MU-NLPC/Calc-aqua_rat huggingface dataset:
Balls of equal size are arranged in rows to form an equilateral triangle. the top most row consists of one ball, the 2nd row of two balls and so on. If 253 balls are added, then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did. How many balls made up the triangle? Choose the correct choice.
A) 903	B) 2209	C) 2878	D) 1210	E) 1560

Solution: As expected, this question boils down to 2 equation,   Consider total number of Balls in Triangle = T and number of balls in last row = x.   1+2+3+...+x = T   x(x+1)/2 = T ----(a)   As mentioned in the question, side of a square will be (x-8) and total number of Balls in square will be (T+253)   (x-8)^2 = T+253 -----(b)   Now the hardest part of the question will be to solve these 2 equations and this looks like time consuming BUT the easy way will be plug and play. Also, we've to find a value of T (from 5 optiosn given below) which can make a square of a a number. One we know this, it will be a cake walk.   We can see that option A fits this criteria in eq (b). Add - 903+253 = 1156 = 34^2 = (x-8)^2 Hence, x = 42.   Cross check by putting in eq (a) = x(x+1)/2 = T = > 42*43/2= 
42*43/2 = 903
903   Hence, answer is 903.
Answer: A
2 gears one with 12 teeth and other one with 14 teeth are engaged with each other. One teeth in smaller and one tooth in bigger are marked and initially those 2 marked teeth are in contact with each other. After how many rotations of the smaller gear with the marked teeth in the other gear will again come into contact for the first time? Options.
A) 6  B) 7  C) 8  D) 9  E) 2

Solution: Assume the distance between the teeth is 1 cm. Then the circumference of first gear is 12 cm and the second is 14 cm.   Now LCM (12, 14) = 84. So to cover 84 cm, the first gear has to rotate 84128412 = 7 rounds (the second gear rotates 84 / 14= 
84 / 14 = 6
6 rounds as it is bigger)   Correct Option : 6
Answer: A
A total of m different points are selected on a particular line, and a total of n different points are selected on another line parallel to the first, where each of m and n is greater than 1. In how many different ways can a triangle be made with its vertices at three of the selected points?
Choose the correct choice from the following choices:  A) m^2n+mn^2  B) mn(m+n-2)  C) mn(m+n−2)/2  D) (m+n)(m+n−1)(m+n−2)/6  E) (m+n)!/m!n!

Solution: ase 1: One point on particular line and other 2 points on parallel line. #ways=   m* nc2   Case 2: one point on parallel line and other 2 on particular line.   n* mc2   Total   m* nc2+ n* mc2   mn(m+n-2)   ANS:mn(m+n-2)
Answer: B
A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is?
Choose one.
A) 25/42	B) 25/46	C) 25/48	D) 25/18	E) 25/29

Solution: Total fruits = 9   Since there must be at least two apples,   (⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃   = 25/42.   25/42nswer: 25/42
Answer: A
At what rate percent on simple interest will Rs.1750 amount to Rs.2000 in 5 years?	Choose the correct choice from the following answers:
A) 4 %	B) 3 6/7 %	C) 2 6/7 %	D) 5 %	E) 6 %

Solution: Explanation:   250 = (1750x5xR)/100   250 = (175xR)/2   500 = (175xR)   R = 500/175   R = 2 6/7 %   Answer: Option 2 6/7 %
Answer: C
How many times the keys of a writter haveto be pressedin order to write first 400 counting no.'s?
Choose the correct choice from the following answers:	A) 998	B) 1000	C) 1092 times	D) 1100	E) 1200

Solution: 1 to 9 = 9 * 1= 
9 * 1 = 9
9   10 to 99= 90 * 2= 
90 * 2 = 180
180   100 to 400= 301 * 3= 
301 * 3 = 903
903   -----------   1092   1092 times
Answer: C
In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?  Choices:
A) 1/3	B) 2/3	C) 1/4	D) 1/5	E) 2/5

