MU-NLPC/Calc-aqua_rat huggingface dataset:
A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is:  Choose the correct choice
A) 5.15 kmph	B) 4.14 kmph	C) 4.25 kmph	D) 4.4 kmph	E) 4.8 kmph

Solution: in 100 m race   A's speed is 5kmph so in m/s it is 5*5/18   time taken by A=D/S=100*18/25= 
100*18/25 = 72
72 sec   Now   4.14 kmph would take   72+8= 
  72+8 = 80
80 seconds   Speed of 4.14 kmph is=(100-8)=(92/80)*18/5= 
(92/80)*18/5 = 207/50 = around 4.14
4.14kmph   ANSWER:4.14 kmph
Answer: B
John and Jacob set out together on bicycle traveling at 15 and 10 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible) Choose the correct choice from the following:
A) 1 1/2
B) 3 1/3
C) 3 1/2
D) 4
E) 4 1/2

Solution: John's speed - 15 miles/hr   Jacob's speed - 10 miles/hr   After 40min (i.e 2/3hr), distance covered by John = 15x2/3 = 10 miles.   Jacob continues to ride for a total of 1hour and 40min (until John's bike is repaired). Distance covered in 1 hour 40min (i.e 5/3hr) = 10x5/3 = 16.7 miles.   Now, when John starts riding back, the distance between them is 6.7 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be   15-10= 
  15-10 = 5
5 miles/hr.   Thus, to cover 6.7 miles at 5 miles/hr, John will take  6.7/5= 
 6.7/5 = 1.34
1.34 hours   1 1/2nswer 1 1/2
Answer: A
A fruit seller had some mangoes. He sells 30% mangoes and still has 280 mangoes. Find the number of mangoes he had.  Choose the correct option
A) 228 mangoes
B) 400 mangoes
C) 287 mangoes
D) 408 mangoes
E) 289 mangoes

Solution: Explanation:   Suppose originally he had X mangoes.   Then, (100 – 30)% of X = 280   70/100 * X = 280   X = (280 * 100) / 70= 
(280 * 100) / 70 = 400
400   ANSWER: 400 mangoes
Answer: B
A certain sum of money at simple interest amounted Rs.860 in 10 years at 3% per annum, find the sum?  Select the correct option:
A) 661.54  B) 662.54  C) 663.54  D) 664.54  E) 665.54

Solution: 860 = P [1 + (10*3)/100]   P = 661.54   661.54nswer: 661.54
Answer: A
A boat running downstream covers a distance of 12 km in 2 hours while for covering the same distance upstream,it takes 4 hours.What is the speed of the boat in still water ?  Choose the correct choice from the following options:
A) 4.5 km/hr
B) 6 km/hr
C) 8 km/hr
D) Data inadequate
E) None of these

Solution: Solution   Rate downstream =(12/2)= 
(12/2) = 6
6 kmph, Rate upstream=(12/4)= 
(12/4) = 3
3 kmph.   ∴ Speed in still water=1/2(6+3) kmph = 4.5 kmph.   4.5 km/hrnswer 4.5 km/hr
Answer: A
A sum of money was invested in a bank at 8% simple interest p.a. for 3 years. Instead had it been invested in mutual fund at 8.5% p.a. simple interest for 4 years, the earning would have been Rs.500 more. What is the sum invested?
Choose one
A) Rs.4500  B) Rs.5000  C) Rs.3500  D) Rs. 5500  E) Rs. 6500

Solution: Let the sum be Rs.x   S.I from the bank = x*8*3/100 = 34x/100Earnings in the form of interest from mutual fund = (x * 8.5   *4)/100 = 34x/100   Given that 34x/100 - 34x/100 = Rs.500 ; x = 5000   : . The sum invested = 5000   ANSWER:Rs.5000
Answer: B
In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 6 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?	Choose the correct choice from the following.
A) 30  B) 45  C) 60  D) 90  E) 120

