mathewhe/aqua_rat huggingface dataset:
Question: Cindy has her eye on a sundress but thinks it is too expensive. It goes on sale for 15% less than the original price. Before Cindy can buy the dress, however, the store raises the new price by 25%. If the dress cost $61.2 after it went on sale for 15% off, what is the difference between the original price and the final price?
(A) $0.00
(B) $4.50
(C) $3.40
(D) $5.00
(E) $6.80
Rationale: 0.85*{Original Price} = $61.2 --> {Original Price} = $72.
{Final Price} = $61.2*1.25 = $76.5.
The difference = $76.5 - $72 = $4.5
Answer: B.
Answer: (B) $4.50
Question: A certain clock marks every hour by striking a number of times equal to the hour,and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 33 seconds. at 12:00 ,how many seconds elapse between the beginning of the first stroke and the end of the last stroke?
(A) A.72
(B) B.50
(C) C.48
(D) D.69
(E) E.44
Rationale: At 6:00 it'll chime 6 times. If we assume that the time taken to chime is x, then time between chimes is also x. So you have 6 chimes, which is 6x and 5 time intervals between chimes. This means that 11x = 33 seconds. Thus x = 3 seconds.
By a similar logic, at 12:00, there are 12 chimes and 11 intervals so the total time is (12+11)x = 23x = 69 seconds.
Answer D
Answer: (D) D.69
Question: A contractor agreeing to finish a work in 150 days, employed 75 men each working 8 hours daily. After 90 days, only 2/7 of the work was completed. Increasing the number of men by ________ each working now for 10 hours daily, the work can be completed in time.
(A) 322 men
(B) 232 men
(C) 838 men
(D) 539 men
(E) 150 men
Rationale: One day’s work = 2 / (7 * 90)
One hour’s work = 2 / (7 * 90 * 8)
One man’s work = 2 / (7 * 90 * 8 * 75)
The remaining work (5/7) has to be completed within 60 days, because the total
number of days allotted for the project is 150 days.
So we get the equation
(2 * 10 * x * 60) / (7 * 90 * 8 * 75) = 5/7 where x is the number of men
working after the 90th day.
We get x = 225
Since we have 75 men already, it is enough to add only 150 men.
Answer:E
Answer: (E) 150 men
Question: A special municipal payroll tax charges not tax on a payroll less than $200,000 and only 0.2% on a company’s payroll above $200,000. If Belfried Industries paid $200 in this special municipal payroll tax, then they must have had a payroll of?
(A) $180,000
(B) $202,000
(C) $220,000
(D) $300,000
(E) $2,200,000
Rationale: ANSWER : D , ( with different approach) :
The 200 paid is 0.2% of the additional amount above 200,000. Let it be X
Now 0.2% of X = 200
Therefore X= 100,000
Total = 200,000 + X= 300,000
Answer: (D) $300,000
Question: If 1,000 microns = 1 decimeter, and 1,000,000,000 angstroms = 1 decimeter, how many angstroms equal 1 micron?
(A) 1,000
(B) 100
(C) 1,000,000
(D) 10
(E) 10,000
Rationale: Given that 1,000 microns = 1 decimeter =1,000,000,000 angstroms
So, 1 micron = 1,000,000,000/1,000
=1,000,000
Answer : C
Answer: (C) 1,000,000
Question: If an article with marked price of $400 is sold at successive discount of 15%,25% and 15%,what is the price the customer has to pay?
(A) 360
(B) 108
(C) 230
(D) 216
(E) 224
Rationale: discount=0.85*.75*.85=.54
so .54*400=216
ANSWER:D
Answer: (D) 216
Question: Angela, Bernie, and Colleen can complete a job, all working together, in 5 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 6 hours. How long would it take Colleen, working alone, to complete the entire job?
(A) 8 hours
(B) 10 hours
(C) 12 hours
(D) 30 hours
(E) 20 hours
Rationale: A+B+C complete the job in 5 hours.
A+B complete the job in 6 hours.
A+B and C complete the job in 5 hours -->1/(A+B) + 1/C = 1/5-->1/6+1/C=1/5 ----> C=30 hours. ANS D
Answer: (D) 30 hours
Question: The parameter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 10 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square.
