MU-NLPC/Calc-aqua_rat huggingface dataset:
By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent of solution B. If 500 grams of solution A are mixed with 700 grams of solution B, then liquid X accounts for what percent of the weight of the resulting solution?
Choose the correct choice from the following choices.
A) 1.66%
B) 1.96%
C) 10%
D) 15%
E) 19%

Solution: I think there is a typo in question.   It should have been "By weight Liquid 'X ' makes up..... "   Weight of Liquid X = 0.8 % of Weight of 1.66% + 1.8% of Weight of B   When 500gms of 1.66% and 700gms of B is mixed :   Weight of Liquid X = (0.8 * 500)/100 + (1.8* 700)/100= 
(0.8 * 500)/100 + (1.8* 700)/100 = 16.6
16.6gms   % of Liquid X in resultant mixture= (16.6/1000) *100= 
(16.6/1000) *100 = 1.66
1.66%   1.66%
Answer: A
What is the remainder when 17^200 is divided by 18 ? Select the correct option:
A) 3
B) 1
C) 2
D) 4
E) 7

Solution: (17^200 - 1^200) is completely divisible by (17 + 1) as 200 is even.   => (17^200 - 1) is completely divisible by 18.   Hence, when 17^200 is divided by 18, we will get 1 as remainder.   Answer is 1
Answer: B
Josh spends a total of $5.5 buying W items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then W may be which of the following?
Answers:
A) 99	B) 100	C) 101	D) 112	E) 113

Solution: W items in the convenience store$5.5 = 550 cents   550 = 50a + 5b   =>110 = 10a + b   b = 110 - 10a = 10(11-a)   Hence b is even and multiple of 10.   Possible values of b:   b = 10,20,30,40,50,60,70,80,90,100   a = 11,9,8,7,6,5,4,3,2,1   The total (a+b) is 21,29,38,47,56,65,74,83,92,101   The only option is 101. Hence 101.
Answer: C
18800 / 470 / 20  Choose the most appropriate option:
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: Explanation:   18800 / 470 / 20 = (18800 / 470) / 20 = 40 / 20= 
40 / 20 = 2
2   Answer: 2
Answer: B
The three sides of an acute angled triangle (all in cms) are 12, 19 and x. How many integer values can x take?
Answers:	A) 23	B) 22	C) 15	D) 8	E) 7

Solution: In acute angle triangles all angles in the triangle should be less than 90.   The maximum length of x can be when it is the hypotenuse of the triangle.   So, x= sqrt(12^2 + 19^2) = 22.5 (approx)   The maximum length of x can be when side of length 12 is the hypotenuse of the triangle.   So, x = sqrt (19^2 - 12^2) = 14.7 (approx)   So, x>14.7 and x<22.5.   Hence, possible values for x can be 15,16,17,18,19,20,21 and 22. Total 8 values.   Answer 8.
Answer: D
A firm has 3 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Note that two groups are considered different if at least one group member is different.)
Answers:
A) 64  B) 68  C) 72  D) 76  E) 80

Solution: The number of ways to form a group of 3 is 9C3 = 84   The number of groups with no senior partner is 6C3 = 20   The number of groups with at least one senior partner is 84-20= 
84-20 = 64
64   The answer is 64.
Answer: A
If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 5:7 then find the largest number?
Choose the most appropriate option: A) 34 B) 38 C) 40 D) 42 E) 44

Solution: 2:3   2x + 10 : 3x + 10 = 5 : 7   7[2x + 10] = 5[3x + 10]   14x + 70 = 15x + 50   15x - 14x = 70 - 50= 
70 - 50 = 20
20   Then the first number is= 2   2x = 40   Short cut method:   a:b = 2:3   c:d = 5:7   1.Cross multiplication with both ratios   a * d ~ b * c = 2 * 7 ~ 3 * 5 = 14 ~ 15 = 1   2. If 10 is added both the number means   10 * 5= 
  10 * 5 = 50
50 and   10 * 7= 
  10 * 7 = 70
70,   Then 50 ~ 70= 20   ===> 1 -----> 20   ===> 2 -----> 40 (Answer is = 40)   40
Answer: C
Which number is the odd one out?
321
265
143
234
567
890 Select.
A) 321
B) 142
C) 653
D) 845
E) 658

