MU-NLPC/Calc-aqua_rat huggingface dataset:
Car A is 40 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour.How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?  Choose the correct option
A) 5	B) 6	C) 7	D) 5.5	E) 6.5

Solution: Relative speed of car A is 58-50= 
58-50 = 8
8 miles per hour, to catch up 40 miles and drive 8 miles ahead so to drive 48 miles it'll need 48/8= 
48/8 = 6
6 hours.   Answer: 6
Answer: B
Tough and Tricky questions: Combinations.
The product of the digits of the four-digit number h is 54. No two digits of h are identical. How many different numbers are possible values of h? Choose the correct choice.
A) 24	B) 28	C) 30	D) 36	E) 48

Solution: 24nswer = 24 = 24   Let number =abcd   Given that a*b*c*d = 54   a,b,c,d can be 1,2,3,9   Number of ways = 4*3*2= 
4*3*2 = 24
24
Answer: A
A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?  Choose the correct choice from the following options:	A) 20	B) 24	C) 10	D) 27	E) 16

Solution: Distance from A and B be 'd'   Average Speed = total distance/total time   Average Speed = (2d)/[(d/20) + (d/30)]   = (2d)/[5d/60) => 24 kmph.   Answer: 24
Answer: B
Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together? Choose the correct choice from the following answers: A) 17 1/7 B) 17 1/9 C) 17 1/2 D) 17 1/7 E) 17 1/5

Solution: 1/30 + 1/40 = 7/120   120/7 = 17 1/7 days   17 1/7nswer: 17 1/7
Answer: A
Set D consists of 19 elements. The average of set D is L. If a new element is added to the set and the average grows by K, what is the value of the new element?  Options.
A) a) L(1 + K / 5)	B) b) L * (K/100) - 20L	C) c) 20L(1+K/100)	D) d) 20(1+K/100)-19L	E) e) L*(K/5)-19

Solution: Let's assume the value of new element to bea. So converting the word problem into equation,   (19*L + a) / (19 + 1) = L + k ==> after solving the equation we will get a (value of newly added element) = L + 20K   But according to the answer options, problem writer wanted to conveyk% percent rise in average value.   If we consider this case than resulting equation will be,   (19*L + a) / ( 19+1 ) = L + (K/100)*L ==> 19L + a = 20 [ L + KL/100]   ==> a= 20L + KL/5 -19L   ==> a= L + KL/5 , which is equivalent to option [a) L(1 + K / 5)]
Answer: A
Rahul went to a shop and bought things worth Rs. 65, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?  Choose the correct option: A) A)19.7 B) B)19.9 C) C)39.9 D) D)49.9 E) E)59.7

Solution: Total cost of the items he purchased = Rs.65   Given that out of this Rs.65, 30 Paise is given as tax   => Total tax incurred = 30 Paise = Rs.30/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (65−30/100−x)6/100 = 30/100   ⇒ 6(65 −0.3 −x) = 30   ⇒ (65 − 0.3 − x) = 5   ⇒ x = 65 − 0.3 − 5 = 59.7   59.7)
Answer: E
In a question on division with zero remainder, a candidate took 12 as divisor instead of 21. The quotient obtained by him was 35. The correct quotient is/
Choices
A) 20 B) 22 C) 24 D) 26 E) 27

Solution: Number = (35 * 12)= 
(35 * 12) = 420
420   Correct quotient= 420/21= 
420/21 = 20
20   20)
Answer: A
Subtracting 10% from X is the same as multiplying X by what number?	Pick one.
A) 98%	B) 90%	C) 93%	D) 96%	E) 34%

Solution: X - (10/100) X = X * ?   ? = 90%   Answer:90%
Answer: B
If 2^5, 3^3, and 12^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w?
Choose the most appropriate option:
A) 26
B) 39
C) 42
D) 144
E) 156

Solution: Here 156 has three two's   two three's   and one 13   rest of them must be in w   so w= 12*3*4= 
12*3*4 = 144
144   Smash 144
Answer: D
There is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 19 days more? Pick one:
A) 22
B) 40
C) 99
D) 88
E) 66