(A) 44.0
(B) 23.59
(C) 23.55
(D) 23.53
(E) 23.57
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(18 + 10) = 56 cm Parameter of the square = 56 cm
i.e. 4a = 56
A = 14
Diameter of the semicircle = 14cm
Circimference of the semicircle
= 1/2(âˆ)(14)
= 22/7*14 = 44 cm
Answer: A
Answer: (A) 44.0
Question: Find the unit's digit in the product (2467)163 x (341)72.
(A) 7
(B) 5
(C) 3
(D) 4
(E) 1
Rationale: Clearly, unit's digit in the given product = unit's digit in 7153 x 172.
Now, 74 gives unit digit 1.
7^152 gives unit digit 1,
7^153 gives unit digit (l x 7) = 7. Also, 1^72 gives unit digit 1.
Hence, unit's digit in the product = (7 x 1) = 7
Answer is A.
Answer: (A) 7
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 60 hrs and a machine of type S does the same job in 90 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
(A) 12
(B) 15
(C) 16
(D) 18
(E) 20
Rationale: Type R completes 1/60 of the job each hour.
Type S completes 1/90 of the job each hour.
Together R and S complete 1/60 +1/90 = 1/36 of the job each hour.
Let n be the number of each type of machine.
2*n*(1/36) = 1 job completed
n = 18
The answer is D.
Answer: (D) 18
Question: Find the greatest number which on dividing 1661 and 2045, leaves a reminder of 10 and 13 respectively
(A) 125
(B) 127
(C) 129
(D) 131
(E) 150
Rationale: Explanation:
In this type of question, its obvious we need to calculate the HCF, trick is
HCF of (1661 - 10) and (2045 -13)
= HCF (1651, 2032) = 127
Option B
Answer: (B) 127
Question: If a certain manager had received a 10% raise instead of the 8% raise that she actually received, her salary would have been $60,500. What was her actual salary after the raise?
(A) 55,000
(B) 58,806
(C) 59,290
(D) 59,400
(E) 61,620
Rationale: salary(let X) included 10% increase can be written as
(1+10/100)X=60500
X=60500/110------>55000
if there is 8% rise in 55000
then the salary now is 8% of 55000
8*55000/100=4400
then total salary after increment=55000+4400----->59400
Ans D
Answer: (D) 59,400
Question: A cistern can be filled by a tap in 2 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled ?
(A) 2.57 hrs
(B) 5 hrs
(C) 6.57 hrs
(D) 7.2 hrs
(E) 9.27 hrs
Rationale: Net part filled in 1 hour= 1/2 -1/9= 7/18
Therefore the cistern will be filled in 18/7 hours or 2.57 hours.
ANSWER:A
Answer: (A) 2.57 hrs
Question: Sakshi can do a piece of work in 20 days.Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work :
(A) 15
(B) 16
(C) 18
(D) 25
(E) None of these
Rationale: Solution
Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4 .
Suppose Tanya taken x days to do the work.
5 : 4 : : 20 : x ⇒ x = (20 x4 /5)⇒ x = 16 days.
Hence,Tanya takes 16 days is complete the work.
Answer B
Answer: (B) 16
Question: Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 54 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
(A) 30 minutes
(B) 17 minutes
(C) 15 minutes
(D) 6 minutes
(E) 12 minutes
Rationale: Part of the filled by all the three pipes in one minute
= 1/18 + 1/15 - 1/54 = (15 + 18 - 5)/270 = 28/270 = 14/135
So, the tank becomes full in 6 minutes.
Answer: D
Answer: (D) 6 minutes
Question: Nicole cycles at a constant rate of 10 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?
(A) a) x minutes
(B) b) x/2 minutes
(C) c) 2x/3 minutes
(D) d) 3x/2 minutes
(E) e) 2x minutes
Rationale: Speed of nicole = 20km/h or 20/60 km/min = 1/3 km/min.
Once jessica passed the nicole, the distance between the nicole and jessica will increase at the rate of (30-20) = 10km/h or 1/6 km/min
now jessica is cycling for x minutes after passing the nicole, so in those x minutes distance between jessica and nicole would be (1/6)*x = x/6 km.
So, the time taken by nicole to travel x/6 km = (x/6)/(1/3) = 2x/3. hence answer should be C.
