MU-NLPC/Calc-aqua_rat huggingface dataset:
A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 20 miles per gallon, and from Town B to Town C, the car averaged 25 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?  Choose the correct choice from the following options: A) 20 B) 18 C) 21.4 D) 16 E) 10

Solution: step 1) took LCM of 20 and 25.. came as 100.   step 2) 100 distance between B to C... do 100/25 hence 4 gallons used   step 3) twice distance.. hence 100*2= 200... do as above.. 200/20= 10 gallons used   step 4) total gallons.. 4+10= 14 gallons   step ) total miles= 100+200= 
100+200 = 300
300 miles   hence.. average of whole journey= 300/14 which comes to 21.4   Answer : 21.4
Answer: C
A can do a piece of work in 7 days of 9 hours each and B can do it in 6 days of 7 bours each. How long will they take to do it, working together 8 hours a day?  Choose the correct option
A) 8 days B) 2 days C) 7 days D) 1 day E) 3 days

Solution: A can complete the work in (7 x 9) = 63 hours.   B can complete the work in (6 x 7) = 42 hours.   A’s 1 hour's work = (1/63) and B's 1 hour's work =(1/42)   (A + B)'s 1 hour's work =(1/63)+(1/42)=(5/126)   Both will finish the work in (126/5) hrs.   Number of days. of (42/5) hrs each =(126 x 5)/(5 x 42)=3 days   Answer is 3 days.
Answer: E
In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
Choices:
A) 5/21
B) 5/81
C) 5/29
D) 9/21
E) 5/61

Solution: Explanation:   Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ * ⁶C₁)   As remaining person can be any one among three couples left.   Required probability = (⁵C₂ * ⁶C₁)/¹⁰C₅   = (10 * 6)/252 = 5/21   5/21nswer: Option 5/21
Answer: A
In what time will a train 100 meters long cross an electric pole, if its speed is 144 km/hr
Choices.
A) 5 seconds	B) 4.5 seconds	C) 3 seconds	D) 2.5 seconds	E) None of these

Solution: Explanation:   First convert speed into m/sec   Speed = 144*(5/18)= 
144*(5/18) = 40
40 m/sec   Time= 2.5 secondsistance/speed   = 100/40= 
100/40 = 5/2 = around 2.5
2.5 seconds   Answer: 2.5 seconds
Answer: D
Find the odd man out. 3576, 1784, 888, 440, 216, 105, 48	Choices:	A) 1784	B) 888	C) 216	D) 105	E) 48

Solution: 3576   (3576-8)/2= 
(3576-8)/2 = 1_784
1784   (1784-8)/2= 
(1784-8)/2 = 888
888   (888-8)/2= 
(888-8)/2 = 440
440   (440-8)/2= 
(440-8)/2 = 216
216   (216-8)/2= 
(216-8)/2 = 104
104   (104-8)/2= 
(104-8)/2 = 48
48   Hence, 105 is wrong. 104 should have come in place of 105   Answer is 105
Answer: D
In how many different ways can 3 identical gold shirts and 3 identical sliver shirts be distributed among 6 children such that each child receives a shirt? Select the correct option.
A) 100
B) 400
C) 20
D) 96416
E) 62

Solution: Approach 1:   1st Child: 6 has options   2nd Child: 5 has options…   Therefore, for all kids: 6 x 5 x 4 x 3 x 2 = 720 arrangements.   Since the golds are identical, we divide by 3!; Since the silvers are identical, we divide by another 3!   So: in all, 720/[ 3! X 3! ] = 20 ways.   (e.g. Answer: 20)
Answer: C
If 5^z is a factor of 160!, which of the following could be the value of z?	Choose the most appropriate option:
A) 40	B) 32	C) 51	D) 39	E) 60

Solution: 5^z is a factor of 160!, what values can z take.   Powers of 5 in 160! = [160/5] + [160/25] +[160/125] , where [x] is the integral part of x   Powers of 5 in 160! = 32 + 6 + 1= 
32 + 6 + 1 = 39
39   Hence the maximum value of 5^z in 160!= 5^39   Correct Option: 39
Answer: D
In the xy-plane, the line y = k is the perpendicular bisector of the line segment PQ and the line x = h is the perpendicular bisector of the line segment RQ. If the coordinates of the point R are (-h, -k), then what are the coordinates of the point P? Choose one:
A) (-5h, -5k)
B) (-3h, -3k)
C) (2h, 2k)
D) (3h, 3k)
E) (5h, 5k)