Solution: Total number of balls = (8 + 7 + 6)= 
(8 + 7 + 6) = 21
21.   Let E= event that the ball drawn is neither red nor green   = event that the ball drawn is blue.   n(E) = 7   =>7/21 = 1/3   1/3NSWER 1/3
Answer: A
The average age of 25 students of a class is 25 years. Out of these, the average age of 10 students is 22 years and that of the other 14 students is 28 years. The age of the 25th student is?
Choose the correct choice from the following answers
A) 10
B) 15
C) 13
D) 11
E) 9

Solution: Age of the 25th student = 25*25 - (10*22+14*28) = 625-612= 
625-612 = 13
13 years   Answer is 13
Answer: C
A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 95, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?
Choose the correct answer:
A) 74 B) 75 C) 76 D) 77 E) 81

Solution: ratio is 4:6:5 , numbers are 4x, 6x, 5x   total scores of each class is (65*4x + 6x * 95 + 77*5x) = 260x+570x+385x = 1215x   total number of students 260 +570 +385= 
260 +570 +385 = 1_215
1215x   total number of students= 15x   average = 1215x/15x = 81   81 is the answer1215 /15= 
1215 /15 = 81
81   81 is the answer
Answer: E
A train 280 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?	Choose the correct option.
A) 15	B) 6	C) 7	D) 9	E) 5

Solution: Speed of train relative to man = 60 + 6= 
60 + 6 = 66
66 km/hr.= 66 * 5/18 = 55/3 m/sec.   Time taken to pass the men = 280 * 3/55 = 15 sec.15nswer: 15
Answer: A
How many integers between 324,805 and 458,705 have tens digit 1 and units digit 3?
Pick one.
A) 1,349 B) 1,353 C) 10,040 D) 1,354 E) 10,400

Solution: There is one number in hundred with 1 in the tens digit and 3 in the units digit: 13, 113, 213, 313, ...   The difference between 324,805 and 458,705 is 458,705-324,805=134,900 - one number per each hundred gives 134,900/100=1,349 numbers.   1,349nswer: 1,349.
Answer: A
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 90 kmph. In how much time will the trains cross each other? Select:	A) 11	B) 10	C) 12	D) 13	E) 14

Solution: Relative speed = (54 + 90)* 5/18 = 7 * 5 = 40 mps.   The time required = d/s = (100 + 100 + 200)/40   = 400/40= 
400/40 = 10
10 sec.   Answer: 10
Answer: B
Find the least number which when divided by 35 and 11 leaves a remainder of 1 in each case.
Choose the most appropriate option: A) 366 B) 236 C) 367 D) 365 E) 386

Solution: Explanation:   The least number which when divided by different divisors leaving the same remainder in each case   = LCM(different divisors) + remainder left in each case.   Hence the required least number   = LCM(35, 11) + 1 = 386.   Answer: 386
Answer: E
A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey? Choose the correct answer:
A) 8
B) 4
C) 3
D) 2
E) 6

Solution: M = 45   S = 1.5   DS = 6   US = 3   AS = (2 * 6 * 3) /9= 
(2 * 6 * 3) /9 = 4
4   Answer: 4
Answer: B
A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank? Choose the correct choice from the following options.
A) 76 hrs	B) 97 hrs	C) 35 hrs	D) 16 hrs	E) 12 hrs

Solution: Suppose pipe A alone takes x hours to fill the tank.   Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.   1/x + 2/x + 4/x   = 1/5   7/x = 1/5 => x = 35 hrs.   Answer: 35 hrs
Answer: C
If a positive even number n is not divisible by 3 or 4, then the product (n + 6)(n + 8)(n + 10) must be divisible by which of the following?
I. 24
II. 32
III. 96  Choose the correct choice:
A) None  B) I only  C) II only  D) I and II only  E) I, II, and III

