RikoteMaster/aqua-rat-mcqa huggingface dataset:
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 20 hrs and a machine of type S does the same job in 30 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.4
B.5
C.6
D.8
Answer: C.6
Explanation: Type R completes 1/20 of the job each hour.
Type S completes 1/30 of the job each hour.
Together R and S complete 1/20 +1/30 = 1/12 of the job each hour.
Let n be the number of each type of machine.
2*n*(1/12) = 1 job completed
n = 6
The answer is C.
Question: A letter lock consists of three rings each marked with nine different letters. The number of distinct unsuccessful attempts to open the lock is at the most?
A.176
B.178
C.728
D.789
Answer: C.728
Explanation: Since each ring consists of nine different letters, the total number of attempts possible with the three rings is
= 9 * 9 * 9= 729. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts
= 729 - 1 = 728.
Answer: C
Question: The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160. The time after which it is due is:
A.6 months
B.8 months
C.9 months
D.10 months
Answer: D.10 months
Explanation: TD=Amt*R*T/(100+RT)
given TD=160,Amt=1760,R=12,T=?
by substituting the values we get,
160=(1760*12T)/(100+12T)
160(100+12T)=1760*12T
100+12T=(1760*12T)/160
100+12T=132T
120T=100
t=100/120=5/6yrs i.e (5/6)*12=10months
ANSWER:D
Question: On dividing 15968 by a certain number, the quotient is 89 and the remainder is 37. Find the divisor.
A.170
B.179
C.37
D.67
Answer: B.179
Explanation: Divisor = (Dividend – Remainder/Quotient)
=(15968-37)/89 =179
ANSWER B 179
Question: For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 6*+2 and 6*+6, inclusive ?
A.1
B.None of the above
C.2
D.3
Answer: B.None of the above
Explanation: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6* + 2 = 6! + 2 and 6* + 6 = 6! + 6.
Now, notice that we can factor out 2 our of 6! + 2 so it cannot be a prime number, we can factor out 3 our of 6! + 3 so it cannot be a prime number, we can factor out 4 our of 6! + 4 so it cannot be a prime number, ... The same way for all numbers between 6! + 2 and 6! +7, inclusive. Which means that there are no primes in this range.
Answer: B
Question: Two trains of equal lengths are running at speeds of 30 kmph and 60 kmph. The two trains crossed each other in 30 seconds when travelling in opposite direction. In what time will they cross each other when travelling in the same direction?
A.90 sec
B.75 sec
C.85 sec
D.80 sec
Answer: A.90 sec
Explanation: Let the length of each train be x m.
(x + x) / (60 + 30)5/18 = (750 * 18) / (30 * 5) = 90 sec.
ANSWER:A
Question: Two cars cover the same distance at the speed of 32 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
A.73
B.38
C.64
D.83
Answer: C.64
Explanation: Explanation:
32(x + 1) = 64x
X = 1
32 * 2 = 64 km
Answer: Option C
Question: A Steel 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 24 hrs and a machine of type S does the same job in 12 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.3
B.4
C.6
D.9
Answer: B.4
Explanation: Rate of machine R =1/24
Rate of machine S =1/12
since same no of machines used for R and S to do the same work in 2 hrs
So collective rate needed to finish the work in 2 hrs= 1/2
Let the no of machine be x
So, x/24 +x/12 =1/2
3x/24=1/2
x=24/6=4
So no of machine R is 4
Answer B
Question: Of the integers between 200 and 799, inclusive, how many do not have digit 2 and 7?
A. 256
B. 326
C. 410
D. 426
Answer: A. 256
Explanation: Options for the first digit 6-2(2 and 5)=4;
Options for the second digit 10-2=8;
Options for the third digit 10-2=8;
Total numbers possible 4*8*8=256.
Answer: A.
Question: 3x^2-6x+3 = 0 Find the above equation find the value of x
A.0
B.1
C.2
D.3
Answer: B.1
Explanation: a = 3, b = -6, c = 3
x1,2 = (6 ± √( (-6)2 - 4×3×3)) / (2×3) = (6 ± √(36-36)) / 6 = (6 ± 0) / 6
x1 = x2 = 1
B
Question: In a parallelogram, the length of one diagonal and the perpendicular dropped on that diagonal are 30 and 20 metres respectively. Find its area
A.600 m2
B.540 m2
C.680 m2
D.574 m2
Answer: A.600 m2
Explanation: In a parallelogram.