Answer: (C) c) 2x/3 minutes
Question: Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 20% and 20% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of
(A) 18%
(B) 20%
(C) 21%
(D) 23%
(E) Cannot be determined
Rationale: Answer: A.
Answer: (A) 18%
Question: John has 10 pairs of matched socks. If he loses 13 individual socks, what is the greatest number of pairs of matched socks he can have left?
(A)  7
(B)  3
(C)  5
(D)  4
(E)  1
Rationale: Because we have to maximize the pair of matched socks, we will remove 6 pairs(12 socks) out of 10 pairs 1 sock from the 7th pair.
Thus the no of matching socks pair remaining = 10 - 7 = 3
Answer B
Answer: (B)  3
Question: The income derived from a Rs. 100, 13% stock at Rs. 105, is :
(A) Rs. 5
(B) Rs. 8
(C) Rs. 13
(D) Rs. 18
(E) Rs. 19
Rationale: Solution
Income on Rs. 100 stock = Rs. 13.
Answer C
Answer: (C) Rs. 13
Question: It rained as much as on Wednesday as on all the other days of the week combined. If the average rainfall for the whole week was 5 cms, How much did it rain on Wednesday?
(A) 10.9
(B) 17.5
(C) 10.2
(D) 10.1
(E) 10.6
Rationale: Explanation:
Let the rainfall on wednesday = 6x.
âˆ´ Rainfall on the remaining days = 6x
Given,
(6x + 6x )/7 = 5
â‡’12x = 35
â‡’6x = 17.5
Answer: B
Answer: (B) 17.5
Question: If 15 people contributed a total of $30.00 toward a gift and each of them contributed at least $1.00, then the maximum possible amount any one person could have contributed is
(A)  $1.00
(B)  $16
(C)  $5.00
(D)  $6.00
(E)  $20.00
Rationale: B for me
14 people with 1$ each -> maximum = 16
Answer: (B)  $16
Question: After distributing the sweets equally among 25 children, 8 sweets remain. Had the number of children been 28, 22 sweets would have been left after equal distribution. What was the total number of sweets ?
(A) 328
(B) 348
(C) 358
(D) 362
(E) Data inadequate
Rationale: Explanation:
Let the total number of sweets be (25x + 8).
Then, (25x + 8) - 22 is divisible by 28
(25x - 14) is divisible by 28 28x - (3x + 14) is divisible by 28
(3x + 14) is divisible by 28 x = 14.
Therefore Total number of sweets = (25 x 14 + 8) = 358.
Answer:C
Answer: (C) 358
Question: What will be the product of (50-1)*(50-2)*(50-3)*..............*(50-99)*(50-100)?
(A) less than -100,000
(B) -2500
(C) 0
(D) 2500
(E) more than 100,000
Rationale: One of the terms is (50-50) so the product is 0.
The answer is C.
Answer: (C) 0
Question: Sonika deposited Rs.8000 which amounted to Rs.11200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?
(A) 9680
(B) 2277
(C) 11680
(D) 12068
(E) 1212
Rationale: (8000*3*2)/100 = 480
11200
--------
11680
Answer:C
Answer: (C) 11680
Question: In an examination, the percentage of students qualified to the students appeared from school 'P' is 70%. In school 'Q', the number of students appeared is 30% more than the students appeared from school 'P' and the number of students qualified from school 'Q' is 50% more than the students qualified from school 'P'. What is the % of students qualified to the number of students appeared from school 'Q' ?
(A) 80.76%
(B) 75.5%
(C) 60.50%
(D) 43 %
(E) None of these
Rationale: Explanation:
Number of students appeared from school 'P' = 100, say
Number of students qualified from school 'P' = 70
and Number of students appeared from school 'Q' = 130
Number of students qualified from school 'Q' = 50% more than those qualified from school 'P'.
= 70 + 35 = 105 % of students qualified to the number of students appeared from school B = 105 / 130 * 100
= 80.76%
ANSWER A
Answer: (A) 80.76%
Question: Rs. 50000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 7000 Find money given by 10% ?
