MU-NLPC/Calc-aqua_rat huggingface dataset:
Find the simple interest on Rs.520 for 7 months at 8 paisa per month?
Choose the correct choice from the following answers
A) 277 B) 270 C) 291 D) 266 E) 121

Solution: I = (520*7*8)/100 = 291   Answer: 291
Answer: C
If the digits of a two-digit number are interchanged, the number so obtained is greater than the original number by 18. If the sum of the two digits of the number is 14. What is the original number ? Choose the correct option.
A) 68 B) 77 C) 95 D) 86 E) 89

Solution: Explanation :   Let the no. be 10x + y.   No. formed by the interchange of digits = 10y + x   We have y - x = 2 .....(i)   y + x = 14 .....(ii)   Solving (i) and (ii), we get x = 6, and y = 8   ∴ the no. is 68.   68nswer : Option 68
Answer: A
Marco rode his dirt bike at 40 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 20mph, what was his average speed over the three hour portion of his ride? Choose the correct choice from the following answers
A) 14 mph
B) 20/3 mph
C) 70/3 mph
D) 80/3 mph
E) 34 mph

Solution: Average speed for first two hours, S1 = 40 mph   Distance travelled in these two hours, D1 = 80 miles   Average speed for the entire 5 hour ride, S = 20 mph   Total Distance traveller in the entire 5 hour ride, D = 20 x 5 = 100 miles.   Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 100 - 80= 
100 - 80 = 20
20   Average speed for the latter 3 hour period S2= D2/3 = 20/3   Hence, the correct answer is 20/3 mph
Answer: B
If n=4p where p is a prime number greater than 1, how many different positive even divisors does n have, including n? Choose the correct choice: A) 1 B) 2 C) 3 D) 4 E) 5

Solution: We're told that N = 4P and that P is a prime number greater than 1. Let's TEST P = 2; so N = 8   The question now asks how many DIFFERENT positive EVEN divisors does 8 have, including 8?   8:   1,8   4,2   How many of these divisors are EVEN? 2,4,8…..3 even divisors.   ANSWER:3
Answer: C
The perimeter of one square is 24m & that of another is 32m. Perimeter of a square whose area is equal to the sum of the areas of the 2 squares will be  Choose the correct option:
A) 20 m B) 24 m C) 28 m D) 40 m E) 43 m

Solution: Perimeter of square = 4 * Side   Perimeter of first square = 24 m.   Side of first square =   ∴ Area of first square =   Perimeter of second square = 32 m.   Side of second square =   ∴ Area of second square =   Sum of the areas of two squares = 36 + 64= 
36 + 64 = 100
100 m2   ∴ Side of square=   ∴ Perimeter of square = 4 * 10= 
4 * 10 = 40
40 m.   40 m
Answer: D
The price of a gallon of gasoline was $30 on the 15th of March. By the 15th of April, the price per gallon had increased by 20%, and by the 15th of May the price had increased again to a total of $45 per gallon. What was the percent change in the price of a gallon of gasoline between the 15th of April and the 15th of May?	Choose one:
A) 20%
B) 25%
C) 30%
D) 35%
E) 50%

Solution: Price of a gallon of gasoline was $30 on the 15th of March   Price of a gallon of gasoline increased by 20 %so the price on 15th of April = 1.2*30= 
1.2*30 = 36
$36   Price of a gallon of gasoline was $45 on 15th of May   so there was a increase of $9 from 15th of april to 15 th of may   % increase= 9/36 * 100= 
9/36 * 100 = 25
25 %   Correct answer - 25%
Answer: B
In two triangles, the ratio of the areas is 4 : 3 and the ratio of their heights is 3 : 4. Find the ratio of their bases.  Select
A) 2:3  B) 4:5  C) 16:9  D) 7:9  E) 8:5

Solution: Sol. Let the bases of the two triangles be x and y and their heights be 3h and 4h respectively.   Then,   ((1/2) X xX 3h)/(1/2) X y X 4h) =4/3  x/y =(4/3 X 4/3)=16/9   Required ratio = 16 : 9.   Ans: 16:9
Answer: C
Rectangle A has sides a and b, and rectangle B has sides c and d. If a/c=b/d=4/5, what is the ratio of rectangle A’s area to rectangle B’s area?
Choose the correct option: A) 5/4 B) 25/16 C) 4/5 D) 16/25 E) 16/5