Solution: firstly the Question tells us that RQ and PQ are perpendicular at Q..   Now the coordinates of the point R are (-h, -k), so R is at a distance of 2h from line x and at dist of 2k from line Y..   as line X bisect RQ .... length of RQ =4h and coord (3h,-k)..   as line Y bisect PQ .... length of PQ =4k and coord (3h,3k).   ANSWER:(3h, 3k)
Answer: D
Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 20 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York?  Choose the correct choice from the following answers:
A) 1 hour
B) 1 hour 10 minutes
C) 2 hours 30 minutes
D) 1 hour 20 minutes
E) 2 hours 10 minutes

Solution: Both cars leave at the same time   Both cars travel at constant speed   Stealing a useful piece of information from Paragkan:   If two objects A and B start from opposite points and, after having met en route, reach their respective destinations in a and b mins (or any other measure of time) respectively, then the ratio of their speeds   ratio of speed: (a/b) = sq. rt(b/a)   sq. rt(b/a)   sq. rt(90/20)   sq. rt(3/2)   So, for every three units of distance A travels, B travels two. Because we know the ratio of speed and the time it took B to travel the distance A hasn't yet covered, we can find the time it took A to cover the distance B did in 90 minutes.   90*(2/3)where 2/3 represents the lesser amount of time it took A to travel the distance B did in 90 minutes.   = 60 minutes.   Therefore, A took 20 minutes to travel the first portion then 60 minutes to travel the distance B did in 90 minutes. A spent (20+60)= 
(20+60) = 80
80 minutes on the road.   D. 1 hour 20 minutes
Answer: D
A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?  Choose one:
A) 240  B) 88  C) 77  D) 26  E) 22

Solution: Speed = 54 * 5/18= 
54 * 5/18 = 15
15 m/sec.   Length of the train= 15 * 20= 
15 * 20 = 300
300 m.   Let the length of the platform be x m . Then,   (x + 300)/36= 15 => x = 240 m.   240nswer: 240
Answer: A
A owner of a mart earns an income of Re 1 on the first day of his business. On every subsequent day, he earns an income which is just double of that made on the previous day. On the 10th day of business, he earns an income of:
Choose the correct choice from the following answers
A) 18 B) 21 C) 22 D) 20 E) 30

Solution: 2nd day he earns = 2(2 – 1)   3rd day he earns = 2(3 – 1)   On 10th day he earns 2(10 -1) = 18 rupees   18NSWER:18
Answer: A
Three hundred multiples of seven are chosen at random, and 300 multiples of eight are chosen at random. Approximately what percentage of the 600 selected numbers are odd?
Choose the correct choice from the following answers.
A) 26.67% B) 36.67% C) 25% D) 46.67% E) 56.67%

Solution: --> Multiples of 7 are 7, 14, 21, 28, 35, 42....   Out of first 4 multiples, 2 are odd; out of first 6 multiples, 3 are odd.   So approx. 50 % of the 300 multiples are odd i.e 150 multiples.   --> Similalrly, for 8 multiples are:8,16,24...   All are even so 0 % are odd.   Total odd= (150+0)/(300+300)= 150/600=(1/4) = 25%   Answer 25%
Answer: C
The calendar of the year 2080 can be used again in the year?  Answers:
A) 2105  B) 1955  C) 1945  D) 1935  E) 2108

Solution: Explanation:   Given year 2080 when divided by 4, leaves a remainder 0.   NOTE: When remainder is 0, 28 is added to the given year to get the result.   So, 2080 + 28 = 2108   Answer: 2108
Answer: E
The ratio of three numbers is 1:2:4 and the sum of their squares is 1701. The sum of the numbers is?  Pick one
A) A)10  B) B)12  C) C)15  D) D)14  E) E)9

