=4⇒ distance travelled on foot = 4x=4×4=16 km   Answer : 16
Answer: C
how many 6 digit no. can be formed using digits 0 to 5,without repetition such that number is divisible by digit at its unit place?
Pick:
A) 420 B) 426 C) 432 D) 456 E) 485

Solution: when unit place is 1 then numbers which are divisible by 1 = 96 (4*4*3*2*1*1 ways)   when unit place is 2 then numbers which are divisible by 2 = 96 (4*4*3*2*1*1 ways)   when unit place is 3 then numbers which are divisible by 3 = 96 (4*4*3*2*1*1 ways)   when unit place is 3 then numbers which are divisible by 4 = 42 (3*3*2*1*1*1 ways when last two digits are 24 and 4*3*2*1*1*1 ways when last two digits are 04)   when unit place is 3 then numbers which are divisible by 5 = 96 (4*4*3*2*1*1 ways)   total=426   ANSWER:426
Answer: B
The sum of the ages of 5 children born at the intervals of 3 years each is 70 years. What is the age of the youngest child?	Pick.
A) 2 years B) 4 years C) 6 years D) 8 years E) 10 years

Solution: Let the ages of the children be x, (x + 3), (x + 6), (x + 9) and (x +12) years.   Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 70   5x = 40 => x = 8.   Age of youngest child = x = 8 years.   ANSWER:8 years
Answer: D
In how many ways can three boys and five girls sit in a row such that all boys sit together?
Answers:
A) A)4320 B) B)9022 C) C)2880 D) D)1097 E) E)2781

Solution: Treat all boys as one unit. Now there are Six students and they can be arranged in 6! ways. Again three boys can be arranged among themselves in 3! ways.   Required number of arrangements   = 6! * 3! = 720 * 6= 
720 * 6 = 4_320
4320.   4320nswer:4320
Answer: A
A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year? Choose the correct choice from the following choices.
A) 53000	B) 58000	C) 50000	D) 59000	E) 69000

Solution: Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.   Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.   Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)   Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.   Income of A = Twice the income of B   (2500 + 18000 + P) = 2(P)   P = 20500   Total profit = 2P + 18000   = 2*20500 + 18000= 
2*20500 + 18000 = 59_000
59000   ANSWER:59000
Answer: D
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 90 kmph and 72 kmph. After how much time will the trains meet?  Answers
A) 20/8 sec B) 20/9 sec C) 20/7 sec D) 22/7 sec E) 60/7 sec

Solution: They are moving in opposite directions, relative speed is equal to the sum of their speeds.   Relative speed = (90 + 72)*5/18 = 9*5= 
9*5 = 45
45 mps.   The time required= d/s = 100/45 = 20/9 sec.Answer:20/9 sec
Answer: B
The sum of the numbers is 264. If the first number be twice the second and third number be one-third of the first, then the second number is: Options: A) 48 B) 54 C) 72 D) 84 E) 27

Solution: Let the second number be x. Then, first number = 2x and third number = 2x/3.   2x + x + 2x/3 = 264   11x/3 = 264   x = 72   ANSWER:72
Answer: C
The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, what is the weight of B?
Choose the correct choice.
A) 28	B) 30	C) 32	D) 34	E) 31

Solution: Let the weight of A, B and C are a,b and c respectively.   Average weight of A,B and C = 45   a + b + c = 45 × 3 = 135 --- equation(1)   Average weight of A and B = 40   a + b = 40 × 2 = 80 --- equation(2)   Average weight of B and C = 43   b + c = 43 × 2 = 86 --- equation(3)   equation(2) + equation(3) - equation(1)   => a + b + b + c - (a + b + c) = 80 + 86 - 135   => b = 80 + 86 -135 = 166 - 135= 
166 - 135 = 31
31   Weight of B= 31 Kg   Answer is 31.
Answer: E
Two taps can separately fill a cistern 5minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 20 minutes. The waste pipe can empty the full cistern in?  Pick one:	A) A)7	B) B)4.6	C) C)8	D) D)9	E) E)5

Solution: 1/5 + 1/15 - 1/x = 1/20   x = 4.6   Answer:4.6
Answer: B
The speed of a boat in still water is 65kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?	Choose the correct choice from the following choices:
A) 80,47 kmph B) 80,80 kmph C) 80,42 kmph D) 80,40 kmph E) 85,45 kmph

Solution: Speed downstream = 65 + 20= 
65 + 20 = 85
85 kmph   Speed upstream= 65 - 20= 
65 - 20 = 45
45 kmph.Answer:85,45 kmph
Answer: E
A mixture contains milk and water in the ratio 3:2. On adding 10 litters of water, the ratio of milk to water becomes 2:3. Total quantity of milk & water before adding water to it? Choose the correct choice from the following answers:	A) 10	B) 30	C) 50	D) 20	E) 30