Solution: The area of rectangle A is ab.   c=5a/4 and d=5b/4.   The area of rectangle B is cd=25ab/16.   The ratio of rectangle A's area to rectangle B's area is ab / (25ab/16) = 16/25.   The answer is 16/25.
Answer: D
There are two positive numbers in the ratio 5:8. If the larger number exceeds the smaller by 18, then find the smaller number?
Choose the correct choice from the following choices
A) 30	B) 66	C) 77	D) 88	E) 44

Solution: Let the two positive numbers be 5x and 8x respectively.   8x - 5x = 18   3x = 18 => x = 6   => Smaller number = 5x = 30.   30nswer: 30
Answer: A
A 100-litre mixture of milk and water contains 49 litres of milk. 'x' litres of this mixture is removed and replaced with an equal quantum of water. If the process is repeated once, then the concentration of the milk stands reduced at 25%. What is the value of x? Choose the correct choice from the following answers.
A) 27.5 litres	B) 26.67 litres	C) 27.67 litres	D) 28.57 litres	E) 26 litres

Solution: Working formula ...   Initial Concentration*Initial Volume=Final Concentration*Final Volume.   Let X is the part removed from 100 lts.   49%(1-X/100)^2 = 25% * 100%   (1-x/100)^2=25/49------>(1-x/100)^2=(5/7)^2   100-X=500/7   x=28.57...   Ans 28.57 litres
Answer: D
A marble shop contains 6 blue marbles, 7 red marbles, and 7 green marbles. If 4 marbles are purchased at random from the shop, what is the probability that the 4 marbles will be blue?	Choose the most appropriate option.
A) 5/19  B) 9/20  C) 1/57  D) 15/57  E) 15/684

Solution: It doesn't matter which type of card you choose, so:   Probability of choosing 1st card: 6/20   Probability of choosing 2nd card of the same type: 5/19   Probability of choosing 3rd card of the same type: 4/18   Multiply and you get 1/57   Answer 1/57.
Answer: C
Which greatest possible length can be used to measure exactly 12 meter 65 cm, 15 meter 25 cm and 10 meter 65 cm
Pick one
A) 45cm	B) 5cm	C) 4cm	D) 15cm	E) 50cm

Solution: Explanation:   Convert first all terms into cm.   i.e. 1265 cm, 1525cm, 1065cm.   Now whenever we need to calculate this type of question, we need to find the HCF. HCF of above terms is 5.   Option 5cm
Answer: B
Albert buys 4 cows and 9 cows for $13,400. If he sells the cows at 10% profit and the cows at 20% profit, then he earns a total profit of $1880. The cost of a cow is:
Choose the most appropriate option.
A) 1000 B) 3000 C) 2000 D) 4000 E) 5000

Solution: C   2000   Let C.P. of each cow be $x and C.P. of each cow be $y.   Then, 4x + 9y = 13400 -- (i)   And, 10% of 4x + 20% of 9y = 1880   2/5 x + 9/5 y = 1880 => 2x + 9y = 9400 -- (ii)   Solving (i) and (ii), we get : x = 2000 and y = 600.   2000ost price of each cow = $2000.
Answer: C
A wheel that has 4 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
Choose the correct choice from the following answers:
A) 49	B) 4	C) 12	D) 6	E) 27

Solution: Let the required number of revolutions made by larger wheel be x.   Then, More cogs, Less revolutions (Indirect Proportion)   14 : 4 :: 21 : x 14 * x = 4 x 21   x =	(4 x 21)/14   x = 6.   Answer is 6.
Answer: D
Maxwell leaves his home and walks toward Brad's house. One hour later, Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 94 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the total time it takes Maxwell before he meets up with Brad? Pick one:
A) 3 B) 4 C) 5 D) 6 E) 10