Solution: 760 ---- 22   760 ---- 20   x ----- 19   x*19 = 760*20   x = 800   760   -------   40   Answer: 40
Answer: B
A metallic sheet is of rectangular shape with dimensions 52 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:	Choose one:
A) 4830
B) 5120
C) 6420
D) 7500
E) 5760

Solution: l = (52 - 16)= 
(52 - 16) = 36
36 m,   b= (36 -16)= 
(36 -16) = 20
20 m,   h= 8 m.   Volume of the box = (36 x 20 x 8) m3 = 5760 m3.   Answer: Option 5760
Answer: E
A certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 7 consecutive spaces in a random direction, what is the probability Q the piece ends no more than 7 spaces from the square numbered 49?	Choose one:
A) 7% B) 8% C) 14% D) 15% E) 28%

Solution: OA is E   required prob is 7 spaces any side of 49.   so total 14 spaces are required in 7 moves which can be achieved by max 7 move on any side   so total spaces = 28   probability Q= 28%.28%
Answer: E
The distance between two stars is 3 × 10^5 light years. What is the distance between the two stars in parsecs? (1 parsec = 3.26 light years)  Select
A) 3.1 × 10^4  B) 9.2 × 10^4  C) 9.7 × 10^5  D) 8.5 × 10^6  E) 7.1 × 10^7

Solution: 3 × 10^5 ly / (3.26 ly/parsec) = (3/3.26) x 10^5 = 0.92 x 10^5 = 9.2 x 10^4 parsec   The answer is 9.2 × 10^4.
Answer: B
How many seconds will a 1000 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? Pick one
A) 287
B) 300
C) 500
D) 277
E) 121

Solution: Let length of tunnel is x meter   Distance = 1000+x meter   Time = 1 minute = 60 seconds   Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s   Distance = Speed*Time   1000+x = (65/3) * 60   1000+x = 20 * 65= 
20 * 65 = 1_300
1300   x= 1300 - 1000= 
1300 - 1000 = 300
300 meters   Answer: 300
Answer: B
Find the value of y from (12)^3 x 6^4 ÷ 432 = y?  Select the correct option:
A) 3456  B) 4567  C) 4789  D) 5678  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
Ram bought 50 books for Rs.1750 from one shop and 10 books for Rs.650 from another. What is the average price he paid per book ?  Select.
A) 28 B) 18 C) 27 D) 29 E) 21

Solution: Average price per book   = (1750 + 650) / (50 +10)   = 2400/ 60   = Rs.40   Answer:29
Answer: D
In wardrobe Marry has 3 trousers. One of them is grey the 2nd blue and the 3rd brown. In his wardrobe he also has 4 shirts. One of them is grey and the other 3are white. He opens hiswardrobe in the dark and pick out one shirt trouser pair without examination the color. What is the likelihood that neither the shirt nor the trouser is grey?  Answers:
A) 1/2 B) 2/3 C) 3/5 D) 2/7 E) 3/8

Solution: Probability that trouser is not grey = 2/3   Probability that shirt is not grey = 3/4   ∴ Required probability = 2/3 x 3/4 = 1/2   1/2
Answer: A
The letters P,O,C and Y are rearranged to form the word 'Copy'. Find its probability.	Options: 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 P gets the first position is 1/4.   The probability that O is in the second position is 1/3.   Likewise, probability for C and Y 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
Two trains are running at 40 kmph and 20 kmph respectively in the same direction.Fast train completely passes a man sitting in the slower train in 7 seconds.What is the length of the fast train? Select the correct option
A) 23 m
B) 38 8/9 m
C) 27m
D) 27 7/9m
E) 33 7/9m

Solution: relative speed=20kmph=50/9m/sec   length of the train=50/9*7= 38 8/9   ANSWER:38 8/9 m
Answer: B
n is a positive integer and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1500, then what is the smallest possible value of n?  Choose the correct option
A) 8 B) 10 C) 12 D) 15 E) 20

Solution: 1500=2^2*3*5^3   5^3 means that n must be at least 15. That is, we need 5, 10, and 15.   The answer is 15.
Answer: D
In a small snack shop, the average (arithmetic mean) revenue was $400 per day over a 10-day period. During this period, if the average daily revenue was $360 for the first 6 days, what was the average daily revenue for the last 4 days? Select:
A) $420
B) $440
C) $450
D) $460
E) $480