Solution: n is a multiple of 2 but not a multiple of 3 or 4   Possible values of n = 10, 14, 22.....   @n=10 : (n + 6)(n + 8)(n + 10) = 16*18*20 i.e. Divisible by 24, 32 and 96 all   @n=14 : (n + 6)(n + 8)(n + 10) = 20*22*24 i.e. Divisible by 24, 32 and 96 all   @n=22 : (n + 6)(n + 8)(n + 10) = 28*30*32 i.e. Divisible by 24, 32 and 96 all   Answer: Option I, II, and III
Answer: E
Mysoon collects glass ornaments. Ten more than 1/6 of the ornaments in her collection are handmade, and 1/2 of the handmade ornaments are antiques. If 1/10 of the ornaments in her collection are handmade antiques, how many ornaments are in her collection?	Choose the most appropriate option.
A) 36	B) 60	C) 108	D) 144	E) 300

Solution: The number of ornaments = a   Ten more than 1/6 of the ornaments in her collection are handmade => Handmade = 10+a/6   1/2 of the handmade ornaments are antiques => Handmade ornaments = 1/2*(10+a/6) = 5 + a/12   1/10 of the ornaments in her collection are handmade antiques => Handmade ornaments = a/10   => 5 + a/12 = a/10 => a = 300   Ans: 300
Answer: E
Every letter in the alphabet has a number value that is equal to its place in the alphabet. Thus, the letter A has a value of 1, the letter B has a value of 2, the letter C has a value of 3, etc... The number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word. What is the number value of the word "COW"? Select.
A) 120	B) 123	C) 126	D) 129	E) 132

Solution: "COW" = (3+15+23)*3= 
(3+15+23)*3 = 123
123.   The answer is 123.
Answer: B
The owner of a cell phone shop charges his customer 23% more than the cost price. If a customer paid Rs.7,011 for a cell phone, then what was the cost price of the cell phone?  Choose the correct choice from the following answers.
A) Rs.5,845  B) Rs.6,750  C) Rs.5,700  D) Rs.6,925  E) None of these

Solution: Explanation:   123% of Rs.5,700P =SP   Therefore, Rs.5,700P = Rs.7,011x100/123 = Rs.5700   Answer: Option Rs.5,700
Answer: C
A cube of edge 5 cm is cut into cubes of each edge 1 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to Choose the correct option
A) 1 : 5
B) 1 : 25
C) 1 : 125
D) 1 : 625
E) None

Solution: Solution   Required ratio	=(6x1x1 / 6x5x5)   ‹=› 1/ 25   ‹=› 1 : 125.   Answer 1 : 25
Answer: B
In a school of 650 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities? Choose the correct answer:	A) 173	B) 163	C) 153	D) 143	E) 117

Solution: 44 + 28 + 10= 
44 + 28 + 10 = 82
82%   100 – 82= 18%    650 * 18/100= 
 650 * 18/100 = 117
117   ANSW117R:117
Answer: E
Mr Amin borrowed some money from Mr Vishwas. The rate of interest for first two years is 8% p.a., for the next three years is 11 % p.a. and for the period beyond 5 years 14% p.a. Mr Vishwas got an amount of 10920 as an interest at the end of eight years. Then what amount was borrowed by Mr Amin ?  Choose one:
A) 12000  B) 15000  C) 1400  D) Data inadequate  E) None of these

Solution: Let ‘x’ be the amount borrowed by Mr Amin.   ∴ x×2×8/100+x×3×11/100+x×3×14/100=10920   or, 91⁄100x = 10920 or x = 10920×100/91=12000   12000nswer 12000
Answer: A
The ‘moving walkway’ is a 300-foot long conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a combined rate (including both walkway and foot speed) of 6 feet per second, reaches the group of people, and then remains stationary until the walkway ends. What is Bill’s average rate of movement W for his trip along the moving walkway? Choose the correct choice from the following options:
A) 2 feet per second
B) 2.5 feet per second
C) 3 feet per second
D) 4 feet per second
E) 5 feet per second