Solution: 321   321   In the rest there is the same difference between each digit, eg: 3 (Ã¢â‚¬â€œ1) 2 (Ã¢â‚¬â€œ1)1.
Answer: A
If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 350, what is the least possible value of n?  Answers: A) 5 B) 7 C) 12 D) 13 E) 14

Solution: 350 = 2 * 5 * 5 * 7   so the least value forNcan be 7.   7
Answer: B
A Man can row upstream at 52kmph and downward stream at 12 kmph. Find Man's rate of the current  Choose one
A) 2.8km/hr  B) 52km/hr  C) 20km/hr  D) 50km/hr  E) 6.8km/hr

Solution: Rate of the current=1/2(52-12)km/hr   =20km/hr   correct option is :20km/hr
Answer: C
A shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent? Select the correct option
A) 200  B) 177  C) 188  D) 166  E) 129

Solution: Profit on first article = 20% of 1000   = 200.   200nswer:200
Answer: A
A retailer bought a machine at a wholesale price of $108 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price of the machine? Choose the correct choice from the following:	A) 81	B) 100	C) 120	D) 135	E) 144

Solution: My solution: Wholesale Price= 108   Retail Price, be = x   He provides 10 % discount on Retail price= x-10 x/100   This Retail price = 20 % profit on Wholesale price   x-10 x/100 = 108+ 1/5(108)   x=144;   ANSW144R:144
Answer: E
A certain office supply store stocks 2 sizes of self-stick notepads, each in 7 colors. The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?  Options
A) 6	B) 8	C) 16	D) 84	E) 92

Solution: Notepads of the same color = 7 (we have 7 colors). As we have two sizes then total for the same color=7*2= 
7*2 = 14
14   Notepads of the different colors= 7C3=35 (we should choose 3 different colors out of 7). As we have two sizes then total for the different color=35*2= 
35*2 = 70
70   Total=70+14= 
70+14 = 84
84   Answer: 84.
Answer: D
Exactly 3/7 of the people in the room are under the age of 21, and exactly 5/11 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?
Choose the correct choice from the following options:
A) 21  B) 35  C) 33  D) 60  E) 65

Solution: The total number of the people in the room must be a multiple of both 7 and 11 (in order 3/7 and 5/11 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 7 and 11, which is 77.   Since, the total number of the people in the room is greater than 50 and less than 100, then there are 77 people in the room.   Therefore there are   3/7*77= 
  3/7*77 = 33
33 people in the room under the age of 21.   Answer: 33.
Answer: C
In a game of billiards, A can give B 10 points in 50 and he can give C 40 points in 50. How many points can B give C in a game of 100?
Choose one:
A) 18
B) 27
C) 25
D) 75
E) 17

Solution: A scores 50 while B score 40 and C scores 10.   The number of points that C scores when B scores 100 = (100 * 10)/40= 
(100 * 10)/40 = 25
25   In a game of 100 points, B gives (100 - 25)= 
(100 - 25) = 75
75 points to C.   Answer: 75
Answer: D
At the start of an experiment, a certain population consisted of 3 animals. At the end of each month after the start of the experiment, the population size was double its size at the beginning of that month. Which of the following represents the population size at the end of 12 months?  Options:
A) 2^3  B) 3^2  C) 2(3^10)  D) 3(2^12)  E) 3(10^2)

Solution: 3*2^n where n is the #of month --> 3*2^12 Answer (3(2^12))
Answer: D
In a recent head-to-head run-off election, 18,000 absentee ballets were cast. 3/7 of the absentee ballets were thrown out and 2/9 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive?  Select the correct option:
A) 2,000  B) 3,000  C) 6,000  D) 8,000  E) 9,000

Solution: 4/7 * 7/9 (total absentee votes) = 4/9 (total votes)=4/9*18000= 
4/9*18000 = 8_000
8000   Answer is 8,000
Answer: D
A marketing survey of Anytown found that the ratio of trucks to sedans to motorcycles was 3:7:2, respectively. Given that there are 9,100 sedans in Anytown, how many motorcycles are there? Select the correct option: A) 1260 B) 2600 C) 3600 D) 4200 E) 5200