Solution: The average revenue was $400 per day over a 10-day period --> total revenue over 10-day period is 10*$400=$4,000;   The average daily revenue was $360 for the first 6 days --> total revenue for the first 6 days is 6*$360=2,160;   Total revenue for the last 4 days is $4,000-2,160=$1,840;   Average daily revenue for the last 4 days is $1,840/4=$460.   Answer: $460.
Answer: D
Which of the following correctly lists the data sets in order of least to greatest standard deviation?
I. 3, 16, 54, 12, 13, 64
II. 52,53,54,55,56,57
III. 8, 8, 8, 8, 8, 8	Choose the correct answer:
A) I, II, II	B) II, III, I	C) III, I, II	D) II, III, I	E) III, II, I

Solution: out of three given sets,   III has all numbers same, so it has zero standard deviation hence it is Least   only answer choices A, B and D have III in least position.   II has consecutive numbers , hence all are closedly spaced hence std deviation will be less   while in I,numbers are spread widely hence std deviation should be more than III   hence order should be III, II,I   Option: III, II, I
Answer: E
At the end of a business conference the 5 people present all shake hands with each other once. How many handshakes will there be altogether ? Pick:
A) 20  B) 45  C) 55  D) 90  E) 10

Solution: number of handshakes = 5C2= 5*4/2= 
5*4/2 = 10
10   ANSW10R: 10
Answer: E
A card is randomly drawn from a deck of 52 cards. What is the probability getting either a King or a Diamond? Answers
A) 5/43  B) 8/32  C) 6/26  D) 4/13  E) 2/31

Solution: Total number of cards = 52   Total Number of King Cards = 4   P(King) = 4/52   P(4/13iamond) = 13/52   P(King and 4/13iamond) = 1/52   P(King or a 4/13iamond) = P(King) + P(4/13iamond) â€“ P(King and 4/13iamond)   =4/52+13/52â€“1/52=16/52=4/13   Answer 4/13
Answer: D
The incomes of two persons A and B are in the ratio 3:4. If each saves Rs.100 per month, the ratio of their expenditures is 1:2 . Find their incomes?	Options
A) 150,217
B) 150,218
C) 150,200
D) 150,276
E) 150,212

Solution: The incomes of A and B be 3P and 4P.   Expenditures = Income - Savings   (3P - 100) and (4P - 100)   The ratio of their expenditure = 1:2   (3P - 100):(4P - 100) = 1:2   2P = 100 => P = 50   Their incomes = 150, 200   Answer:150,200
Answer: C
A bike covers a certain distance at the speed of 64km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel?	Select:
A) 80 km/h  B) 85 km/h  C) 90 km/h  D) 75 km/h  E) 70 km/h

Solution: Ans.(B)   Sol. Total distance = 64 × 8 = 512 km   Now speed = 512/6 = 85.34 km/h
Answer: B
Each week, Harry is paid X dollars per hour for the first 30 hours and 1.5X dollars for each additional hour worked that week. Each week, James is paid X dollars per hour for the first 40 hours and 2X dollars for each additional hour worked that week. Last week James worked a total of 53 hours. If Harry and James were paid the same amount last week, how many hours did Harry work last week? Select the correct option
A) 35 B) 36 C) 37 D) 38 E) 54

Solution: Amount earned by James = 40*x + 13*2x = 66x   Therefore, Amount earned by Harry = 66x   But we know the amount Harry earned assuming working y hours (y>30) is 30*x + (y-30)*1.5x   [[We know y>30 because in 30h the most Harry could earn is 30x, but he has earned 66x]]   So x*(1.5y -45 +30) = 66x   Or x*(1.5y - 15) = 66x   So 1.5y - 15 = 66   So 1.5y = 81   So y = 54   Answer is 54
Answer: E
A card is drawn from a pack of 52 cards. The probability of geƫng a queen of club or a king of heart is
Pick.
A) 1/13  B) 2/13  C) 1/26  D) 1/52  E) None of these

Solution: Explanation:   Total number of cases = 52   Favourable cases = 2   Probability = 2/56 = 1/26   Answer: 1/26
Answer: C
Two trains start together to travel to a certain destination,one at speed of 55 km/hr and another at 65 km/hr. The former arrives 3 hours after the latter. What is the total distance. Choose the correct choice from the following answers:  A) 768 km.  B) 887 km.  C) 9002.5 km.  D) 1002 km.  E) 1072.5 km.