Solution: Explanation:   milk:water = 3:2   after adding 10 liters of water   milk:water = 2:3   Olny water patrs increase when mixture of water   milk:wate = 3:2 = 2*(3:2) = 6:4   after adding 10 liters of water   milk:water = 2:3 = 3*(2:3) = 6:9   milk parts always same   Short cut method:   milk:water = 6 : 4   after adding 10 liters of water   milk:water = 6 : 9   milk is same but water increse 10liters then the water ratio is increse 5 parts   5 part -----> 10 liters   The quantity of milk in the original mixture is = 6 : 4 = 6 + 4= 
6 + 4 = 10
10   10 parts -----> 20 liters (Answer is= 20)   Short cut method - 2 : for Only milk problems   milk : water   6 : 4   6 : 9   milk ratio same but water ratio 5 parts incress per 10 liters   5 part of ratio -------> 10 liters   10 part of ratio ------> 20 liters   Answer: Option 20
Answer: D
A car traveled the first quarter of a certain distance at six times the speed it traveled the remaining distance. What proportion of the total time traveled, was the time taken to travel the first quarter of the distance?
Choose the correct option
A) 1/14  B) 1/15  C) 1/16  D) 1/17  E) 1/19

Solution: These problems can be solved through algebra or sly number picking. Being a big fan of solving problems with numbers, let's pick a total distance divisible by 4 (say 40) so we can break it up into quarters, and a speed that can easily be one sixth, say 10. Each quarter is thus 10 kilometers (or miles or feet or angstroms for all it matters), and the runner's speed is 10 km/h for the first quarter and 1 2/3 km/h for the remaining quarters.   He'll take 1 hour to do the first quarter and then 6 hours for the second quarter, 6 hours for the third and 6 hours for the fourth. On total he will take 19 hours to complete this race, of which 1 hour was spent on the first quarter. So 1/19. Answer 1/19.
Answer: E
Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 5 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?	Choose the most appropriate option
A) 1/7 B) 1/5 C) 1/4 D) 5/17 E) 1/3

Solution: Alice's take-home pay was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did not save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?   solution:   Suppose the portion of her salary that she saved is X   and the remaining portion is Y   X+Y= total take home salary   given, 12X = 5Y   or 12/5X = Y   Total take-home salary= X+12/5X= 17/5 X   hence, she saved 5/17-th portion of her take home salary   5/17
Answer: D
8,27,64,125,216,???,512 Choose the correct option:
A) 346	B) 343	C) 348	D) 339	E) 340

Solution: it is a series of cubes of numbers....   8=2^3   27=3^3   64=4^3   125=5^3   216=6^3   512=8^3   So, 7^3=343 is the missing number.   ANSWER:343
Answer: B
Donovan took a math test and got 35 correct and 12 incorrect answers.
What was the percentage of correct answers? (Round to the nearest
hundredth) Pick one
A) 57.78%  B) 67.78%  C) 74.47%  D) 47.78%  E) 97.78%

Solution: 35 correct our of 47 total (35+12)   35/47   correct answer 74.47%
Answer: C
One copy machine can make 20 copies a minute, and a second copy machine makes 10 copies a minute. If the two copiers work together, how long would it take them to make 900 copies?  Pick one:
A) 10 minutes  B) 20 minutes  C) 25 minutes  D) 30 minutes  E) 35 minutes

Solution: Total work done by both machines in a minute = 20 + 10= 
20 + 10 = 30
30 copies   Total number of copies required= 900   Time = 900/30= 
900/30 = 30
30 mins   Answer 30 minutes
Answer: D
Find the fraction which has the same ratio to 2/13 that 5/34 has to 7/48.	Choose the correct choice from the following options: A) 240/1542 B) 230/1521 C) 240/1547 D) 240/1528 E) 240/1521

Solution: P : 2/13 = 5/34 : 7/48   As the product of the means is equal to the product of the extremes.   P*7/48 = 2/13 * 5/34   P*7/48 = 10/442   P = 480/3094 => P = 240/1547   Answer: 240/1547
Answer: C
Two men X and Y started working for a certain company at similar jobs on January 1, 1950. X asked for an initial salary of Rs. 300 with an annual increment of Rs. 30. Y asked for an initial salary of Rs. 200 with a rise of Rs. 15 every 6 months. Assume that the arrangements remained unaltered till December 31, 1959. Salary is paid on the last day of the month. What is the total amount paid to them as salary during the period? Choose the correct choice from the following answers:
A) Rs. 93,300  B) Rs. 93,200  C) Rs. 93,100  D) None of these  E) Cannot be determined