Solution: Let the total number of trucks = 3x   total number of sedans = 7x   total number of motorcycles = 2x   total number of sedans = 9100   => 7x = 9100   => x = 1300   total number of motorcycles =2x = 2*1300= 
2*1300 = 2_600
2600   Answer 2600
Answer: B
in a certain flower shop, which stocks four types of flowers, there are 1/4 as many violets as carnations, and 1/2 as many tulips as violets. If there are equal numbers of roses and tulips, what percent of the flowers in the shop are carnations?  Choose the correct answer:
A) 60 B) 62 C) 66.66 D) 64 E) 68

Solution: Given :-   Violets - 66.66/4   66.66arnations - 66.66   Tulip - 66.66/8   Rose - 66.66/8   Total flowers in terms of 66.66 = 66.66/4+66.66+66.66/8+66.66/8 = 3/2 66.66   Percentage of 66.66arnations = 66.66/366.66/2 *100 =66.66%   Answer 66.66
Answer: C
7 liters of a 22 percent solution of alcohol in water are mixed with 3 liters of an 11 percent alcohol in water solution. What is the percentage of alcohol in the new solution?	Options.
A) 17.5%
B) 17.8%
C) 18.1%
D) 18.4%
E) 18.7%

Solution: The total amount of alcohol is 0.22(7) + 0.11(3) = 1.87 liters.   The percentage is 1.87 / 10 = 18.7 / 100 which is 18.7%   The answer is 18.7%.
Answer: E
60 men shake hands with each other. Maximum no of handshakes without cyclic handshakes.	Choose the correct answer:
A) 190
B) 200
C) 210
D) 1770
E) 230

Solution: 1st person will shake hand with 59 people   2nd person will shake hand with 58 people   3rd person will shake hand with 57 people   ......   total no. of handshakes = 59+58+57+...+3+2+1 = 19*(19+1)/2 = 1770   or, if there are n persons then no. of shakehands = nC2 = 60C2 = 1770   ANSWER: 1770
Answer: D
A zookeeper counted the heads of the animals in a zoo and found it to be 80. When he counted the legs of the animals he found it to be 260. If the zoo had either pigeons or horses, how many horses were there in the zoo? Options.
A) 30
B) 40
C) 50
D) 60
E) 70

Solution: Explanation :   Let the number of horses =x   Then the number of pigeons =80−x.   Each pigeon has 2 legs and each horse has 4 legs.   Therefore, total number of legs =4x+2(80−x)=260.   =>4x+160−2x=260.   =>2x=100.   =>x=50.   Answer : 50
Answer: C
A motorcyclist X drives along a circular fence at a rate of 2 rounds per hour and another motor cyclist Y at a rate of 4 rounds per hour. After how long they will cross each other for the first time?
Choices:
A) 10 min B) 20 min C) 30 min D) 40 min E) None of these

Solution: Explanation :   Since X and Y move in the same direction they cross each other when there is a difference of two round between the two. Relative speed of X and Y=4-2= 
4-2 = 2
2.   Time taken to complete one round at this speed= 1/2 hour   = 30minutes   Answer : 30 min
Answer: C
A train is moving at 4/5 of its usual speed. The train is 45 minutes too late. What is the usual time (in hours) for the train to complete the journey?	Pick:  A) 1  B) 1.5  C) 2  D) 2.5  E) 3

Solution: new time = d / (4v/5) = 5/4 * usual time   45 minutes represents 1/4 of the usual time.   The usual time is 4* 45 minutes = 3 hours.   The answer is 3.
Answer: E
If 3 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?	Choose the most appropriate option:
A) -7	B) -6	C) -3	D) 1	E) 6