Solution: Total Distance = 94 kms   Maxwell Speed = 4 kms/hr   Maxwell travelled for 1hour before Brad started , therefore Maxwell traveled for 4 kms in 1 hour.   Time taken = Total Distance / Relative Speed   Total Distance after Brad started = 90 kms   Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4= 
6+ 4 = 10
10 kms/hr   Time taken to meet Brad after Brad Started= 90 / 10= 
90 / 10 = 9
9 hrs   Distance traveled by Maxwell= Maxwell's speed * time taken = 4 * 9= 
4 * 9 = 36
36+4= 
36+4 = 40
40 kms...   Therefore Total Time taken by Maxwell to meet Brad= Distance travelled by Maxwell / Maxwell's Speed = 40 /4= 
40 /4 = 10
10 hrs ... Answer 10
Answer: E
If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players? Choose the correct choice from the following options.
A) 1230 B) 1340 C) 1350 D) 1540 E) 1365

Solution: A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.   =. Required number of ways = 14C10 = 14C4   = 14!/4!x19! = 1365   1365
Answer: E
A sum of money becomes double itself in 8 years at simple interest. How many times will it become 10 years at the same rate?
Choose one:  A) 10  B) 99  C) 87  D) 66  E) 12

Solution: P ---- 2P ---- 8 years   2 1/4 P ---- 10 years   10nswer: 10
Answer: A
Two children want to walk together to visit their aunt, who lives exactly 8 blocks north and 7 blocks east of their current location. If they travel only along streets and do not travel diagonally, the shortest possible route connecting the two points is exactly 15 blocks. How many different 15-block routes may they take to travel the shortest possible distance to their aunt’s house?
Choose the correct choice from the following choices.
A) 15!*8!*7!  B) 15!*8*7  C) 23!/(8!*7!)  D) 15!/(8!*7!)  E) 15/(8*7)

Solution: If they need to walk 8 blocks north and 7 blocks east, we can express this route as NNNNNNNNEEEEEEE. The question thus asks us how many ways we can arrange those letters.   The number of arrangements of 15 things is 15!   We then divide by the repetitions of N's and E's, which are 8! and 7! respectively.   The number of walking routes is 15!/(8!*7!).   The answer is 15!/(8!*7!).
Answer: D
If the square root of 1,600 is 40, then what is 40 squared?  Choose the most appropriate option
A) 1,600
B) 16
C) 4
D) 440
E) 64,000

Solution: A number squared is a number multiplied by itself   Ex) 4 squared is 16 because 4*4= 
4*4 = 16
16   The square root of a number is a number, that if squared, would equal the number you're trying to find the square root of.   Ex) What is the square root of 16? The square root of 16=4, so 4 squared equals 16   So to solve this equation you would do:   The square root of 1,600=40, so 40 squared equals 1,600   (1,600)
Answer: A
There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of $ 12,000 after 3 years at the same rate?
Options.
A) 2160	B) 3120	C) 3972	D) 6240	E) None of these

Solution: Let P = $ 100. Then, S.I. $. 60 and T = 6 years.   R = 100 x 60 = 10% p.a.   100 x 6   Now, P = $ 12000. T = 3 years and R = 10% p.a.   3972I = 3972   ANSWER 3972
Answer: C
A can complete a project in 20 days and B can complete the same project in 40 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?	Choose the correct choice from the following answers
A) 18 days  B) 20 days  C) 26.67 days  D) 16 days  E) 12 days

Solution: Let X = the number of days taken to complete the project.   The amount of work done by A is (x-10) * (1/20).   The amount of work done by B is (x) * (1/40).   (1/20)*(x-10) + (1/40)*(x) = 1   (x/20) + (x/40) - (10/20) = 1   3x/40 = 3/2   x = 20   Therefore, the answer is 20 days: 20.
Answer: B
How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
Answers
A) 5040 B) 2548 C) 300 D) 547 E) 3000

Solution: LOGARITHMS' contains 10 different letters.   Required number of words	= Number of arrangements of 10 letters, taking 4 at a time.   = 10P4   = (10 x 9 x 8 x 7)   = 5040.   5040NSWER 5040
Answer: A
Each of the products produced yesterday was checked by worker x or worker y. 0.5% of the products checked by worker x are defective and 0.8% of the products checked by worker y are defective. If the total defective rate of all the products checked by worker x and worker y is 0.65%, what fraction of the products was checked by worker y?
Choose the correct choice from the following:
A) 1/5
B) 1/2
C) 2/3
D) 1/4
E) 2/5