Area = Diagonal × length of perpendicular on it.
= 30 × 20 = 600 m2
Answer A
Question: The average of 7 numbers is 24. If each number be multiplied by 5. Find the average of new set of numbers?
A.110
B.122
C.120
D.125
Answer: C.120
Explanation: Explanation:
Average of new numbers = 24 * 5 = 120
Answer: Option C
Question: In a college election between two rivals, a candidate who got 40% of the total votes polled, was defeated by his rival by 160 votes. The total number of votes polled was
A.900
B.800
C.700
D.600
Answer: B.800
Explanation: Let total number of votes polled be x.
Then, votes polled by other candidate
= (100 – 40)% of x = 60% of x
Now 60% of x – 40% of x = 160
⇒ 20x⁄100 = 160 ⇒ x = 800 votes
Answer B
Question: The number obtained by interchanging the two digits of a two-digit number is less than the original number by 45. If the sum of the two digits of the number so obtained is 13, then what is the original number?
A.94
B.66
C.39
D.87
Answer: A.94
Explanation: A
94
Let the number be in the form of 10a + b
Number formed by interchanging a and b = 10b + a.
a + b = 13 --- (1)
10b + a = 10a + b - 45
45 = 9a - 9b => a - b = 5 --- (2)
Adding (1) and (2), we get
2a = 18 => a = 9 and b = 4
The number is: 94.
Question: A pack of baseball cards consists of 12 outfielder cards and 8 infielder cards. What is the lowest number of outfielder cards that would have to be removed from the pack so that no more than 55 percent of the pack would be outfielder cards?
A.4
B.5
C.6
D.7
Answer: B.5
Explanation: let the number of O card to be removed=X
then remaning cards=12-X
now this 12-X cards should count less than 55% of toatal Ocards
12-X<.55*12
X<12-6.6
X<5.4
X=5
Ans B
Question: A man can row upstream at 20 kmph and downstream at 80 kmph, and then find the speed of the man in still water?
A.32 kmph
B.50 kmph
C.30 kmph
D.45 kmph
Answer: B.50 kmph
Explanation: US = 20
DS = 80
M = (20 + 80)/2 = 50
Answer:B
Question: In an office, 30 percent of the workers have at least 5 years of service, and a total of 16 workers have at least 10 years of service. If 90 percent of the workers have fewer than 10 years of service, how many of the workers have at least 5 but fewer than 10 years of service?
A. 480
B. 48
C. 50
D. 144
Answer: B. 48
Explanation: (10/100)Workers = 16 = > number of workers = 160
(30/100)*Workers = x+16 = > x = 48
Answer B
Question: A,B,C can complete a piece of work in 24,8,12 days. Working together, they complete the same work in how many days?
A.4
B.4/5
C.7/9
D.10
Answer: A.4
Explanation: A+B+C 1day work = 1/24 + 1/8 + 1/12 = 6/24 = 1/4
A,B,C together will complete the job in 4 days
Answer is A
Question: The sum and the product of two numbers are 16 and 15 respectively, the difference of the number is?
A.14
B.6
C.7
D.8
Answer: A.14
Explanation: Explanation:
x + y = 16
xy = 15
(x- y)2 = (x + y)2 - 4xy
(x- y)2 = 256 - 60 => (x - y) = 14
Answer: A
Question: In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 17 years replaced by a new boy. The age of the new boy is?
A.14 years 8 months
B.15 years
C.13 years 8 months
D.17 years 10 months
Answer: C.13 years 8 months
Explanation: Total decrease = (20 x 2) months
= 3 years 4 months
Age of the new boy
= 17 years - 3 years 4 months.
= 13 years 8 months.
ANSWER:C
Question: There are 600 boys in a hostel. Each plays either hockey or football or both. If 75% play hockey and 55% play football, how many play both?
A.120
B.150
C.200
D.180
Answer: D.180
Explanation: n(A) = 75*600/100 = 450
n(B) = 55*600/100 = 330
n(AUB) = 600
n(AnB) = 450+330-600 = 180
Answer is D
Question: The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is
A.1/2
B.2/3
C.3/5
D.3/7
Answer: A.1/2
Explanation: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2
Ans.(A)
Question: A five digit number is to be formed using each of the digits 1, 2, 3, 4 and 5 ONLY ONCE. How many numbers can be formed when 1 and 2 are not together ?