Solution: Let the numbers be x,2x,4x   then, x^2+4x^2+16x^2 = 1701   21x^2 = 1701   x^2 = 81   x=9   Answer is 9
Answer: E
What is the remainder when the number Y=14^2 * 15^8 is divided by 5?  Choose the correct choice: A) 0 B) 1 C) 2 D) 4 E) 5

Solution: 14^2 has units digit 6   15^8 has units digit 5   Thus Y=14^2*15^8 has units digit 0 and will be divisible by 5. The remainder will be zero   0nswer: (0)
Answer: A
The number of six digit numbers that can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 so that digits do not repeat and the terminal digits are even is Choices:	A) 144	B) 72	C) 288	D) 720	E) None of these

Solution: The first and the last (terminal) digits are even and there are three even digits. This arrangement can be done in 3P2 ways. For any one of these arrangements,two even digits are used; and the remaining digits are 5 (4 odd and 1 even) and the four digits in the six digits(leaving out the terminal digits) may be arranged using these 5 digits in 5P4 ways. The required number of numbers is 3P2 × 5P4 = 6 × 120 = 720.   Answer 720
Answer: D
If x is 20 percent greater than 40, then x =  Choose the correct answer.
A) 48	B) 70.4	C) 86	D) 105.6	E) 108

Solution: X is 20% greater than 40 means X is 1.2 times 40 (in other words 40 + 20/100 * 40 = 1.2 * 40)   Therefore, X = 1.2 * 40= 
1.2 * 40 = 48
48   48NSWER:48
Answer: A
If the perimeter of a rectangular house is 1400 m, its length when its breadth is 300 m is?	Pick:
A) 300
B) 400
C) 500
D) 600
E) 700

Solution: 2(l + 300) = 1400 => l = 400 m Answer: 400
Answer: B
There are 6 boxes numbered 1, 2,…,.6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is Select.
A) 22
B) 21
C) 45
D) 27
E) 25

Solution: List down possibilities: From only 1 box all the way to all 6   If only one of the boxes has a green ball, it can be any of the 6 boxes. So, we have 6 possibilities.   If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.   If 3 of the boxes have green balls, there are 4 possibilities: 123, 234, 345, 456.   If 4 boxes have green balls, there are 3 possibilities: 1234, 2345, 3456.   If 5 boxes have green balls, there are 2 possibilities: 12345, 23456.   If all 6 boxes have green balls, there is just 1 possibility.   Total number of possibilities = 6 + 5 + 4 + 3 + 2 + 1= 
6 + 5 + 4 + 3 + 2 + 1 = 21
21.   Ans: 21
Answer: B
A circular logo is enlarged to fit the lid of a jar. The new diameter is 30 per cent larger than the original. By what percentage has the area of the logo increased?	Choose the correct choice from the following answers:
A) 50 B) 80 C) 69 D) 125 E) 250

Solution: Let old diameter be 4 , so radius is 2   Old area = 4π   New diameter is 5.2 , so radius is 2.6   New area = 6.76π   Increase in area is 2.76π   % increase in area = 2.76/4*100   So, % increase is 69%   Answer will be (69)
Answer: C
In Town X, 64 percent of the population are employed, and 35 percent of the population are employed males. What percent of the employed people in Town X are females?  Choose the correct choice from the following answers
A) 16%	B) 25%	C) 32%	D) 45%	E) 52%

Solution: We are asked to find the percentage of females in employed people.   Total employed people 64%, out of which 35 are employed males,hence 29% are employed females.   (employed females)/(total employed people)=29/64=45%   Answer:45%.
Answer: D
A train 60 m long is running with a speed of 54 km per hour. In what time will it pass a telegraph post? Pick one
A) 11 s	B) 10 s	C) 7 s	D) 4 s	E) None of these

Solution: We know from the formula Time = Distance/ Speed   Thus, Time = 60/ 54 x 5/18   or, Time = 4 sec.   ANSWER:4 s
Answer: D
Four different objects 1,2,3,4 are distributed at random in four places marked 1,2,3,4. What is probability that none of the objects occupy the place corresponding to it's number?
Choose one:
A) 17/24
B) 3/8
C) 1/2
D) 5/8
E) 1/3