Solution: I get E.   Their rate is 3 ft/sec and his is 6 ft/sec. Their distance is d-120 and his distance is d.   So we get two equations:   3t=d-120   6t=d   Substituting, we get 3t=6t-120, or t=40 which means that d=240 so Bill traveled 240 ft and they traveled 120 ft. (They were at 240 on the conveyor belt when they met.   So, Bill's average rate of movement W is:   He traveled 6 ft/sec for 240 ft and 40 seconds. He traveled 3 ft/sec for the remaining 60 ft for 20 seconds.   (240+60)/(20+40)= 
(240+60)/(20+40) = 5
5 ft/sec=5 feet per second
Answer: E
In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?
Choices: A) 144 B) 119 C) 113 D) 88 E) 31

Solution: Greatest Possible Number taken both should be 144 (As it is maximum for One)   Smallest Possible Number taken both should be given by   Total - Neither = A + B - Both   Both = A+B+Neither - Total (Neither must be 0 to minimize the both)   So 144 + 119 + 0 - 232= 
144 + 119 + 0 - 232 = 31
31   Greatest - Smallest is  144-31= 
 144-31 = 113
113   So answer must be C. 113
Answer: C
In a certain circle there are 9 points. What is the number of the triangles connecting 3 points of the 9 points?	Choose the correct choice
A) 12	B) 84	C) 108	D) 120	E) 132

Solution: IMO : B   HERE we have to select 3 points out of 9 points. Order is not important   So the answer will be 9c3 = 84   answer 84
Answer: B
In an office, 10 percent of the workers have at least 5 years of service, and a total of 16 workers have at least 10 years of service. If 90 percent of the workers have fewer than 10 years of service, how many of the workers have at least 5 but fewer than 10 years of service?
Select:  A) 16  B) 64  C) 50  D) 144  E) 160

Solution: (10/100)Workers = 16 = > number of workers = 160   (10/100)*Workers = x+16 = > x = 16   16nswer 16
Answer: A
John makes $50 a week from his job. He earns a raise andnow makes $75 a week. What is the % increase?  Choices:
A) 15% B) 16.66% C) 50% D) 19% E) 21%

Solution: Increase = (25/50)*100 = (1/2)*100= 
(1/2)*100 = 50
50%.   50%
Answer: C
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1000 resolutions?	Select the correct option:
A) 1408 m B) 1704 m C) 1479 m D) 1427 m E) 1297 m

Solution: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 1000 resolutions.   = 1000 * 2 * 22/7 * 22.4= 
1000 * 2 * 22/7 * 22.4 = 140_800
140800 cm= 1408 m   1408 mnswer:1408 m
Answer: A
Two trains are moving in opposite directions @100kmph and 120kmph. Their length are 500m and 700m. The time taken by the slower train to cross faster train in second is?  Choose the correct answer:
A) 15sec  B) 18.3sec  C) 19.6sec  D) 20.4sec  E) 22.5sec

Solution: Relative speed = 100+120= 
100+120 = 220
220*5/18= 550/9 m/s   Distance covered = 500+700= 
500+700 = 1_200
1200m   Required time= 1200*9/550 = 19.6sec   Answer is 19.6sec
Answer: C
A vendor bought dog for Rs. 1, and a cat for Rs. 1.20, a pig for Rs.1.34, He totally purchased 100 animals for 100 Rs. Then find no of cats.  Choose the correct choice from the following options.
A) 10	B) 12	C) 14	D) 15	E) 16

Solution: 50 - pigs   10 - cats   10NSWER:10
Answer: A
A man can row a boat at 24 kmph in still water. If the speed of the stream is 8 kmph, what is the time taken to row a distance of 54 km downstream?	Choose the correct choice from the following answers:  A) 27/16 hours  B) 27/33 hours  C) 28/13 hours  D) 27/13 hours  E) 30/13 hours

Solution: Speed downstream = 24 + 8= 
24 + 8 = 32
32 kmph.   Time required to cover 54 km downstream= d/s = 54/32 = 27/16 hours.27/16 hoursnswer:27/16 hours
Answer: A
A certain auto manufacturer sold 2% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.3 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?	Pick one:
A) 22,50,000	B) 22,80,000	C) 22,90,000	D) 22,95,000	E) 23,00,000