Solution: The phrase “3 is one solution of the equation” means that one value of x is 3. Thus, we first must plug 3 for x into the given equation to determine the value of k. So we have   3^2 + (3)(3) + k = 10   9 + 9 + k = 10   18 + k = 10   k = -8   Next we plug -8 into the given equation for k and then solve for x.   x^2 + 3x – 8 = 10   x^2 + 3x – 18 = 0   (x+6)(x-3) = 0   x = -6 or x = 3   Thus, -6 is the other solution. Answer -6.
Answer: B
The salary of A, B, C, D, E is Rs. 8000, Rs. 5000, Rs. 14000, Rs. 7000, Rs. 9000 per month respectively, then the average salary of A, B, C, D, and E per month is  Choose the correct choice from the following choices.
A) Rs. 7000	B) Rs. 8000	C) Rs. 8600	D) Rs. 9000	E) None

Solution: Answer   Average salary   = 8000 + 5000 + 14000 + 7000 + 9000 / 5   = Rs. 8600   Rs. 8600orrect Option: Rs. 8600
Answer: C
If two women starting from same point, walking in the opposite directions with 8km/hr and 7km/hr as average speeds respectively. Then the distance between them after 3 hours is?  Choose the correct choice from the following choices:
A) 23
B) 33
C) 43
D) 53
E) 63

Solution: Explanation:   Total distance = Distance traveled by person A+ Distance traveled by person B   = (8Ã— 3) + (7Ã— 3)   = 24+ 21   = 43 Km   Answer:43
Answer: C
When positive integer m is divided by positive integer x, the reminder is 7 and when positive integer n is divided by positive integer y, the reminder is 11. Which of the following T is a possible value for x + y?
I. 18
II. 19
III. 20
Choose the correct choice from the following:
A) I only
B) II only
C) T=III only
D) II and III only
E) None

Solution: TIP FOR SUCH QUESTIONS: Make Algebraic Equation in the beginning to understand how to proceed further. Then Start thinking the possible values of variables asked about   i.e.When positive integer m is divided by positive integer x, the reminder is 7can be understood as   m = ax +7which means thevalue of x must be greater than 7as the remainder 7 is possible only when the Divisor is bigger than the Remainder 7   i.e. Min Value of x = 8   AND   i.e.When positive integer n is divided by positive integer y, the reminder is 11can be understood as   n = by +11which means thevalue of y must be greater than 11as the remainder 11 is possible only when the Divisor is bigger than the Remainder 11   i.e. Min Value of y = 12   i.e. Minimum Value of x+y = 8+12= 
8+12 = 20
20   Hence III only can be True   Answer: Option   T=III only
Answer: C
If |x^2 − 30| = x, which of the following could be the value of x?
Options:
A) -6
B) -5
C) 1
D) 5
E) 15

Solution: The LHS is not negative, so the RHS is also not negative. Thus x >= 0.   First, let's assume that x^2-30 is negative.   -(x^2 -30) = x   x^2 + x - 30 = 0   (x+6)(x-5) = 0   x = 5 or x = -6 (However, x can not be negative.)   Then x = 5 is a possible value for x.   The answer is 5.
Answer: D
The average of 11 results is 45, if the average of first five results is 49 and that of the last seven is 52. Find the fifth result? Pick.
A) 114 B) 116 C) 117 D) 118 E) 119

Solution: 1 to 11 = 11 * 45= 
11 * 45 = 495
495   1 to 5= 5 * 49= 
5 * 49 = 245
245   5 to 11= 7 * 52= 
7 * 52 = 364
364   5th= 245 + 364 – 495=114   114NSWER:114
Answer: A
On a map the distance between two mountains is 312 inches. The actual distance between the mountains is 136 km. Ram is camped at a location that on the map is 25 inch from the base of the mountain. How many km is he from the base of the mountain?
Pick one.
A) 10.89	B) 14.81	C) 14.8	D) 14.82	E) 14.12

Solution: Explanation:   Since 312 inch = 136 km   So 1 inch = 136/312 km   So 25 inch = (136 Ã— 25)/ 312 = 10.89 km   10.89nswer: 10.89
Answer: A
A project has three test cases. Three teams are formed to study the three different test cases. James is assigned to all three teams. Except for James, each researcher is assigned to exactly one team. If each team has exactly 8 members, then what is the exact number of researchers required?	Choose the correct answer
A) 23  B) 22  C) 21  D) 20  E) 19