Solution: Whole trip = distance by foot + distance by bus + distance by car   x = 1/5x + 2/3x + 6   x - 13/15x = 6   2/15x = 6 => so x = (15/2)*6= 
(15/2)*6 = 45
45Km   Answer 45
Answer: B
The population of a bacteria colony doubles every day. If it was started 8 days ago with 3 bacteria and each bacteria lives for 12 days, how large is the colony today?	Choose the correct choice from the following choices:
A) 512
B) 768
C) 13122
D) 2048
E) 4096

Solution: 3^8*(2) = 13122   The answer is 13122
Answer: C
There are 20 poles with a constant distance between each pole. A car takes 24 seconds to reach the 12th pole . How much time will it take to reach the last pole?
Choose the correct choice from the following answers
A) 25.25 s	B) 17.45 s	C) 35.75 s	D) 41.45 s	E) None of these

Solution: Let the distance between each pole be x m.   Then, the distance up to 12th pole = 11 xm   Speed = 11x⁄24 m/s   Time taken to covers the total distance of 19x   = 19x×24/11x=41.45s   Answer 41.45 s
Answer: D
A train 175 m long running at 36 kmph crosses a platform in 40 sec. What is the length of the platform?	Choose the correct choice from the following options
A) 271 B) 266 C) 225 D) 277 E) 232

Solution: Length of the platform = 36 * 5/18 * 40= 
36 * 5/18 * 40 = 400
400 – 175= 225   Answer:225
Answer: C
A certain company charges $25 per package to ship packages weighing less than 5 pounds each. For a package weighing 5 pounds or more, the company charges an initial fee of $25 plus $6 per pound. If the company charged $36 to ship a certain package, which of the following was the weight of the package, in pounds?	Options.
A) 10  B) 6  C) 12  D) 18  E) 20

Solution: Let the weight of the package be X. Then the cost is 6*X + 25= 61 ---> 6X=36 ---> X=6   Answer : 6
Answer: B
A trader bought a car at 15% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?  Choose the correct option:
A) 119  B) 110  C) 112  D) 113  E) 115

Solution: Original price = 100   CP = 85   S = 85*(140/100)= 
85*(140/100) = 119
119   100 - 119= 19%   119nswer: 119
Answer: A
Machine A and machine B are each used to manufacture 330 sprockets. It takes machine A 10 hours longer to produce 330 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces? Choose the correct option
A) 5  B) 4  C) 6  D) 8  E) 3

Solution: Machine B: Takes x hours to produce 330 sprockets   Machine A: Takes (x+10) hours to produce 330 sprockets   Machine B: In 1 hour, B makes 330/x sprockets   Machine A: In 1 hour, A makes 330/(x+10) sprockets   3quating:   1.1(330/(x+10)) = 330/x   484/(x+10) = 330/x   363x = 330x+3300   33x = 3300   x = 100   A makes   330/(110)= 
  330/(110) = 3
3 sprockets per hour   Answer : 3
Answer: E
A man can row upstream at 45km/hr and down stream at 36km/hr find mans rate of the current ? Choose the correct choice from the following
A) 6.3km/hr	B) 9.6km/hr	C) 4.5km/hr	D) 5.9km/hr	E) 9.8km/hr

Solution: given upstream(u) =45km/hr   down stream (v)= 36km/hr rate of the current =1/2(u-v) =1/2(45-36)=4.5km/hr   Answer is (4.5km/hr)
Answer: C
What is the 11th term in this sequence?
1,4,5,11,18,29,49,80,129,211, Choices.
A) 352
B) 442
C) 345
D) 342
E) 362

Solution: 1+4= 
1+4 = 5
5 +0= 
5 +0 = 5
5   5+4= 
5+4 = 9
9+2= 
9+2 = 11
11   11+5= 
11+5 = 16
16+2= 
16+2 = 18
18   18+11= 
18+11 = 29
29+0= 
29+0 = 29
29   29+18= 
29+18 = 47
47+2= 
47+2 = 49
49   49+29= 
49+29 = 78
78+2= 
78+2 = 80
80   80+49= 
80+49 = 129
129+0= 
129+0 = 129
129   129+80= 
129+80 = 209
209+2= 
209+2 = 211
211   211+129= 
211+129 = 340
340+2= 
340+2 = 342
342   so 11th term is 342   ANSWER:342
Answer: D
A deer is standing 70 meters in from the west end of a tunnel. The deer sees a train approaching from the west at a constant speed ten times the speed the deer can run. The deer reacts by running toward the train and clears the exit when the train is 40 meters from the tunnel. If the deer ran in the opposite direction it would barely escape out the eastern entrance just as the train came out of the eastern entrance. How long is the tunnel in meters?
Pick one.
A) 160
B) 240
C) 520
D) 190
E) 720