Solution: Let's assume in 2006 the manufacturer sold X.   In 2007 he sold X-2/100(X)   If sales in 2006,X= 2.3 million find X-2/100(X)   (2.3 x 10^6)-2/100(2.3 x 10^6)   2300000-46000=22,54,000-----> 22,50,000(approx)   22,50,000nswer-22,50,000
Answer: A
You have a bag of 9 letters: 3 Xs, 3 Ys and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different R ways can you place one letter into each area such that there are no rows or columns with 2 or more of the same letter?	Choices.
A) 5	B) 6	C) 9	D) 12	E) 18

Solution: Consider one particular arrangement of the first row: XYZ, then we can construct only two boxes with so that no rows or columns have 2 or more of the same letter:   XYZ   YZX   ZXY   And:   XYZ   ZXY   YZX   Now, the first row itself can be arranged in 3!=6 ways (since there are three distinct letter), hence the total number of boxes possible R is   2*6= 
  2*6 = 12
12.   Answer: 12.
Answer: D
Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:  Choose the correct choice from the following choices.
A) 10  B) 50  C) 40  D) 20  E) 30

Solution: Let the numbers be 3x, 4x and 5x.   Then, their L.C.M. = 60x.   So, 60x = 2400 or x = 40.   {\color{Blue} \therefore } The numbers are (3 x 40), (4 x 40) and (5 x 40).   Hence, required H.C.F. = 40.   Answer: Option 40
Answer: C
A discount dealer professes to sell his goods at cost price
but uses a weight of 960 gms for a Kg weight .Find his gain %?	Choose the correct choice from the following answers:
A) 25%
B) 6%
C) 6/25%
D) 25/6%
E) 42%

Solution: Gain%=[(error*100)/(true value-error)]%   =[(40*100)/1000-40)]%=25/6%   ANSWER 25/6% 25/6%
Answer: D
eight family members: 5 grandchildren (3 brothers and 2 sisters) and their 3 grandparents are to be seated around a circular table. How many different seating arrangements are possible so that 2 sisters are seated between any two of the three brothers?  Choose the most appropriate option:
A) 120	B) 288	C) 1440	D) 2880	E) 8640

Solution: Answer: 288.
Answer: B
A large tanker can be filled by two pipes A and B in 30 and 15 hours respectively. How many hours will it take to fill the tanker from empty state if A and B fill it together?
Answers:
A) 8hr  B) 10hr  C) 12hr  D) 9hr  E) 5hr

Solution: Part filled by A in 1hr = 1/30   Part filled by 10hr in 1hr = 1/15   part filled by A+10hr = 1/30 + 1/15 = 1/10   10hroth the pipes can fill the tank in = 10 hours   Answer is 10hr
Answer: B
In the fifth grade at Parkway elementary school there are 450 students. 320 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?
Select the correct option: A) 69. B) 73. C) 81. D) 95. E) 108.

Solution: Total students = 450   Boys = 320, Girls = 130   Total playing soccer = 250   86%of 250 = 215 are boys who play soccer.   Girls who play soccer = 35.   Total girls who do not play soccer = 130 - 35= 
130 - 35 = 95
95.   Correct option: 95.
Answer: D
8 is 4% of a, and 4 is 8% of b. c equals b/a. What is the value of c?	Choose the correct choice:
A) 1/32	B) 1/4	C) 1	D) 4	E) 5

Solution: Explanation :   Given,   =>4a/100=8.   =>a=8×(100/4)=200. ---------(i)   And,   =>(8/100)×b=4.   =>b=50. ---------(ii)   Now, c=b/a ( from (i) and (ii) )   =>50/200.   =>1/4.   Answer : 1/4
Answer: B
A sock drawer contains seven socks, each one a different solid color. The colors of the socks are blue, indigo, and violet. A person reaches into the drawer, pulls out two socks, and puts a single sock on each foot. If each sock can fit either the left or the right foot, and if it matters whether a particular sock is on the left or the right foot, how many different sock fashion combinations could the person make from the three socks?  Choose the most appropriate option
A) 12
B) 15
C) 21
D) 36
E) 6