(A) Rs.30029
(B) Rs.30120
(C) Rs.30000
(D) Rs.31209
(E) Rs.30121
Rationale: Let first part is 'K' and second part is 'L'
then K + L = 50000---------eq1
Total profit = profit on x + profit on y
7000 = (K x 10 x 1)/100 + (L x 20 x 1)/100
70000 = K + 2L-----------------------------------eq2
70000 = 50000 + L
so L = 20000 then K = 50000 - 20000 = 30000
first part on 10% is = Rs.30000
Answer: C
Answer: (C) Rs.30000
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 7 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
(A) 480
(B) 487
(C) 481
(D) 840
(E) 268
Rationale: 1/x - 1/20 = -1/24
x = 120
120 * 7 = 840
Answer:D
Answer: (D) 840
Question: Ram and Shakil run a race of 2000 meters. First, Ram gives Shakil a start of 200 meters and beats him by one minute. If , Ram gives Shakil a start of 6 minutes Ram is beaten by 1000 meters. Find the time in minutes in which Ram and Shakil can run the races separately.
(A) 7,10
(B) 8,10
(C) 9,10
(D) 10,10
(E) 10,12
Rationale: Let x and y are the speeds of Ram and Shakil.. Then by problem we got following equation
2000/x=(1800/y)-1
1000/X=(2000/y)-6
solve equation 1 and 2, we get x=250 and y=200
Therefore, Time taken by Ram and Shakilk to complete a race of 2000m is 8 min and 10 Min
ANSWER:B
Answer: (B) 8,10
Question: Ravi purchased a refrigerator and a mobile phone for Rs. 15000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 9 percent. Overall he make a.
(A) 228
(B) 288
(C) 27
(D) 120
(E) 881
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 9/100) = 8000 + 720
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 720 = Rs. 120
As this is positive, an overall profit of Rs. 200 was made.Answer:D
Answer: (D) 120
Question: A wolf eats 5.5 Kg of meat in 3 days. A baby tiger eats 3 Kg of meat in 3 days. How much meat can the two combined eat in three days?
(A) 10.5
(B) 9.5
(C) 8.5
(D) 7.5
(E) 6.5
Rationale: 3/3*5.5+3/3*3=8.5 kg
C
Answer: (C) 8.5
Question: How many different 6-letter sequences are there that consist of 2A, 60B's and 10C's ?
(A) 6
(B) 60
(C) 120
(D) 360
(E) 720
Rationale: How many different 6-letter sequences are there that consist of 2 A, 60B's, and 10 C's?
(A) 6
(B) 60
(C) 120
(D) 360
(E) 720 (ANS E)
Answer: (E) 720
Question: The average of first 10 even numbers is?
(A) 19
(B) 18
(C) 16
(D) 11
(E) 17
Rationale: Sum of 10 even numbers = 10 * 11 = 110
Average = 110/10 = 11
Answer:D
Answer: (D) 11
Question: In what time will Rs.4000 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?
(A) 8 1/3
(B) 8 1/6
(C) 8 1/4
(D) 8 1/8
(E) 8 1/9
Rationale: (4000*3*R)/100
= (5000*5*4)/100
R = 8 1/3
Answer: A
Answer: (A) 8 1/3
Question: A man is 26 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is
(A) 78 years
(B) 22 years
(C) 88 years
(D) 66 years
(E) 24 years
Rationale: Let's Son age is x, then Father age is x+26.
=> 2(x+2) = (x+26+2)
=> 2x+4 = x+28
=> x = 24 years
Answer: E
Answer: (E) 24 years
Question: How many digits will be there to the right of the decimal point in the product of 95.75 and .02554 ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Sum of decimal places = 7.
Since the last digit to the extreme right will be zero (since 5 x 4 = 20)
so there will be 6 significant digits to the right of the decimal point.
Answer is E.
Answer: (E) 6
Question: In 6 years, A will be thrice as old as B was 4 years ago. If A is now 6 years older than B, find the present age of B.
(A) 16 years
(B) 24 years
(C) 8 years
(D) 12 years
(E) 18 years
Rationale: let present age of A be A
let presennt age of B be B
in 6 yrs
A+6:B+6=3(B-4):B=6
ie A+6=3(B-4)
but given A=B+6
so B+6+6=3(B-4)
B=12
ANSWER:D
Answer: (D) 12 years
Question: A driver just filled the car's gas tank with 45 liters of gasohol, a mixture consisting of 5% ethanol and 95% gasoline. If the car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance?