Solution: x: 0.5% is 0.15%-points from 0.65%.   y: 0.8% is 0.15%-points from 0.65%.   Therefore the ratio of products checked by y:x is 1:1.   Thus, worker y checked 1/2 of the products.   The answer is 1/2.
Answer: B
50 men took a dip in a water tank 30 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4m3 , then the rise in the water level in the tank will be:	Pick one
A) 20 cm	B) 25 cm	C) 33.3 cm	D) 50 cm	E) None of these

Solution: Explanation:   Total volume of water displaced =(4 x 50) m3 = 200 m3   Rise in water level = 200/30Ã—20= 0.333m = 33.3cm   Answer: 33.3 cm
Answer: C
The difference between a two-digit number and the number obtained by interchanging the two digits is 63. Which is the smaller of the two numbers?  Pick:
A) 29 B) 70 C) 92 D) Cannot be determined E) None of these

Solution: Explanation:   Let the ten's digit be x and units digit by y.   Then,   (10x + y) - (10y + x) = 63   9(x - y) = 63   x - y = 7   Thus, none of the numbers can be determined.   ANSWER IS Cannot be determined
Answer: D
Mrs. Napier has 26 stickers to give to 4 students for a reward. How many
stickers will each student get? Will there be any stickers left over?	Choose the correct choice from the following answers:
A) 6-5
B) 5-4
C) 3-6
D) 2-3
E) 2-8

Solution: 26/4 = 2 R 5 Mrs. Napier will give each student 6 stickers and there   will be 5 left over.   correct answer 6-5
Answer: A
A motor pool has 300 vehicles of which 30 percent are trucks. 15 percent of all the vehicles in the motor pool are diesel, including 15 trucks. What percent of the motor pool is composed of vehicles that are neither trucks nor diesel?	Choose one:  A) 165%  B) 90%  C) 60%  D) 55%  E) 10%

Solution: Trucks = 30% of 300 = 90   Other Vehicles (Excluding Trucks) = 300-90= 
300-90 = 210
210   Diesel Vehicle= 15% of 300 = 45 (Including 15 Trucks)   Other Diesel Vehicles (Excluding Trucks) = 45-15= 
45-15 = 30
30   Trucks that are NOT diesel= 90 - 15= 
90 - 15 = 75
75   Other Vehicles that are NOT diesel Vehicles= 210-30= 
210-30 = 180
180   Required %= (180/300)*100= 
(180/300)*100 = 60
60%   Answer: option 60%
Answer: C
The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?  Select: A) 2000 B) 2098 C) 2028 D) 2218 E) 2021

Solution: Let C.P. be Rs. x.   Then, (1920 - x)/x * 100 = (x - 1280)/x * 100   1920 - x = x - 1280   2x = 3200 => x = 1600   Required S.P. = 125 % of Rs. 1600 = 125/100 * 1600 = Rs. 2000.2000nswer: 2000
Answer: A
As a bicycle salesperson, David earns a fixed salary of $40 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true? I. y<3x II. y>x III. y>3
Choose one.
A) I only  B) III only  C) II,III only  D) I,III only  E) II only

Solution: II. y>x --> since this week, David earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week);   III. y>3 --> if David sold 3 bicycles this week then this week he earned 40+3*6= 
40+3*6 = 58
$58, which cannot be more than twice as much as he earned the last week, since the minimum salary is fixed to $40. So y must be more than 3;   I. y<3x --> is not always true.   Answer: II,III only
Answer: C
In a group of 100 people, 55 have visited Iceland and 43 have visited Norway. If 61 people have visited both Iceland and Norway, how many people have visited neither country?
Select the correct option.
A) 60
B) 61
C) 62
D) 63
E) 64

Solution: This is an example of a standard Overlapping Sets question. It has no 'twists' to it, so you'll likely find using the Overlapping Sets Formula to be a fairly easy approach. If you're not familiar with it, then here is the Formula:   100= 55 + 43 - 61 + (# in Neither Group)   =63   The prompt gives you all of the numbers you need to get to the correct answer. Just plug in and solve.   63
Answer: D
In a race of 4Kms A beats B by 100m or 25 seconds, then time taken by A is	Choose the correct choice from the following answers:	A) 15 min 8 sec	B) 16 min 15 sec.	C) 8 min 15 sec.	D) 10 min 17 sec.	E) 10 min 18 sec.