Solution: It's a question of permutation since order matters here ....   It can be deduced to-   3P2 = 3!/1! = 3*2 3 /1= 
3 /1 = 3
3*2= 
3*2 = 6
6 .........Answer is - 6
Answer: E
A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 2, 3, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following ?  Choose the most appropriate option:
A) 1/625	B) 2/625	C) 4/625	D) 50/625	E) 25/625

Solution: I think most of the answers are missing a point. Let me try to put it across:   Total number of possible numbers are : 5x5 = 25   Correct number =1   Case 1: When he gets it right in first attempt: P(E1) = 1/25   Case 2: He gets 1st attempt wrong and second right:   When he gets it wrong then the probability of getting wrong is 24/25.   Now there are 24 cases with him and he chooses the right one this time.   Probability of right case is 1/24   Thus, P(E2) = 24/25 x 1/24   =1/25   Probability of getting it right in at most two cases = P(E1) + P(E2)   = 1/25 + 1/25   = 2/25   = 50/625   Option (50/625) is therefore right as most of you mentioned but the method employed was wrong.
Answer: D
If b=4p where p is a prime number greater than 2, how many different positive even divisors does b have, including b? Choose the correct choice from the following answers
A) two	B) three	C) four	D) six	E) eight

Solution: b=2, 2, p (p is in the prime factorization since were told it is a prime number in the question)   2   4 (because of 2*2)   2p (because of 2 * p)   4p (because of 2 * 2 * p)=four
Answer: C
A watch was sold at a loss of 10%. If the watch was sold for $20 more, there would have been a gain of 6%. What is the cost price?  Choices:  A) $95  B) $105  C) $115  D) $125  E) $135

Solution: 0.9x + 20 = 1.06x   0.16x = 20   x = 125   The answer is $125.
Answer: D
a goes to place x and b goes to place y.
after a travelled 180 km more than b they together meet at a point between xy. they together had their lunch for half an hour. after that a took 2 hrs to reach x and b took 4.5 hrs to reach y. find distance between x and y? Choose the correct choice from the following answers.
A) 900km
B) 540km
C) 720km
D) 820km
E) 920km

Solution: let speed of 900km be-------Sa   let speed of B be--------Sb   let the distance covered by B while going to position XY be-----------x   so distance covered by 900km in same time while going to XY is----------180 +x(it's given in the question)   so total distance b/w X and Y is=x+(x+180)   while going to position XY :-   time taken by 900km = time taken by B   (x+180)/Sa= x/Sb   Sa/Sb=(x+180)/x---------------------1   900kmfter lunch:-   900km.C.T(according to question)   Sa=x/2   Sb=(x+180)/4.5   dividing Sa/Sb=(x*4.5) / ((x+180)*2)--------------------2   equating equations 1 and 2   9/4 = (x+180)^2 / x^2   now taking square root on both sides we get   3/2 = (x+180) / x   x=360   therefore distance between x and y =x+(x+180)=900km   900kmNSWER:900km
Answer: A
The length of the bridge, which a train 180 meters long and travelling at 45 km/hr can cross in 30 seconds, is?  Answers
A) 195 m	B) 156 m	C) 245 m	D) 156 m	E) 156 m

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time   = 30 sec. Let the length of bridge be x meters. Then, (180 + X)/30 = 25/2   ==> 2(180 + X) = 750 ==> X   = 195 m.   195 mnswer: 195 m
Answer: A
A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1.2 cm when a man gets on it. The mass of man is Choose the correct option.
A) 72 kg  B) 60 kg  C) 72 kg  D) 96 kg  E) None

Solution: Solution   Volume of water displaced	= (3 x 2 x 0.012)m3   = 0.072 m3.   Mass of man	=Volume of water displaced ×Density of water   = (0.072×1000) kg   = 72 kg.   72 kgnswer 72 kg
Answer: A