Solution: Let x be the length of the tunnel.   When the deer runs 70 meters west, the train goes 700 meters to a point 40 meters from the west entrance of the tunnel.   When the deer runs east, the deer runs x-70 meters while the train goes x + 700 + 40 meters.   x + 700 + 40 = 10(x-70)   9x = 1440   x = 160 meters   The answer is 160.
Answer: A
In a certificate by mistake a candidate gave his height as 25% more than actual height. In the interview panel, he clarified that his height was 5feet 5 nches. Find the % correction made by the candidate from his stated height to his actual height?
Choose the correct choice from the following answers.
A) 10 B) 20 C) 40 D) 50 E) 60

Solution: His height was = 5 feet 5 inch = 5 + 60= 
5 + 60 = 65
65 inch. Required % correction=65*(1.25-1)* 100 = 20   20
Answer: B
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train. Choose the correct choice from the following choices:  A) 150  B) 160  C) 180  D) 170  E) 190

Solution: Speed = 60*(5/18) m/sec = 50/3 m/sec   Length of Train (Distance) = Speed * Time     (50/3) * 9= 
  (50/3) * 9 = 150
150 meter   150nswer: Option 150
Answer: A
An gun can take a maximum of four shots at an enemy plane moving away from it. The probability ofhitting the plane at the 1st, 2nd, third and 4th shots are 1.4, 1.3,1.2 & 1.1 respectively. What is the probability that theplane is hit when all the four shots are fired?  Choose the correct choice from the following answers:  A) 0.6976  B) 0.9753  C) 1.5678  D) 1.7454  E) 2.6548

Solution: Required probability:   =(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)   =0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002   =0.6976=0.6976   Edit: Thank you Vaibhav for providing an alternative method.   0.6976lternate Method:   probability that the plane is hit when all the four shots are fired,   P=1−probability of not hitting the targetP=1−probability of not hitting the target   =1−(0.6×0.7×0.8×0.9)=1−(0.6×0.7×0.8×0.9)   =1−0.3024=1−0.3024   =0.6976   0.6976
Answer: A
A 6" cube is painted in all its faces and then it is cut down into 1" blocks. How many 1" blocks
are there even without a single face being painted?
Choose the correct option.
A) 24	B) 32	C) 64	D) 80	E) 100

Solution: The unpainted blocks are the interior blocks.   These blocks form a 4" cube on the inside.   The number of unpainted blocks is  4*4*4= 
 4*4*4 = 64
64 blocks.   The answer is 64.
Answer: C
A shopkeeper purchased 85 kg of potatoes for Rs. 595 and sold the whole lot at the rate of Rs. 8 per kg. What will be his gain percent? Pick.
A) 18 1/9 % B) 18 9/3 % C) 18 1/3 % D) 14 2/7 % E) 18 7/3 %

Solution: C.P. of 1 kg = 595/85 = Rs. 7S.P. of 1 kg = Rs. 8Gain % = 1/7 * 100 = 100/7 = 14 2/7 %Answer: 14 2/7 %
Answer: D
What is the probability that a leap year has 53 Sundays and 52 Mondays? Select the correct option.
A) 1/8  B) 1/7  C) 1/4  D) 1/3  E) 1/5

Solution: A leap year has 52 weeks and two days   Total number of cases = 7   Number of favourable cases = 1   i.e., {Saturday, Sunday}   Required Probability = 1/7   Answer:1/7
Answer: B
A man spends 2/5 of his salary on house rent, 3/10 of his salary on food and 1/8 of his salary on conveyance. If he has $1400 left with him, find his expenditure on food. Pick
A) $400 B) $1400 C) $3400 D) $2400 E) $4400