Solution: A _________________X Km_______________________B   Let both trains starts from A. Distance is X km. Faster trains take t hour and other one takes (t -3) hours.   For both trains distance is same to travel.   Speed of faster train /speed of slower train = time taken by slower train /time taken by faster train   65/55 = (t +3)/t   13t = 11t + 33   2t = 33   t = 16.5 hours.   Total distance = s *t = 65 * 16.5= 
65 * 16.5 = 1_072.5
1072.5 km.   ANSW1072.5 km.R :OPTION 1072.5 km.
Answer: E
If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 8-letter code words to the number of 6-letter code words?
Choose the correct choice from the following answers:
A) 5 to 4 B) 3 to 2 C) 12 to 1 D) 5 to 1 E) 6 to 1

Solution: Number of ways to form 8-letter code: 10!/2! = 10*9*8*7*6*5*4*3   Number of ways to form 6-letter code: 10!/4! = 10*9*8*7*6*5   Ratio: 12 to 1   Answer : 12 to 1
Answer: C
Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months? Select:
A) 1500
B) 1750
C) 2000
D) 2500
E) 3000

Solution: Compound interest formula   A = P ( 1+r/n)power nt   given, n= 4 (quaterly);r =.08   the approach is substitution,   our interest requirement is 100$ after 6 months, 2 compounding period. interest per compounding period is 2%   lets take 1500, after 3 months interest accumulated is 30$, total amount is 1530   after 6 months, interest is 30.6$ and total is 1560.6$, so not 1500   1500 & 1750 have a difference of 250$ only , but the expected interest different is around 40$ hence you can straightaway rule out 1750   2000 is again can be ruled out as approx 4% interest yeilds only 80$   2500$ is a good bet, first 3 months it earns 50$ as interest, next 3 months it will earn 51$ as interest.   hence answer is 2500
Answer: D
How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board? Answers.
A) 99
B) 626
C) 27
D) 26
E) 28

Solution: 30 * 33/2 = 5/2 * 2 * x => x   = 99   99nswer: 99
Answer: A
If 30% of a class averages 95% on a test, 50% of the class averages 79% on the test, and the remainder of the class averages 60% on the test, what is the overall class average? (Round final answer to the nearest percent).
Choose the correct choice from the following answers
A) 76%	B) 77%	C) 78%	D) 79%	E) 80%

Solution: This question is a Weighted Average question with a series of dependent variables.   The remaining portion of the class represents 100% - 30% - 50% = 20% of the class   Converting the portions of the class population to decimal weights, we find:   Class Average  100  - 30  - 50= 
 100  - 30  - 50 = 20
20% of the class   Converting the portions of the class population to decimal weights, we find:   Class Average= 0.30x95 + 0.50x79 + 0.20x60 = 80   The class average (rounded) is 80%   Final Answer   80%) 80%
Answer: E
A merchant marks goods up by 75% and then offers a discount on the marked price. The profit that the merchant makes after offering the discount is 5%. What % discount did the merchant offer?
Choose the correct choice from the following options: A) 20% B) 25% C) 35% D) 40% E) 45%

Solution: Let P be the original price of the goods and let x be the rate after the markup.   (1.75P)*x = 1.05P   x = 1.05/1.75= 
1.05/1.75 = 0.6
0.6 which is a discount of 40%.   The answer is 40%.
Answer: D
1!+2!+3!+4!+5!+.100! is divided by 24. Find the remainder from this?  Pick
A) 4 B) 6 C) 9 D) 10 E) 11

Solution: By applying rule 2, we divide the terms of the above expression individually, and add them to get the final remainder. But from 4! onwards all the terms leave a remainder 0 when divided by 24.   So the remainder = 1 + 2 + 6 + 0 + 0....... =   9
Answer: C
A train running at the speed of 120 km/hr crosses a pole in 9 seconds. Find the length of the train.
Choose the correct option:
A) 100 meter B) 150 meter C) 200 meter D) 250 meter E) 300 meter