Solution: s=d/t   where t=d/s   therefore   4000*25/100= 
  4000*25/100 = 1_000
1000sec   convert 1000sec into min   we get 16min 15sec   ANSWER:16 min 15 sec.
Answer: B
Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in?	Choose the most appropriate option.
A) 3 9/87 hrs B) 3 9/27 hrs C) 3 9/17 hrs D) 3 2/17 hrs E) 3 9/11 hrs

Solution: Net part filled in 1 hour = 1/5 + 1/6 - 1/12 = 17/60   The tank will be full in 60/17 hrs, i.e., 3 9/17 hrs.   Answer: 3 9/17 hrs
Answer: C
The ratio, by volume, of soap to alcohol to water in a certain solution is 6:30:90. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 150 cubic centimeters of alcohol, how many cubic centimeters of water will it contain? Select
A) 1200
B) 1300
C) 1500
D) 1800
E) 1900

Solution: soap:alcohol   Initial ratio soap:alcohol: water --> 6:30:90   Initial soap:alcohol = 6/30 =6:30   after doubled soap:alcohol =2* 6/30 = 12/30=12:30   Initial soap:water = 6/90=6:90   after halved soap:water: 1/2 * 6/90 = 3/90 = 3:90= 12:360   After soap: alcohol:water --> 12:30:360   given alcohol 150 cubic centimeter.   ratio is 60:150:1800 (12:30:360)   For 150 cubic centimeter of Alcohol ---1800 cu cm water is required.   Answer-1800
Answer: D
Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?  Pick.
A) 337	B) 278	C) 189	D) 271	E) 211

Solution: CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135   SP = CP[(100 + profit%)/100]   = 135 * [(100 + 40)/100] = Rs. 189.   Answer:189
Answer: C
The length of a rectangle is reduced by 20%. By what % would the width have to be increased to maintainthe original area?  Choose the correct choice from the following answers:  A) 15%  B) 20%  C) 25%  D) 30%  E) 35%

Solution: Sol. Required change = (20*100)/(100-20)= 
(20*100)/(100-20) = 25
25%   25%
Answer: C
In a camp, there is a meal for 120 men or 200 children. If 100 children have taken the meal, how many men will be catered to with remaining meal?	Choose the correct choice from the following.
A) 41  B) 30  C) 35  D) 60  E) 49

Solution: D   60   There is a meal for 200 children.   100 children have taken the meal.   Remaining meal is to be catered to 100 children.   Now, 200 children 120 men.   100 children = (120/200)x 100 = 60 men.
Answer: D
If Henry were to add 5 gallons of water to a tank that is already 3/4 full of water, the tank would be 7/8 full. How many gallons of water would the tank hold if it were full?	Choose the most appropriate option: A) 25 B) 40 C) 64 D) 80 E) 96

Solution: 7/8x-3/4x=5 galls   1/8*x=5gallons   x=40 gallons   ANSWER:40
Answer: B
During a recent track meet, Peter ran x meters of the 100 meter dash in 4 seconds; running at the same rate, how many seconds will it take Peter to run z meters of the 200 meter dash?
Choose the most appropriate option
A) 4zx	B) 4z/x	C) 4x/z	D) 4/xz	E) xz/4

Solution: Speed of Peter = x/4 meters per second   Time needed to run z meters = DISTANCE/SPEED = z / (x/4) = 4z/x   Option 4z/x   The values 100m and 200m have no role to play here and are just given to confuse you.
Answer: B
A person want to give his money of $3600 to his 3 children A,B,C in the ratio 2:3:4. What is the B's share? Pick:
A) $2000 B) $1200 C) $2500 D) $1800 E) $1600