A.48
B.36
C.72
D.60
Answer: C.72
Explanation: No. of ways the 5 digit number can be formed = 5! = 120
Let us fuse 1 & 2.
No. of ways in which 1 and 2 are together = 4! x 2! (Multiplying by 2! because 1 and 2 can be arranged in 2! ways) = 24*2 = 48
No. of ways 1 & 2 wont be together = 120 - 48
=72
ANSWER:C
Question: A certain number X when divided by 253 leaves a remainder of 98. Which of the following can be subtracted from X to make X divisible by 81?
A.17
B.27
C.27
D.47
Answer: C.27
Explanation: Least possible value of the number is 253 + 98 = 351
Further it is given the number must be divisible by 81 .
351/81 = Gives remainder as 27
So, 27 must be subtracted from the number , answer is (C)
Question: During a Pizza buffet where A eats more times 2.4 than B, and B eats 6 times less than C.find the leat number of times all the three has to eat
A.50
B.60
C.70
D.80
Answer: B.60
Explanation: A eats more than B if B eats 1 times than the ratio of A and B is A:B is 2.4:1 or 12:5 and as B eat 6 times less the C the the ratio of B : C is 5:30 the the least number of times all three has eat is the LCM of A,B,C that is 60 ..
ANSWER:B
Question: X and Y together can completes a work in 12 days and Y complete the same work in 24 days. Then the number of days X required to complete the work will be?
A.15 days.
B.12 days.
C.24 days.
D.13 days.
Answer: C.24 days.
Explanation: X and y complete in one day =1/12 part, y completes in one day=1/24 parts. Therefore X alone can do in one day =1/24part. Therefore the work can be finished by X = 24 days. Ans: C
Question: If the average (arithmetic mean) of a and b is 215, and the average of b and c is 160, what is the value of a − c?
A.−220
B.−100
C.100
D.110
Answer: D.110
Explanation: Question: a - c = ?
(a + b)/ 2 =215 ===> a + b = 430
(b + c)/2 = 160 ===> b + c = 320
(a + b) - (b + c) =430- 320 ===> a + b - b - c = 110 ===> a - c = 110
Answer: D
Question: A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 27 m * 2 m * 0.75 m?
A.22377
B.27000
C.27891
D.25000
Answer: B.27000
Explanation: 27 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x
27 = 1/1000 * x => x = 27000
Answer: B
Question: Incomes of two companies A and B are in the ratio of 5 : 8. Had the income of company A been more by 20 lakh, the ratio of their incomes would have been 5 : 4. What is the income of company B?
A.32 lakh
B.50 lakh
C.40 lakh
D.60 lakh
Answer: A.32 lakh
Explanation: Let the incomes of two companies A and B be 5x and 8x respectively.
From the question,
5x+20/8x=5/4 ⇒ 20x + 80 = 40x
∴ x = 4
∴ Income of company B = 8x = 32 lakh
Answer A
Question: Resident of town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and std deviation of 8 hrs. The number of hours that pat, a resident of town X, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last week?
A.30
B.20
C.18
D.12
Answer: D.12
Explanation: 21-12 < no of hrs < 21-8
9< no of hrs < 13.
D
Question: Meera is making telescopes, each consisting of 2 lenses, 1 tube, and 1 eyepiece. Lenses can be purchased only in packs of 50, tubes only in packs of 10, and eyepieces only in packs of 30. However, half of the lenses in each pack are not usable for telescopes. If all parts are used only for the telescopes, what is the minimum number of lenses Meera must purchase to make a set of telescopes with no leftover components other than the unusable lenses?
A.75
B.150
C.300
D.3600
Answer: D.3600
Explanation: I'd use backsolving for this question.
Check D:
3600 lenses = 1800 usable lenses = 900 tubes = 900 eyepieces. We CAN buy 900 tubes and 900 eyepieces, so that not to have leftovers.
Answer: D.
Question: Which of the following expressions CANNOT have a negative value
A.|a + b| – |a – b|
B.|a + b| + |a|
C.|2a + b| – |a + b|
D.a^2 - b^2 – 2|ab|
Answer: B.|a + b| + |a|
Explanation: Whenever you are required to find if the equation is a perfect square or not, try to bring everything in the form of a perfect square as they are always positive.