Solution: Part of salary left =1-(2/5+3/10+1/8)   =7/40   Let the monthly salary be $x   Then (7/40) of x=1400   X=8000   Expenditure on food=$2400   Option $2400
Answer: D
How many gallons of water must be mixed with 1 gallon of a 15% salt solution To obtain a 10% salt solution	Choose the correct choice from the following choices
A) 5 B) 67 C) 1.0 D) 1.5 E) 2.00

Solution: Since we are adding pure water then the amount of salt in both solutions will be the same, so 0.15*1=0.1*(1+x) --> x=0.5.   5nswer: 5.
Answer: A
How many different positive integers are factors of 20?
Pick one
A) 6	B) 8	C) 4	D) 10	E) 12

Solution: 2*10   4*5   Answer : 4
Answer: C
S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10k–1). If p is the sum of the first 30 terms of S, what is the 3rd digit of p, counting right to left from the units digit?  Select:
A) 2	B) 4	C) 4	D) 6	E) 9

Solution: --------------------------------------------------2   -------------------------------------------------22   -----------------------------------------------222   ---------------------------------------------2,222   -------------------------------------------22,222   ...   222,222,222,222,222,222,222,222,222,222   Total 30 numbers.   For the first digit (units place) we should add 30 2's --> 30*2=60, so 0 will be units digit and 6 will be carried over;   For the second digit (tens place) we should add 29 2's --> 29*2--  30*2= 
--  30*2 = 60
60, so 0 will be units digit and 6 will be carried over;   For the second digit (tens place) we should add 29 2's --> 29*2=58+6--  29*2= 
--  29*2 = 58
58+6= 
58+6 = 64
64, so 4 will be written for this digit and 6 will be carried over;   for third digit (hundreth) we should add 28 2's --28*2= 
--28*2 = 56
56+6= 
56+6 = 62
62 2 will be written 6 will be carried over...   2
Answer: A
In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 8 eggs. If the cost of each pound of rice is $0.33, then how many Q cents does a liter of kerosene cost? [One dollar has 100 cents.]	Pick one: A) 0.33 B) 0.44 C) 0.55 D) 44 E) 55

Solution: Main thing to remember is answer is asked in cents, however when we calculate, it comes up as 0.44 $   Just multiply by 100, Answer Q= 44.44
Answer: D
If the cost price of 50 articles is equal to the selling price of 15 articles, then the gain or loss percent is?  Select:  A) 16  B) 127  C) 12  D) 18  E) 233

Solution: Percentage of profit = 35/15 * 100 = 233%   Answer: 233
Answer: E
If # is an operation which results in adding the digits of integer until a single digit is left, what is the probability Q that a number picked up in first 90 positive integers will have the result of # as an odd digit ?  Choose the correct choice from the following choices
A) (a) 4/10	B) (b) 4/9	C) (c) 1/2	D) (d) 6/10	E) (e) 5/9

Solution: Here is how I did it. Probably there may be better way to do it.   First of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90.   That will be 17 (8+9+17) Why did I calculate this? I will come to that in a moment.   So to get an odd digit by carrying out the operation #, the sum of the digits of the integer should be 1, 3, 5, 7, 9, 10, 12, 14, and 16 (Why not 18? Because we know the maximum sum can be 17)   Number of integers, whose digits add to 1: 1 and 10 = 2   Number of integers, whose digits add to 3: 3, 12, 21, 30 = 4   Number of integers, whose digits add to 5: 5, 14, 23, 32, 41, 50 = 6   Number of integers, whose digits add to 7: 7, 16, 25, 34, 43, 52, 61, 70 = 8   Number of integers, whose digits add to 9: 10 multiples of 9 up to 90 = 10   Number of integers, whose digits add to 10: 19, 28, 37, 46, 55, 64, 73, 82 = 8   Number of integers, whose digits add to 12: 39, 48, 57, 66, 75, 84 = 6   Number of integers, whose digits add to 14: 59, 68, 77, 86 = 4   Number of integers, whose digits add to 16: 79, 88 = 2   So in total there are  2+4+6+8+10+8+6+4+2= 
 2+4+6+8+10+8+6+4+2 = 50
50 such numbers   Probability Q= 50/90 = 5/9   Correct answer (e) 5/9
Answer: E
Chris mixed 3 pounds of raisins with 4 pounds of nuts. If a pound of nuts costs 4 times as much as a pound of raisins, then the total cost of the raisins was what fraction of the total cost of the mixture?
Choose the correct option.
A) 1/7	B) 1/5	C) 1/4	D) 1/3	E) 3/19