Solution: Since, we know there are only 24 possible outcomes in TOTAL, it might not be a big deal just LIST the outcomes where no object is in right place.   We'll list the objects (1, 2, 3, and 4) in an order so that no number is in the correct place.   To begin, we'll place a 2 in the first position to get the following:   2134   2341   2413   There are 3 possible outcomes.   IF we place a 3 in the first position, we should also get 3 possible outcomes.   To confirm:   3142   3412   3421   Yep, 3 possible outcomes   IF we place a 4 in the first position, we should also get 4 possible outcomes.   To confirm:   4123   4312   4321   Yep, 3 possible outcomes   # of outcomes where no object is in right place = 3 + 3 + 3= 
3 + 3 + 3 = 9
9   ---------------------------   So, P(no object is in the right place)= 9/24 = 3/8 = 3/8
Answer: B
A train 110 m long is running with a speed of 90 km/h. In how many seconds will the train pass a man who is running at 9 km/h in the direction opposite to that in which the train is going?  Choose one:
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: The speed of the train relative to the man = 90 + 9= 
90 + 9 = 99
99 km/h.   99000 m/h * 1h/3600 s= (990/36) m/s   (110 m) / (990/36 m/s) = (110 * 36) / 990 = 36/9= 
36/9 = 4
4 seconds   The answer is 4.
Answer: B
The letters C,K,L and U are rearranged to form the word 'Luck'. Find its probability.  Choices: A) 1/120 B) 1/235 C) 1/24 D) 1/76 E) 1/53

Solution: Explanation :   There are total 4 letters. The probability that C gets the first position is 1/4.   The probability that K is in the second position is 1/3.   Likewise, probability for L and U are 1/2 and 1/1.   Hence, the required probability is:-   => (1/4) x (1/3) x (1/2) x 1.   => 1/24.   Answer : 1/24
Answer: C
Car A leaves the airport at 8:00 am and travels at a constant rate of 40 km per hour. Car B leaves the airport at 8:15 am and travels in the same direction along the same highway at a constant rate of 46 km per hour. At what time will Car B be 11 km ahead of Car A?  Choose the correct choice from the following answers.
A) 10:45 am
B) 11:00 am
C) 11:15 am
D) 11:45 am
E) 12:15 pm

Solution: At 8:15 am, Car A will be 10 km ahead of Car B.   Car B travels at a rate 6 km per hour faster than Car A.   Car B needs to travel 21 km more than Car A in order to be 11 km ahead.   This will take 21 km/6 km per hour=3.5 hours.   Car B will be 11 km ahead at 11:45 am.   The answer is 11:45 am.
Answer: D
One skirt requires 3.75 yards of cloth. How many skirts you can make from 45 yards	Choose the correct choice from the following options:	A) 9 skirts	B) 10 skirts	C) 11 skirts	D) 12 skirts	E) 13 skirts

Solution: for 1 shirt --> 3.75 yards reqd   for x skirts --> 45 yards   x=45/3.75 --  45= 
--  45 = 45
45/3.75=> 45*100/375= 
45*100/375 = 12
12   We can make 12 skirts from 45 yards   Ans : 12 skirts   ANSWER:12 skirts
Answer: D
Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?	Select the correct option:
A) 2 : 3 : 4 B) 6 : 7 : 8 C) 6 : 8 : 9 D) 7 : 8 : 9 E) None of these

Solution: Explanation:   Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.   Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).   =>(140/100 X 5X), (150/100 X 7X) and (175/100 X 8X)   The required ratio = 7x :	21x/2 : 14X   =>14x : 21x : 28x   =>2 : 3 : 4   2 : 3 : 4NSWER IS 2 : 3 : 4
Answer: A
The average ages of three persons is 27 years. Their ages are in the proportion of 1:3:5. What is the age in years of the youngest one among them ? Choose the correct choice from the following answers:  A) 33  B) 77  C) 55  D) 09  E) 41

Solution: Let the age of three persons be x, 3x and 5x => 9x/3 = 27 = > x = 9   Answer:09
Answer: D
The largest number of six digits	Choose the correct option
A) 100000
B) 222222
C) 333333
D) 888888
E) 999999