Solution: Speed = 120*(5/18) m/sec = 200/6 m/sec   Length of Train (Distance) = Speed * Time     (200/6) * 9= 
  (200/6) * 9 = 300
300 meter   Answer:300 meter
Answer: E
HOW MANY KGS OF TEA WORTH RS.25/KG MUST BE BLENDED WITH 30 KGS OF TEA WORTH RS.30/KG SO THAT BY SELLING THE BLENDED VARIETY AT RS.30/KG THERE SHOULD BE A GAIN OF 5%
Select:
A) 36 B) 40 C) 32 D) 12 E) 45

Solution: (x+30)*30=(105/100)(25x+30*30)   Solving we get 12.   Answer is 12.
Answer: D
judith is practicing her dance steps along with her friends. In a particular sequence, all of them form a row. At that point, judithis standing on the 6th position from either end of the row.
Can you find out how many girls are practicing together?  Choose the correct choice from the following choices:
A) 4
B) 9
C) 11
D) 6
E) 8

Solution: As judith is 6th from either end of the row, it means that 5 girls are on one of her sides and 5 are present on the other.   5 + 5 + 1(judith herself) = 11.   Hence, 11 girls are practicing the dance together.   correct answer is 11)11
Answer: C
A bus leaves Los Angeles at 7:00 a.m. traveling north at 80 miles per hour. At 12:00 p.m. a plane leaves Los Angeles traveling north at 380 miles per hour. At what time will the plane overtake the bus?  Choose one.
A) 1:45 p.m.
B) 1:20 p.m.
C) 12:25 p.m.
D) 12:40 p.m.
E) 2:10 p.m.

Solution: At 12:00pm, the bus is 400 miles ahead of plane   The plane travels at 380 mph, which gains 300 mph on bus   400/300= 4/3 hours = 80 minutes   12:00 + 0:80 = 1:20   The plane will overtake bus at 01:20pm   Answer:1:20 p.m.
Answer: B
The first three terms of a proportion are 3, 9 and 12. The fourth term is? Choose the correct choice from the following answers:
A) 15  B) 87  C) 16  D) 36  E) 12

Solution: (9*12)/3= 
(9*12)/3 = 36
36   Answer: 36
Answer: D
Mike earns $14 per hour and Phil earns $7 per hour. Approximately how much less, as a percentage, does Phil earn than Mike per hour?
Choose the correct choice from the following answers:  A) 25%  B) 32.5%  C) 37%  D) 50%  E) 40%

Solution: What % less of 14 is 7   let it be x % less ,then   =14(1-x/100)=7   1-x/100=7/14   x=100/2= 
100/2 = 50
50%   Ans 50%
Answer: D
A certain amount earns simple interest of Rs. 1200 after 10 years. Had the interest been 2% more, how much more interest would it have earned?
Choose the correct answer:	A) Rs. 25	B) None of these	C) Rs. 120	D) Rs. 100	E) Cannot be determined

Solution: Explanation :   Since we do not have the principal and rate of interest, we can not find out the required details.   Answer : Option Rs. 100
Answer: D
X and Y run a 100m race,where X beats Y by 20 m. To do a favor to Y, X starts 10m behind the starting line in a second 100m race. Both run at the same previous speed. Which of the following is true?
Answers.
A) X Beats Y by 2m  B) X Beats Y by 0.5 m  C) X Beats Y by 4 m  D) X Beats Y by 4 m  E) Y Beats X by 10m

Solution: Let's suppose that the speed of X is 10m/s and that the speed of Y is 8 m/s.   So, in the first race, the results are the following:   X crosses the finish line in 10s. In other words, X has run 100m in 10 s.   In 10s, Y has run 80 meters.   Therefore, there is the difference of 20 meters mentioned in the question.   Now, let's review the second race.   In 12 seconds, X can complete the 100 meters race. We have to remember that X is 4 meters behind the starting line.   But in 12 seconds, Y has covered (96 ) =96 meters. Also, it is important to notice that in 12 seconds Y cannot arrive to the finish line.   So, 100 - 96 = 4 meter   Answer: X Beats Y by 4 m
Answer: D
By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?  Choose the correct choice from the following choices:
A) 54670
B) 12300
C) 38000
D) 43200
E) 45000