Solution: 1 lbs of raisin = $1   3 lbs of raisin = $3   1 lbs of nuts = $4   4 lbs of nuts = $16   Total value of mixture = 16+3= 
16+3 = 19
19   Fraction of the value of raisin= 3/19   Ans:3/19
Answer: E
60% of a number is added to 120, the result is the same number. Find the number?
Choose the correct choice
A) 300	B) 227	C) 288	D) 266	E) 299

Solution: (60/100) * X + 120 = X   2X = 600   X = 300   300nswer: 300
Answer: A
A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?	Pick one
A) 10	B) 88	C) 66	D) 65	E) 22

Solution: 10nswer: Option D   Explanation:   lb = 150   2(l + b) = 50 => l + b = 25   l – b = 5   l = 15 b = 10   10nswer:10
Answer: A
If 60% of 3/5 of a number is 72, then the number is? Select the correct option:
A) 80	B) 100	C) 75	D) 90	E) None of these

Solution: Let the number be x. Then 60% of 3/5 of x=72   60/100*3/5*x=72   x=(72*25/9)= 
(72*25/9) = 200
200   Required number=200.   Correct Option: None of these
Answer: E
Two trains 85 m and 75 m long are running in same direction with speeds of 62 km/hr and 44 km/hr respectively. In what time will the first train cross the second train ?	Pick one.
A) 12 sec
B) 32 sec
C) 82 sec
D) 92 sec
E) 13 sec

Solution: Explanation:   Given that,   1st train speed = 62 km/hr   2nd train speed = 44 km/hr   Hence the relative speed of two trains is   62-44= 
  62-44 = 18
18 km/hr m/s= 5 m/s.   There fore, the first train crosses the second train i.e (85+75)mts of distance with a speed of 5m/s in,   time = \frac{distance}{speed} \frac{(85+75)}{5} = 32 sec.   Answer: 32 sec
Answer: B
Stacy has a 63 page history paper due in 3 days. How many pages per day would she have to write to finish on time?	Choices.
A) 9
B) 8
C) 10
D) 8.5
E) 21

Solution: 63/3= 
63/3 = 21
21   Answer : 21
Answer: E
If p, q, and r are three different positive integers whose sum is prime, which of the following statements could be true?	Select the correct option
A) Each of p + 3, q + 3, and r + 3 is prime.
B) Each of p, q, and r is prime.
C) Each of p + q, p + r, and q + r is prime.
D) The average (arithmetic mean) of p, q, and r is prime.
E) p + q = r

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 p, q, and r is prime. is the answer.
Answer: B
A furniture dealer purchased a desk for $150 and then set the selling price equal to the purchase price plus a markup that was 25% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?  Options:
A) 40%  B) 38%  C) 36%  D) 33.33%  E) 35%

Solution: Anyway, in this question, there is no discount but the mark up is given as 25% of the selling price. So it is not 25% of $150 but instead, 40% of Selling price which is obtained by adding mark up to $150.   So if selling price is S,   150 + 25% of S = S   S = 200   Profit = 50 which is calculated on cost price in % terms. So 50/150 * 100 =33.33% is profit.   33.33%
Answer: D
The average of runs of a cricket player of 10 innings was 15. How many runs must he make in his next innings so as to increase his average of runs by 4?	Choose the correct choice.
A) 87  B) 16  C) 10  D) 76  E) 59

Solution: Average after 11 innings = 19   Required number of runs   = (19* 11) - (15* 10) = 209- 150= 
209- 150 = 59
59.   Answer: 59
Answer: E
Insert the missing number. 2, 7, 8, 17, 16, 27, 22, 37
Select the correct option:
A) 42	B) 52	C) 46	D) 28	E) 68