Solution: answer : option 999999
Answer: E
If the cost price is 94% of sp then what is the profit % Choose the correct choice:
A) 5.07%
B) 6%
C) 5.7%
D) 6.50%
E) 6.25%

Solution: Sol. sp=Rs100 : then cp=Rs 94:profit =Rs 6.   Profit={(6/94)*100}%=6.25%   Answer is 6.25%.
Answer: E
The average of five numbers is 100. If one number is excluded, the average becomes 110. The excluded number is?
Pick.
A) 8  B) 6  C) 58  D) 60  E) 96

Solution: Excluded number   = (100 * 5) - (110 * 4)   = 500 - 440= 
500 - 440 = 60
60   Answer:60
Answer: D
If the average (arithmetic mean) of 5b,6b+4,7b,8b-4 and 2b is 140, what is the value of b?
Choose the most appropriate option.
A) 20
B) 22
C) 25
D) 30
E) 48

Solution: AM of 5b,6b+4,7b,8b-4 and 2b=5b+6b+4+7b+8b-4+2b= 28b/5   Given that 28b /5 5 +6 +4+7 +8 -4+2= 
5 +6 +4+7 +8 -4+2 = 28
28b/5   Given that 28b /5= 140   b= 25   Answer is 25
Answer: C
A, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the sum of the profits of B and C. Find the total profit?	Pick one.
A) 3888	B) 277	C) 29889	D) 3000	E) 22341

Solution: A:B:C = 5:6:4   Let the total profit = 100 - 30= 
100 - 30 = 70
70   5/15 * 70= 70/3   A share = 70/3 + 30 = 160/3   B + C share = 100 - 160/3 = 140/3   A-(B+C) = 160/3 - 140/3 = 20/3   20/3 ---- 200   100 ---- ? => 3000   Answer: 3000
Answer: D
A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 5,000 and at the same time n is a perfect square and a perfect cube? Choose the correct choice: A) 2 B) 3 C) 4 D) 5 E) 6

Solution: If n is a perfect square and a perfect cube, then n = a^6 for some integer a.   The numbers are 1^6=1, 2^6=64, 3^6= 729, 4^6=4096.   The answer is 4.
Answer: C
Today John, who is 38 years old, and his daughter, who is 13 years old, celebrate their birthdays. How many years will pass before John’s age is twice his daughter’s age?	Choose the correct answer
A) 13
B) 14
C) 15
D) 16
E) 12

Solution: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.   After x years passes John’s age will be (38+x) years old, and his daughter’s age will be (13+x) years old. Since the John’s age is twice his daughter’s age (38+x)= 2 * (13+x) --->   38+x=26+2x ---> x= 12   The answer is (12).
Answer: E
If n is an integer and 101n^2 is less than or equal to 12100, what is the greatest possible value of n?
Choose the most appropriate option:
A) 7 B) 8 C) 9 D) 10 E) 11

Solution: 101 * n^2 <=12100   n^2 <=12100/101 which will be less than 121 since  12100/100= 
 12100/100 = 121
121 which is the square of 9   Next closest value of n where n^2<=121 is 10   Ans 10
Answer: D
The perimeter of a rectangular yard is completely surrounded by a fence that measures 14 meters. What is the length of the yard if the area of the yard is 6 meters squared?  Choose the correct choice from the following options:  A) 8  B) 6  C) 2  D) 4  E) 3

Solution: Perimeter of rectangular yard = 2(l + b) = 14 --> l + b = 7   Area = l * b = 6   b = 7 - l   l(7 - l) = 6   7l - l^2 = 6   l^2 - 7l + 6 = 0   Upon simplifying we get l = 1 or 6. Only 6 is there in the answer choice.   Answer: 6
Answer: B
A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?	Choose the correct option:
A) 8 kmph	B) 9 kmph	C) 2 kmph	D) 4 kmph	E) 1 kmph

Solution: DS = 6   US = 4   S = ?   S = (6 - 4)/2= 
(6 - 4)/2 = 1
1 kmph   Answer:1 kmph
Answer: E
Set X consists of all two-digit primes and set Y consists of all positive odd multiples of 7 less than 100. If the two sets are combined into one, what will be the range of the new set?  Choose the correct option:  A) 84  B) 89  C) 90  D) 92  E) 95