Solution: Explanation :   Amount of money given to X   = 12 x 300 + 12 x 330 + ....... + 12 x 570.   = 12[ 300 + 330 + .........+ 540 + 570 ].   = 12 x (10/2) [ 600 + 9 x 30 ].   = 52200.   Amount of money given to Y is   = 6 x 200 + 6 x 215 + 6 x 230 + 6 x 245 + ... upto 20 terms   = 6 [ 200 + 215 + 230 + .....485 ]   = 6 x (20/2)[ 400 + 19 x 15]   = 6 x 10 [ 400 + 285 ] .   = 60 x 685 = 41110   Hence, the total amount paid is 52200 + 41110 = Rs 93,300.   Rs. 93,300nswer : Rs. 93,300
Answer: A
A is half good a work man as B and together they finish a job in 18 days. In how many days working alone B finish the job? Choose the correct answer:
A) 23
B) 22
C) 27
D) 36
E) 48

Solution: 27   27   W27 = 1:2   2x + x = 1/18 => x = 1/54   2x = 1/27 => 27 days
Answer: C
The sum of 55 consecutive integers is 5555. What is the greatest integer in the set?
Choose the correct choice
A) 126  B) 128  C) 130  D) 132  E) 134

Solution: Let x be the first integer in the set, then x+54 is the largest integer.   The sum is: x+(x+1)+(x+2)+...+(x+54)   = 55x + 54*55/2   = 55(x+27)   Then x+27=101   x=74   The largest integer in the set is  74+54= 
 74+54 = 128
128   The answer is 128.
Answer: B
On dividing a number by 999, the quotient is 366 and the remainder is 103. The number is:	Choose one
A) 364724
B) 365387
C) 365737
D) 366757
E) None of these

Solution: Required number= 999*366+103= (1000-1)*366+103= 366000-366+103= 
366000-366+103 = 365_737
365737.   Answer: 365737
Answer: C
The ratio of three numbers is 1:2:3 and their sum is 60. The second number of the three numbers is?
Pick:
A) 24 B) 26 C) 20 D) 29 E) 30

Solution: 1:2:3   Total parts = 6   6 parts --> 60   1 part ---->10   The second number of the three numbers is =2 * 10= 
2 * 10 = 20
20   Answer : 20
Answer: C
Carl can wash all the windows of his house in 6 hours. His wife Maggie can wash all the windows in 7 hours. How many hours will it take for both of them working together to wash all the windows?	Choose the correct option:
A) 2 B) 2 1/4 C) 42 3/3 D) 4 1/2 E) 5

Solution: Work hrs=AB/(A+B)= 42/13 =42 3/3   Answer is 42 3/3
Answer: C
Gordon is twice as old as Tony was when Gordon was as old as Tony is now. The combined age of Gordon and Tony is 112 years. How old are Gordon and Tony now?
Choose the correct choice from the following.
A) Gordon 64 and Tony 48
B) Gordon 74 and Tony 38
C) Gordon 84 and Tony 48
D) Gordon 64 and Tony 58
E) None of the above

Solution: When Gordon was 48, Tony was 32(ie half the age Gordon is now).   Gordon 64 and Tony 48nswer : Gordon 64 and Tony 48
Answer: A
If an object travels 300 feet in 5 seconds, what is the object's approximate speed in miles per hour? (Note: 1 mile = 5280 feet)
Answers:
A) 39  B) 38  C) 40  D) 41  E) 34

Solution: 1 mile = 5280 feet   => 1 feet = 1/5280 miles   If the object travels 300 feet in 5 sec   then it travels 300/5 * 60 * 60 feet in 1 hour (1 hr = 60 min * 60 sec)   = 3600 * 60 feet in 1 hour   = 216000 feet in 1 hr   = 216000/5280 miles in 1 hour   = 21600/528 miles/hr ~ 41 miles/hr   Answer - 41
Answer: D
Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?
Choose the correct option
A) 2977	B) 9261	C) 2890	D) 2890	E) 3243

Solution: A = 8000(21/20)3   = 9261   Answer: 9261
Answer: B
In a company 10% of male staff are same in number as 1/4th of the female staff. What is the ratio of male staff to female staff Choose the correct choice from the following options:
A) 3 : 2  B) 5 : 2  C) 2 : 1  D) 4 : 3  E) 1 : 2