Solution: $1200's share = 3600*3/9= 
3600*3/9 = 1_200
$1200   Answer is $1200
Answer: B
On decreasing the price of a cooler by 25 %, its sale is increased by 50%. The effect on the revenue is?
Choose the correct choice from the following choices:	A) 4 % decrease	B) 12.5 % increase	C) 16% decrease	D) 16% increase	E) none of these

Solution: Net% change in revenue   = ( x + y + xy/100) %   = [-25 + 50+ ( -25 x 50)/100]% or 12.5%   ANSWER:12.5 % increase
Answer: B
The average (arithmetic mean) of eight numbers is 47.1. If the sum of half of these numbers is 158.4, what is the average of the other half?	Answers:
A) 12.8
B) 24.2
C) 54.6
D) 72.1
E) 96.8

Solution: arithmetic mean = sum / total numbers   sum = 47.1 * 8= 
47.1 * 8 = 376.8
376.8   sum of half of these numbers is 158.4. So, 4 numbers sum is 158.4. Rest 4 numbers sum= 376.8-158.4= 
376.8-158.4 = 218.4
218.4   Arithmetic mean of the 4 nos= 218.4/4= 
218.4/4 = 54.6
54.6   Hence, 54.6 is the answer.
Answer: C
In how many different ways can the letters of the word 'DETAIL' be arranged such that the vowels must occupy only the odd positions? Choose the correct choice
A) None of these  B) 64  C) 120  D) 36  E) 22

Solution: Explanation :   The word 'DETAIL' has 6 letters which has 3 vowels (EAI) and 3 consonants(DTL)   The 3 vowels(EAI) must occupy only the odd positions.   Let's mark the positions as (1) (2) (3) (4) (5) (6).   Now, the 3 vowels should only occupy the 3 positions marked as (1),(3) and (5) in any order.   Hence, number of ways to arrange these vowels = 3P3   = 3! = 3 x 2 x 1 = 6   Now we have 3 consonants(DTL) which can be arranged in the remaining 3 positions in any order   Hence, number of ways to arrange these consonants = 3P3   = 3! = 3 x 2 x 1 = 6   Total number of ways   = number of ways to arrange the vowels x number of ways to arrange the consonants   = 6 x 6 = 36. Answer : Option 36
Answer: D
Machine R takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine R to make 40 widgets? Choose the correct choice:
A) 5
B) 6
C) 8
D) 10
E) 12

Solution: i approached this one by plugging in numbers...started with C.   if 40 are made in 8 hours, then 20 are made in 4 hours. so time of R is 4, and time of B is 2.   rate together: 20/4 + 20/2 = 5+10= 
5+10 = 15
15. so in 1 hour, together make 15 widgets. in 3 hours= 45. way too much. we can eliminate right away C, B, and A - because B and R reduces the time - the total # of widgets made will be even higher.   now between D and E -> try only one ..if it doesn't work, then the other one is the answer.   i picked E:   12h to make 40 widgets, and 6 hours to make 20. this is the time of R. time of B=4 hours.   20/6 + 20/4 = 10/3 + 20/4   find LCM of 3 and 4 = 12. multiply first by 4, and second by 3:   40+60/12 = 100/12   divide by 4:   25/3   so this is the rate given.   12 is the correct answer
Answer: E
3 people meet for a business lunch. Each person shakes hands once with each other person present. How many handshakes take place?
Pick one.
A) 10 B) 15 C) 3 D) 9 E) 12

Solution: the formula to count handshakes is n(n−1)2n(n−1)2   Where n is the number of people   => 3(3-1)/2 = 3*2/2 = 6/2= 
6/2 = 3
3=> the answer is 3(3)
Answer: C
The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article?
Choose the most appropriate option
A) 2:7
B) 5:2
C) 7:2
D) Data inadequate
E) None of these

Solution: Let C.P. = Rs. 5x and S.P. = Rs. 7x.   Then, Gain = Rs. 2x   Required ratio = 2x : 5x = 2:5   ANSWNone of theseR:None of these
Answer: E