Solution: Explanation :   There are two series here   2, 8, 16, 22, ... (Increase by 6)   7, 17, 27, 37 ... (Increase by 10)   Hence, next term is   22+6= 
  22+6 = 28
28   Answer : Option 28
Answer: D
If x=kc and y=kt,then y-2x =?
Select the correct option:
A) k(t-c)	B) k(t-2c)	C) c(k-t)	D) t(k-c)	E) k(1-t)

Solution: Just put in the given values of y and x   y - x = kt - kc   Now take k common   y - x = k(t - c)   You get (k(t-2c)) as your answer.
Answer: B
If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle?	Choose one
A) 122 sq.cm	B) 120 sq.cm	C) 277 sq.cm	D) 118 sq.cm	E) 119 sq.cm

Solution: let length = x and breadth = y then   2(x+y) = 46 x+y = 23   x²+y² = 17² = 289   now (x+y)² = 23²   x²+y²+2xy= 529   289+ 2xy = 529   xy = 120   area = xy = 120 sq.cm   Answer: 120 sq.cm
Answer: B
A person travelled from his house to office at 15km/hr and office to house at 25km/hr. Then find the average speed?
Select:
A) 15km/hr
B) 20km/hr
C) 18.75km/hr
D) 24km/hr
E) 25km/hr

Solution: Average speed = (2*15*25)/(15+25)= 
(2*15*25)/(15+25) = 75/4 = around 18.75
18.75km/hr   Answer is 18.75km/hr
Answer: C
In how many ways Chief Minister and Minister be elected from a team of 20 members?	Choose the correct choice.
A) 128 B) 131 C) 132 D) 380 E) 145

Solution: To do this, if captain is elected first, then we have 20 ways of doing this.   For election of vice-captain, we have only 19 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)   So, the ans is 20*19= 
20*19 = 380
380 ways.   Answer : 380
Answer: D
Ricky likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 00,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance.
What is the distance travelled by each tyre?  Options: A) 20000 B) 35000 C) 70000 D) 60000 E) 80000

Solution: E   80,000.   80000xplanation:   The distance travelled by each tyre:   4/5 * 1, 00,000 km = 80,000 km.
Answer: E
A man in a train notices that he can count 41 telephone posts in one minute. If they are known to be
50 metres apart, then at what speed is the train travelling?	Pick one
A) 60 km/hr
B) 100 km/hr
C) 110 km/hr
D) 120 km/hr
E) None of these

Solution: Explanation:   Number of gaps between 41 poles = 40   So total distance between 41 poles = 40*50= 
40*50 = 2_000
2000 meter= 2 km   In 1 minute train is moving 2 km/minute.   Speed in hour = 2*60= 
2*60 = 120
120 km/hour   Answer: 120 km/hr
Answer: D
The standard serial numbers for a bill are 2 letters followed by 5 digits. How many bills are possible if letters and digits can be repeated?  Answers.
A) 26 × 26 × 100 000  B) 24³ × 10 ×10 000  C) 26³ × 10 000  D) 26 × 25 × 24 × 10  E) 26 x 26 x 10 000

Solution: OFFICIAL SOLUTION:   (A) The formula for permutations of events is the product of the number of ways each event can occur. There are 26 letters and 10 digits. So there are 26 × 26 options for the two letters, and 10 × 10 × 10 × 10 x 10 for the five digits. The number of bills is 26 × 26 × 10 × 10 × 10 × 10 x 10 = 26 x 26 x 100 000.   The correct answer is choice (26 × 26 × 100 000).
Answer: A
In May Mrs Lee's earnings were 60 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?	Choose the correct choice from the following.
A) 64% B) 68% C) 72% D) 76% E) 80%

Solution: Say May income = 100   L's income = 60 and rest of the family = 40   In June L's income = 60 * 120 /100= 
60 * 120 /100 = 72
72   So 72 /72 + 40= 64%   64%NSWER:64%
Answer: A
A trader bought a car at 25% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price? Choose the most appropriate option.
A) 118 B) 110 C) 105 D) 113 E) 115

Solution: Original price = 100   105P = 75   S = 75*(140/100)= 
75*(140/100) = 105
105   100 - 105= 5%   Answer: 105
Answer: C