(A) 1.3
(B) 1.7
(C) 2.1
(D) 2.5
(E) 2.9
Rationale: Let x be the number of liters of ethanol added to the gas tank.
0.05(45) + x = 0.1(45+x)
0.9x = 4.5 - 2.25 = 2.25
x = 2.5 liters
The answer is D.
Answer: (D) 2.5
Question: In a group of cows and chickens, the number of legs was 14 more than twice the number of heads. The number of cows was:
(A) 3
(B) 5
(C) 9
(D) 7
(E) 8
Rationale: D
7
Let the number of cows be x and their legs be 4x.
Let the number of chicken be y and their legs be 2x.
Total number of legs = 4x + 2y.
Total number of heads = x + y.
The number of legs was 14 more than twice the number of heads.
Therefore, 2 × (x + y) + 14 = 4x + 2y.
or, 2x + 2y + 14 = 4x + 2y.
or, 2x + 14 = 4x [subtracting 2y from both sides].
or, 14 = 4x – 2x [subtracting 2x from both sides].
or, 14 = 2x.
or, x = 7 [dividing by 2 on both sides].
Therefore, the number of cows = 7.
Answer: (D) 7
Question: If a particular player is always chosen, in how many ways cana cricket-be chosen out of 15 players?
(A) 1223
(B) 1376
(C) 1245
(D) 1456
(E) 1365
Rationale: 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
E
Answer: (E) 1365
Question: A, B and C can do a work in 6, 8 and 12 days respectively doing the work together and get a payment of Rs.1800. What is B’s share?
(A) 300
(B) 245
(C) 600
(D) 743
(E) 215
Rationale: C
600
WC = 1/6:1/8:1/12 => 4:3:2
3/9 * 1800 = 600
Answer: (C) 600
Question: Which of the following is equal to 1(4/5)%?
(A) 0.012/100
(B) 0.12/100
(C) 1.2/100
(D) 1.8/100
(E) 12/10
Rationale: This notation may be confusing for some, since it looks like we're multiplying 1 and 4/5
How about adding a space:Which of the following is equal to (1 4/5)%
(1 4/5)% = 1.8% = 1.8/100
Answer:
D
Answer: (D) 1.8/100
Question: Donna, Chris, and Austin have a total of $93 in their wallets. Donna has $7 more than Chris. Austin has 3 times what Donna has. How much money has Donna?
(A) $20
(B) $40
(C) $60
(D) $80
(E) $100
Rationale: et the amount in Chris’s wallet be $x
Donna has $7 more than Chrish's wallet = $(x + 7)
Austin has 3 times than Donna's wallet = $3(x + 7)
According to the problem, Donna, chris, and Austin have a total of $93 in their wallets.
Therefore,
x + (x + 7) + 3(x + 7) = 93
x + x + 7 + 3x + 21 = 93
5x + 28 = 93
- 28 -28 (subtract 28 from both sides)
5x = 65
or, 5x/5 = 65/5 (Divide both sides by 5)
x = 13
Amount in Chris wallet = $x = $13
Amount in Donna's wallet = $(x + 7) = $(13 + 7) = $20
Amount in Austin 's wallet = $3(x + 7) = $3(13 + 7) = $3(20) = $ 60
so Donna has:$20
correct answer A)$20
Answer: (A) $20
Question: In a certain book club, the members are voting between two books – a mystery novel and a biography – to decide which book the group will read next. There are 3 times as many votes for the mystery novel as there are votes for the biography. The ratio of biography votes to the mystery votes is
(A) 1 to 2
(B) 1 to 3
(C) 1 to 4
(D) 2 to 3
(E) 3 to 4
Rationale: IMO : Answer B 1 to 3
Answer: (B) 1 to 3
Question: If (1+p)q=q, which of the following must be true?
(A) p=-1 or q=0
(B) p=0 or q=0
(C) p=1 or q=1
(D) p=-1 or q=-1
(E) p=0 or q=1
Rationale: By only having pq=0, we cannot say answer is B as A and E options also satisfy the condition pq=0. ans B
Answer: (B) p=0 or q=0
Question: A and B write a test A says " i got a third of the ques. wrong" b says " i got 5 wrong" together they got three quarters of the questions correct.how many did A get correct.