Solution: alternatively, we have   8*3-2( because james is included in all the three teams)   =22   22
Answer: B
A train 110 m long is running with a speed of 82 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?
Select:
A) 7 sec B) 6 sec C) 8 sec D) 4.5 sec E) 2 sec

Solution: Speed of train relative to man = 82+ 6= 
82+ 6 = 88
88 km/hr.= 88 * 5/18 = 24.44 m/sec.   Time taken to pass the men = 110 /24.44   = 4.5 sec.   Answer:4.5 sec
Answer: D
Average score for Virat Kohli in a series of 10 matches is 38.9 runs. If the average for first six matches comes out to be 42 what is his average in the last 4 matches of the series? Choose the correct option.
A) 34.25	B) 35	C) 33.25	D) 34.25	E) None of these

Solution: Explanation:   34.25verage runs scored by Virat Kohli in 10 matches: Total runs scored/10—(1)   34.25verage runs scored by Virat Kohli in 6 matches: (Total runs in 6 matches)/6   => 42 = Runs/6   =>252 runs   Using (1):   =>38.9 = Runs/10   =>389 runs   Runs scored in rest 4 matches:  389 - 252= 
 389 - 252 = 137
> 137 runs   34.25verage runs scored by Virat Kohli in 4 matches:  137/4= 
 137/4 = 137/4 = around 34.25
34.25 runs   34.25NSWER 34.25
Answer: A
If r, s, and t are three different positive integers whose sum is prime, which of the following statements could be true?  Choose the most appropriate option:  A) Each of r + s, r + t, and s + t is prime.  B) Each of r + 3, s + 3, and t + 3 is prime.  C) Each of r, s, and t is prime.  D) The average (arithmetic mean) of r, s, and t is prime.  E) r + s = t

Solution: the question asks could be!!!!   this means that if at least one option works, it is the answer.   3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be - we know automatically that Each of r, s, and t is prime. is the answer.
Answer: C
Two trains are running in opposite directions with the same speed. If the length of each train is 144 m and they cross each other in 12 sec, then the speed of each train is?	Choose the correct answer.
A) 22  B) 77  C) 36  D) 88  E) 19.2

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (144 + 144)/12 => x = 12   Speed of each train = 12 m/sec.   = 12 * 18/5 =19.2 km/hr.   Answer: 19.2
Answer: E
Find the value of y from (12)^3 x 6^4 ÷ 432 = y? Pick one: A) 2234 B) 3245 C) 3456 D) 4567 E) 5184

Solution: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184   432 12 x 62   5184
Answer: E
A train covers a distance in 50 minutes, if it runs at a speed of 48kmph on an average. Find the speed at which the train must run to reduce the time of journey to 40 minutes. Choose the correct choice.
A) 70 km/hr
B) 60 km/hr
C) 10 km/hr
D) 20 km/hr
E) 30 km/hr

Solution: Explanation:   We are having time and speed given, so first we will calculate the distance. Then we can get new speed for given time and distance.   Lets solve it.   Time = 50/60 hr = 5/6 hr   Speed = 48 mph   Distance = S*T = 48 * 5/6= 
48 * 5/6 = 40
40 km   New time will be 40 minutes so,   Time= 40/60 hr = 2/3 hr   Now we know,   Speed = Distance/Time   New speed = 40*3/2= 
40*3/2 = 60
60kmph   Answer: 60 km/hr
Answer: B
The positive numbers w, x, y, and z are such that x is 25 percent greater than y, y is 20 percent greater than z, and w is 20 percent less than x. What percent greater than z is w ? Choose the correct choice from the following
A) 15.2%
B) 16.2%
C) 20.0%
D) 23.2%
E) 24.8%

Solution: My strategy is same as theDobermanbut instead take z=100, which makes life a bit easy. As:   z=100   y=120 (20% greater than z)   z=144(20% greater than y)   Now calculate w 20% less than z = 144*80/100= 
144*80/100 = 576/5 = around 115.2
115.2   Now by just looking, relation between w and z:   w-z/z*100= 16.2 - Answer 16.2%
Answer: B
You buy a piece of land with an area of âˆš100, how long is one side of the land plot?  Pick one:
A) 28  B) 29  C) 10  D) 31  E) 32