Of the given options, only option D can be written in from of a perfect square.
|a + b| + |a|
This will always be positive.
Correct Option: B
Question: Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 210 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
A.1120
B.672
C.560
D.192
Answer: D.192
Explanation: Four members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x.
But we are told that one of these individual works is 30hrs. hence, possible scenarios, if
(1)2x =210 => 16x = 1680 (2) 3x =210 => 16x = 1120 (3) 5x =210 => 16x = 672 (4) 6x =210 => 16x = 560
Hence Answer is D 192 which can not be any of these.
Question: Harkamal purchased 8kg of grapes at the rate of 80 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
A.A)1135
B.B)1075
C.C)1065
D.D)1070
Answer: A.A)1135
Explanation: Cost of 8 kg grapes = 80 × 8 = 640.
Cost of 9 kg of mangoes = 55 × 9 = 495.
Total cost he has to pay = 640 + 495 = 1135.
A)
Question: A property was originally on a 99 years lease and two thirds of the time passed is equal to the four fifth of the time to come.how many years are there to go.
A.33
B.80
C.79
D.27
Answer: B.80
Explanation: Answer:B
Question: Find out the square of a number which when doubled exceeds its one sixth by 11 ?
A.36
B.25
C.19
D.26
Answer: A.36
Explanation: A
Let the number be p, then the square will be p^2
According to question:
2p = (p/6) + 11
=> 12p = p + 66
=> p = 6
p^2 = 6^2 = 36.
Answer : A
Question: A family has two children. find the probability that both the children are boys given that at least
one of them is a boy?
A.1/3
B.1/5
C.1/7
D.2/7
Answer: A.1/3
Explanation: Let g stand for girl and b for boy. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are boys’
F : ‘at least one of the child is a boy’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3
A)
Question: Surekha started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajesh joined him with an amount of Rs. 35,000. In 2001, Surekha invested another additional amount of Rs.10,000 and Jay joined them with an amount of Rs.35,000. What will be Rajesh's share in the profit of Rs.1,80,000 earned at the end of 3 years from the start of the business in 1999?
A.Rs 45000
B.Rs 60000
C.Rs 70000
D.Rs 75000
Answer: B.Rs 60000
Explanation: Surekha:Rajesh:Jay= (25000×12+35000×12+45000×12):(35000×24) : (35000×12) = 1260000 : 840000 : 420000 = 3 : 2 : 1. Rajesh's share =Rs.(180000×2/6) = Rs.60000.
Answer B
Question: A picnic attracts 240 persons. There are 30 more men than women, and 30 more adults than children. How many men are at this picnic?
A.240
B.75
C.85
D.130
Answer: C.85
Explanation: Adult + Children = 240
Let, Children = y
then, Adult = y+30
i.e. y+(y+30) = 210
i.e. y = 115
i.e. Adult = 115+30 = 145
Adults include only Men and Women
i.e. Men + Women = 145
Let women, W = x
then Men, M = x+30
i.e. x+(x+30) = 2x+30 = 145
i.e. x = 55
i.e. Men, M = 55+30 = 85
Answer: Option C
Question: If a boat goes 8km upstream in 80 minutes and the speed of the stream is 5 kmph, then the speed of the boat in still water is ?
A.8
B.9
C.10
D.11
Answer: D.11
Explanation: Rate upsteram =(8/80*60)kmph=6kmph.
speed of the stream =5kmph let speed in still water be xkm/hr. then speed upstream=(x-5)km/hr. x-5=6==>x=11km/hr Answer(D)
Question: A car runs 375 km in 3 hours. What's the car's speed?
A.124
B.125
C.126
D.127
Answer: B.125
Explanation: Solution:
375 ÷ 3 = 125
Answer B
Question: The ratio of spinsters to cats is 2 to 7. If there are 35 more cats than spinsters, how many spinsters are there?
A.14
B.21
C.28
D.35
Answer: A.14
Explanation: Let 2x be the number of spinsters. Then 7x is the number of cats.
7x-2x=35
x=7 and the number of spinsters is 2(7)=14.
The answer is A.