Solution: Set X = {11, 13, 17,............., 83, 89, 97}   Set Y = {7, 21, 35,..............., 77, 91,}   90ombining two sets, say Set Z   Set Z = {7, 11, 13, 17,21,..................., 77, 83, 89, 91, 97}   Range = Max Value - Min Value   Range (Z) = 97 - 7= 
97 - 7 = 90
90   OA 90 is the answer.
Answer: C
75 apples on a scale weigh 18.035 kg. When 5 apples are removed from the scale, the average weight of the 70 apples is 240 grams. What is the average weight (in grams) of the 5 apples which were removed?  Choose the correct answer
A) 241  B) 243  C) 245  D) 247  E) 249

Solution: 70*240= 
70*240 = 16_800
16800.   The other 5 apples weigh a total of 1235 grams.   The average weight is  1235/5= 
 1235/5 = 247
247 grams.   The answer is 247.
Answer: D
The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero ?
Select:	A) 0	B) 1	C) -1	D) -2	E) 2

Solution: Average of 20 numbers = 0.Sum of 20 numbers = (0 * 20)= 
(0 * 20) = 0
0.It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (- a). 0nswer : 0
Answer: A
The speed of a boat in upstream is 40 kmph and the speed of the boat downstream is 100 kmph. Find the speed of the boat in still water and the speed of the stream? Choose the correct option:
A) 10 kmph  B) 17 kmph  C) 30 kmph  D) 17 kmph  E) 29 kmph

Solution: Speed of the boat in still water   = (40+100)/2= 
(40+100)/2 = 70
70 kmph. Speed of the stream= (100-40)/2= 
(100-40)/2 = 30
30 kmph.   Answer: 30 kmph
Answer: C
The denominator of a fraction is 3 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 3/5. Find the fraction?
Choose one.
A) A)2/3 B) B)13/19 C) C)4/7 D) D)11/19 E) of these

Solution: Let the numerator and denominator of the fraction be 'n' and 'd' respectively.   d = 2n - 3   (n + 1)/(d + 1) = 3/5   5n + 5 = 3d + 3   5n + 5 = 3(2n - 3) + 3 => n = 11   d = 2n - 3 => d = 19   Hence the fraction is : 11/19   ANSWER:11/19
Answer: D
A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
Options
A) 647
B) 698
C) 654
D) 847
E) 976

Solution: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.   S.I. for 3 years = Rs.(39 x 3) = Rs. 117.   Principal = Rs. (815 - 117) = Rs. 698.   Answer:654
Answer: C
The average of first 13 natural numbers is? Choose the correct choice from the following options:  A) 5.2  B) 5.5  C) 7  D) 9  E) 10

Solution: Sum of 13 natural no. = 182/2= 
182/2 = 91
91   Average= 91/13= 
91/13 = 7
7   Answer:7
Answer: C
Four of the five parts numbered (a), (b), (c), (d) and (e) are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer. Options:
A) 40% of 160 + 1⁄3 of 240  B) 120% of 1200  C) 38 × 12 – 39 × 8  D) 1648 – 938 – 566  E) 6 1⁄2 of 140 – 2.5 × 306.4

Solution: Others are equal to 144 whereas (b) equals 1440.   Answer 120% of 1200
Answer: B
A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?	Choose the correct choice from the following answers:
A) Rs1589
B) Rs654
C) Rs 400
D) Rs1500
E) Rs. 2400

Solution: Explanation:   1200 * 12: x * 9 = 2:3   x =Rs. 2400   ANSWRs. 2400R:Rs. 2400
Answer: E
In what ratio should a variety of Rice costing Rs. 7 per kg be mixed with another variety of Rice costing Rs. 14.50 per kg to obtain a mixture costing Rs. 9.75 per kg?
Select:
A) 19:10
B) 19 :11
C) 11 :19
D) 12 :18
E) 11 :20

Solution: Let us say the ratio of the quantities of cheaper and dearer varieties = x : y   19 :11y the rule of allegation, x/y = (14.50 - 9.75) / (9.75 - 7) = 31/15   ANSWER:19 :11
Answer: B