Solution: 10% of MS = 1/4th of FS   -> 10MS/100 = 1/4FS   -> MS = 5/2 FS   :. MS/FS = 5/2 = MS : FS = 5 : 2   ANSWER:5 : 2
Answer: B
A train moves fast a telegraph post and a bridge 264 m long in 4 sec and 20 sec respectively. What is the speed of the train?  Select the correct option
A) 89	B) 23	C) 59.4	D) 79.2	E) 67

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 4 => x = 4y   (x + 264)/20 = y   y = 16.5   Speed = 16.5m/sec = 16.5 * 18/5= 
16.5 * 18/5 = 59.4
59.4 km/hr.   Answer: Option 59.4
Answer: C
There are 600 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?
Select the correct option
A) 243 B) 265 C) 375 D) 390 E) 400

Solution: In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 600. Hence   3x + 5x = 600   Solve for x   8x = 600   x = 75   Number of boys   3x = 3 × 75 = 225   Number of girls   5x = 5 × 75 = 375   375
Answer: C
A circular rim 30 inches in diameter rotates the same number of inches per second as a circular rim 15 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?	Choose one
A) 48pi/x
B) 75x
C) 48x
D) 24x
E) 120x

Solution: Revolutions - circumference of the rim.   => 30pi*X*60 = 15pi*Revolutions   => 2/1 *X *60 = Revolutions => 120X - Option 120x
Answer: E
A 160 meter long train crosses a man standing on the platform in 9 sec. What is the speed of the train?
Choose one:
A) 96 kmph	B) 64 kmph	C) 52 kmph	D) 86 kmph	E) 76 kmph

Solution: S = 160/9 * 18/5= 
160/9 * 18/5 = 64
64 kmph   ANSWER:64 kmph
Answer: B
If circles x and y have the same area and circle x has a circumference of 10π, half of the radius of circle y is:
Answers:
A) 16 B) 8 C) 4 D) 2.5 E) 1

Solution: x be radius of circle x   y be radius of circle y   given:   pi*x^2 = pi*y^2   also,   2*pi*x = 10*pi   x =5   thus y = 5   y/2 = 2.5   Ans: 2.5
Answer: D
If $5,000 is invested in an account at a simple annual rate of r percent, the interest is $250. When $20,000 is invested at the same interest rate, what is the interest from the investment? Choose the correct choice from the following choices.
A) $700	B) $750	C) $800	D) $1000	E) $900

Solution: -> 250/5,000=5% and 20,000*5%=1000.   Thus, $1000 is the answer.
Answer: D
If the perimeter of a rectangular garden is 900 m, its length when its breadth is 190 m is?  Choose the correct choice from the following options.
A) 338 m  B) 778 m  C) 200 m  D) 260 m  E) 971 m

Solution: 2(l + 190)   = 900 => l   = 260 m   Answer:260 m
Answer: D
A completes a piece of work in 3/4 of the time in B does, B takes 4/5 of the time in C does. They got a profit of Rs. 40000 how much B gets?	Choices.
A) 12765	B) 121227	C) 26887	D) 19977	E) 26992

Solution: Assume C takes 20 Days. Now B takes 4/5 (20) = 16 days. 12765 takes 3/4(16) = 12   Now their efficiencies ratio = 1/20 : 1/16 : 1/12 = 12 : 15 : 20   B's share in the profit of Rs.40000 = 15/47 (40000) = Rs.12765   12765nswer:12765
Answer: A
A tank is filled by 3 pipes A,B,C in 8 hours. Pipe C is twice as fast as B and B is twice as fast as A. How much will pipe A alone take to fill the tank ? Select: A) 25hr B) 35hr C) 56hr D) 20hr E) 50hr

Solution: Suppose pipe A alone take x hours to fill the tank   Then pipe B and C will take x/2 and x/4 hours respectively to fill the tank.   1/x + 2/x + 4/x = 1/8   7/x = 1/8   x = 56 hours   Answer is 56hr
Answer: C
Apple costs L rupees per kilogram for first 30kgs and Q rupees per kilogram for each additional kilogram. If the price of 33 kilograms is 360 and for 36kgs of Apples is 420 then the cost of first 25kgs of Apples is Choose the correct option.
A) 100	B) 250	C) 125	D) 110	E) 115

Solution: Ans: 250y framing equations we get   30L+3Q=360   30L+6Q=420   Eliminate Q by multiplying the first equation by 2 and subtracting second equation from the first   Then we get L = 10   Cost of 10 kgs of apples =25x 10 = 250   Answer:250
Answer: B
Approximately how many cubic feet of water are needed to fill a circular swimming pool that is 60 feet across and 6 feet deep?	Choose the most appropriate option
A) 900	B) 4000	C) 10000	D) 17000	E) 25000

Solution: Answer Should be D.   V= \pir^2h= \pi*30^2*6= approximately 17000
Answer: D