Solution: Option 38000   Explanation:   38000P + 38000P/8 = 45000   38000P = 40000   SP = 40000*(95/100)= 
40000*(95/100) = 38_000
38000
Answer: C
Hitesh is 40 years old and Ronnie is 60 years old. How many years ago was the ratio of their ages 3 : 5? Choose the correct choice from the following answers
A) 5 years
B) 10 years
C) 20 years
D) 37 years
E) None

Solution: Solution   Suppose, the ratio was 3 : 5, x years ago.   Then,	40 - x / 60 - x   = 3 / 5.   ‹=›5(40-x)=3(60-x)   ‹=›2x= 20   ‹=›x= 10   Answer 10 years
Answer: B
If ab represents a positive two digit number, where a and b are single digit integers, which of the following cannot be true?	Choose the correct choice from the following answers:
A) a+b =9  B) (a)(b)=9  C) a-b = 9  D) b-a= 9  E) a/b = 9

Solution: (A) ab = 45 or 63 or 27   (B) ab = 33 or 19   (C) 90   (D) impossible   (E) ab = 91   (D) is impossible because 09 is not a valid two digit number --- if there's a zero in the ten's place, that's just 9, a single digit number. Therefore, no valid two digit number would satisfy (D).   ans b-a= 9
Answer: D
If n is a positive integer, what is the remainder when (7^(3n+3))(6^n) is divided by 10?	Choose the correct choice from the following choices:
A) 1
B) 2
C) 4
D) 6
E) 8

Solution: This one took me bout 3 1/2 min. Just testin numbers and what not.   First notice that n is positive. Save time by noticing thatI worked out one solution where n=0 only to find that thats not an option :p.   1-7 stands for ^1 thru 7   1: 7*1=7   2: 7*7=9   3: 7*9=3   4: 7*3=1   5: 7*1=7   6: 7*7=9   7: 7*9=3   Pattern repeats every @ 5. Notice every ^4 or multiple of 4 is always going to be 1. This is just for future notice for similar problems.   so 7^4n+3 ---> if n=1 then its ((7^7)*6))/10 which can say is going to be 3*8--> 18/10 --> R=8   Now from here if id double check just to make sure.   7^4(2)+3*6= 
3*6 = 18
18/10 ---> R=6.   6 or J in this problem.
Answer: D
The weights of three boys are in the ratio 4 : 5 : 6. If the sum of the weights of the heaviest and the lightest boy is 47 kg more than the weight of the third boy, what is the weight of the lightest boy?  Pick:
A) 87.6 kg	B) 37.6 kg	C) 98.6 kg	D) 65.6 kg	E) 87 kg

Solution: Let the weights of the three boys be 4k, 5k and 6k respectively.   4k + 6k = 5k + 47   => 5k = 47 => k = 9.4   Therefore the weight of the lightest boy   = 4k = 4(9.4) = 37.6 kg.   Answer:37.6 kg
Answer: B
Find the area of a parallelogram with base 21 cm and height 11 cm? Choose the correct choice from the following options.
A) 231
B) 284
C) 288
D) 255
E) 122

Solution: 231rea of a parallelogram = base * height   = 21 * 11= 
21 * 11 = 231
231 cm2   231nswer: 231
Answer: A
Find the value of 1/(3+1/(3+1/(3-1/3)))
Answers:  A) 21/29  B) 27/89  C) 89/21  D) 29/21  E) None

Solution: 1/[3 + (1/(3+1/(3 - 1/3)))]   => 1/[3 + 1/(3 + 1/(8/3))]   => 1/[3 + 1/(3 + 3/8)]   => 1/[3 + 8/27]   => 1/(89/27)   => 27/89   27/89
Answer: B
X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?
Answers.
A) 1:2	B) 2:1	C) 3:2	D) 2:3	E) 5:3

Solution: Ratio in which they should share the profit   = Ratio of the investments multiplied by the time period   =45000×12:30000×9   =45×12:30×9   =3×12:2×9   =2:1   Answer is 2:1.
Answer: B
Ratio between two numbers is 3: 4 and their sum is 420. Find the smaller number?	Choose the correct choice from the following choices:
A) 240
B) 180
C) 160
D) 140
E) 150

Solution: Explanation:   3x + 4x = 420   x = 60 => 3x = 180   ANSWER IS 180
Answer: B