(A) 1/4
(B) 3/4
(C) 5/4
(D) 1/3
(E) 5/3
Rationale: Total 30 questions. A got 10 (=30/3) wrong and B got 5 wrong. So, A got 20 correct and B got 25 correct. Total = (20+25)/(30+30) = 45/60=3/4 correct
ANSWER:B
Answer: (B) 3/4
Question: a = 5^10 - 625^2 and a/x is an integer, where x is a positive integer greater than 1, such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: This is a tricky worded question and I think the answer is should be D not C...
Here is my reason :
The stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . The stem wants to say that X is a PRIME NUMBER . because any prime
Number has no factor grater than 1 and Itself .
On the other hand the stem says that X COULD get how many different number NOT MUST get different number ( this is very important issue )
AS our friends say, if we simplify Numerator more we can obtain : 5^12 ( 5^3-1) = 5^12 (124) = 5^12 (31*2*2) divided by x and we are told that this fraction is
An integer . so, X COULD Be ( not Must be) 5 , 31 ,or 2 !!! so , X could get 2 different values and answer is C....
Answer: (C) Two
Question: Working together, 7 identical pumps can empty a pool in 6 hours. How many hours will it take 3 pumps to empty the same pool?
(A) 11
(B) 13
(C) 12
(D) 14
(E) 10
Rationale: Answer:	The answer is D
7 pumps take 6 hours. 1 Pump will take 6*7 hours . Hence 3 pumps will take (6*7)/3 = 14 hours
Answer: (D) 14
Question: If Juan takes 13 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
(A) 13x/y
(B) 13y/x
(C) x/(13y)
(D) 13/(xy)
(E) xy/13
Rationale: This problem is testing us on the Rate x Time = Distance relationship. This relationship also tells us that Rate = Distance/Time and Time = Distance/Rate.
Ultimately, we are looking for how many seconds it will take Juan to run x yards. Thus, the equation we’ll use is: Time = Distance/Rate. We know the distance is x yards, and we need to find Juan’s rate.
We can find Juan’s rate as follows: Rate = Distance/Time = y yards/13 seconds
Using that rate, we need to determine how long it takes him to run x yards at the same rate. So we have:
Time = Distance/Rate
Time = x yards/(y yards/13 seconds)
Time = (x yards) x (13 seconds/y yards)
Time = 13x/y seconds
Answer A.
Answer: (A) 13x/y
Question: A shop sells 2 typesof shirts: cotton and woolen. A pair of cottonshirts is sold at 30% profit and a pair of woolen shirts is sold at 50%50% profit. The salesman has calculated that if he sells 100% more woolen shirts than cottonshirts, his overall profit will be 45%. However, he ends up selling 50%50% more cotton trousers than woolen trousers. What will be his overall profit?
(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 65%
Rationale: Let the cost price of 1 cotton trouser and 1 woollen trouser be ‘CC’ and ‘WW’ respectively.
Case I: Number of woollen trousers sold is 100%100% more than cotton trousers.
Let us calculate profit keeping one unit of a cotton trouser.
1.3C+1.5×2×W=1.45(C+2W)1.3C+1.5×2×W=1.45(C+2W)
⇒0.15C=0.1W⇒0.15C=0.1W
⇒3C=2W⇒3C=2W
Case II: Number of cotton trousers sold is 50%50% more than woollen trousers.
Here, we will calculate sales price keeping one unit of a cotton trouser as we did in the case I. Now as per the condition given, cotton trousers sold is 50%50% more than woollen trousers.
⇒⇒ for every woollen trouser 1.51.5 (=32)(=32) cotton trousers are being sold.
⇒⇒ for every cotton trouser 2323 (=13/2)(=13/2) woollen trousers are being sold.
S.P.=1.3C+1.5×2W3S.P.=1.3C+1.5×2W3
⇒S.P.=1.3C+W=2.8C⇒S.P.=1.3C+W=2.8C
⇒CP=C+23×W⇒CP=C+23×W
=2C=2C
Profit
=2.8C−2C2C×100=2.8C−2C2C×100
=40%
C
Answer: (C) 40%