Solution: Try filling the numbers into the answer y x y =   Find the closest to 100.   Answer 10
Answer: C
A bag has 10 blue balls and 15 black balls. How many black balls must be removed from the bag so that 50 percent of the balls in the bag shall be black?	Choose the correct choice from the following answers.
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: Suppose x black balls need to be removed from the bag.   After x black balls are removed, the bag shall have (15 - x) black balls and the same 10 blue balls; and the total number of balls shall be (15-x) + 10 = 25 - x   Now we want the 50 percent of balls in the bag to be black.   This means 50 percent of (25 - x) should be equal to the number of black balls which is (15 - x).   This means,   50 % of (25 - x) = (15 - x)   Solving above equation we get x = 5.   Ans 5
Answer: E
Richard traveled the entire 60 miles trip. If he did the first 2 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 48 miles per hour, what is the his average speed, in miles per hour?	Answers: A) 20mph B) 24mph C) 30mph D) 32mph E) 55mph

Solution: Average speed=sum of distance/sum of time. If he travelled the first 2 miles at 24 miles/hr, it would take 0.083 hr. For the remaining trip, if he went at 48 miles/1hr, it would take 1 hour. Then, the average speed is 60miles/(0.083+1)hrs=55miles/1hr.   Therefore, the answer is 55mph.
Answer: E
To be considered for “movie of the year,” a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy’s 770 members. What is the smallest number of top-10 lists a film can appear on and still be considered for “movie of the year”?
Choose the correct option:
A) 191
B) 193
C) 195
D) 212
E) 213

Solution: Total movies submitted are 770.   As per question we need to take 1/4 of 770 to be considered for top 10 movies = 192.25   approximate the value we 193   IMO option 193 is the correct answer...
Answer: B
Calculate how long it will take a swimmer to swim a distance of 8km against the current of a river which flows at 1.4km/hr, given that he can swim in still water at 3km/h  Select
A) 20 seconds  B) 3  C) 4  D) 1  E) 5

Solution: swim in still water at = 3   speed of river= 1.4   US = 3 - 1.4= 
3 - 1.4 = 1.6
1.6   Distance= 8   T = 8/1.6= 
8/1.6 = 5
5   Answer: 5
Answer: E
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 25 seconds. The speed of the train is: Choose the correct choice from the following choices:  A) 45 km/hr  B) 50 km/hr  C) 95 km/hr  D) 55 km/hr  E) 56 km/hr

Solution: Speed of the train relative to man = (125/25) m/sec =25 m/sec. [(25 * (18/5)] km/hr = 90 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 90 ==> x = 95 km/hr.   ANSWER:95 km/hr
Answer: C
One ball will drop from a certain height. The height it will reach after rebounding from the floor is 50 percent of the previous height. The total travel is 225cm when it touches the floor on third time. What is the value of the original height?
Choose the correct choice from the following answers:
A) 80cm B) 90cm C) 100cm D) 120cm E) 130cm

Solution: when Ball comes down, Then i have indicated the distance covered in green   when Ball goes up, Then i have indicated the distance covered in red   Distance travelled uptil the ball touches the floor 3rd time:h+0.5h+0.5 h+0.5*0.5 h+0.5*0.5 h   h + 2 * 0.5 * h + 2 * 0.25 * h = h (1+2*0.5+2* 0.25) = h (1+1+0.5) = 225   2.5 h = 225   h = 90.   90cm is the answer.
Answer: B
A machine can finish a work in 18days and 2nd machine can finish the work in 15days. 2nd machine worked for 10days and left the job. In how many days, 1st machine can finish the remaining work?	Pick.
A) 4days
B) 6days
C) 8days
D) 10days
E) 5days

Solution: 2nd machine 10days work = 1/15*10 = 2/3   Remaining work = 1 - 2/3 = 1/3   now 1/18 work is done by 1st machine in 1day   1/3 work is done by 1 machine in 18*1/3= 
18*1/3 = 6
6days.   Answer is 6days
Answer: B