Question: A train running at the speed of 60 km/hr crosses a pole in 6 seconds. Find the length of the train.
A.110 meter
B.120 meter
C.100 meter
D.90 meter
Answer: C.100 meter
Explanation: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 6 = 100 meter
Answer:C
Question: Find the missing figures: 0.1% of ? = 0.24
A.12
B.120
C.24
D.240
Answer: D.240
Explanation: Let 0.1% of x = 0.24. Then , 0.1*x/100 = 0.24
X= [(0.24*100)/0.1] = 240.
Answer is D.
Question: A person took some amount with some interest for 4 years, but increase the interest for 1%, he paid Rs.160/- extra, then how much amount he took?
A.Rs.5500/-
B.Rs.6000/-
C.Rs.4000/-
D.Rs.7000/-
Answer: C.Rs.4000/-
Explanation: Explanation:4 years = Rs.160/-year = 160/4Rate of Interest = 1%100/1% × 160/4 = Rs.4000/-P = Rs.4000/- Answer: Option C
Question: A shopkeeper sold an article at $100 with 10% profit. Then find its cost price?
A.$120
B.$100
C.$91
D.$72
Answer: C.$91
Explanation: cost price = selling price *100/(100+profit)
C.P. = 100*100/110 = $91(approximately)
Answer is C
Question: Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?
A.2
B.3
C.3.5
D.4
Answer: B.3
Explanation: Part filled by A + B + C in 1 hour = 1/5 + 1/10 + 1/30 = 1/3
All the three pipes together will fill the tank in 3 hours.
ANSWER B
Question: The difference between the place values of 8 and 3 in the number 587435 is
A.75200
B.79970
C.75460
D.24580
Answer: B.79970
Explanation: Sol.= (Place value of 8) – (place Value of 3)= (80000 - 30)= 79970 Answer B
Question: Car Dealership X, the total profit from sales increased by 10 percent over the previous years, while the number of cars sold decreased by 10 percent over the previous years. Approximately what was the average percent increase in profit per car over the previous year.
A.18%
B.20%
C.22%
D.23%
Answer: C.22%
Explanation: Let Profit be x and cars sold be y
Originally Profit/Car = x/y
Now it is 1.1x / 0.9 y = 11/9 (x/y)
Increase in profit per car = ((2/9) (x/y)) / (x/y) * 100 = 22.22%
Answer = C
Question: At Parkins gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team. What is the lowest possible number of students in the class?
A. 20
B. 24
C. 36
D. 48
Answer: B. 24
Explanation: We are given that Parkins gym class can be divided into 8 teams or 12 teams, with an equal number of players on each team. Translating this into two mathematical expressions we can say, where G is the total number of students in the gym class, that:
G/8 = integer and G/12 = integer
This means that G is a multiple of both 8 and 12.
We are asked to determine the lowest number of students in the class, or the lowest value for variable “G”. Because we know that G is a multiple of 8 and of 12, we need to find the least common multiple of 8 and 12. Although there are technical ways for determining the least common multiple, the easiest method is to analyze the multiples of 8 and 12 until we find one in common.
Starting with 8, we have: 8, 16, 24, 32
For 12, we have: 12, 24
For the multiples of 12, we stopped at 24, because we see that 24 is also a multiple of 8. Thus, 24 is the least common multiple of 8 and 12, and therefore we know that the lowest possible number of students in the gym class is 24.
Answer B.
Question: In a 1300 m race Usha beats Shiny by 50 m. In the same race, by what time margin Shiny beat Mercy who runs at 4 m/s ?
A.65 sec.
B.50 sec
C.25 sec
D.Data not sufficient
Answer: A.65 sec.
Explanation: Speed of Shiny = 50/ 10 = 5m/s
Time taken by shiny to complete the race is B = 1300/5 = 260 sec.
Time taken by Baley to complete the race is D = 1300/4 = 325 sec.
Hence, D-B = 65 sec
ANSWER:A
Question: If the price has fallen by 10% what percent of its consumption be: increased so that the expenditure may be the same as before?
A.11 1/0%
B.11 1/5%
C.11 1/9%
D.11 2/9%
Answer: C.11 1/9%
Explanation: 100 – 10 = 90
90------10
100------? => 11 1/9%
Answer: C
Question: If a man buys 40 purse for $110 and sold them for $3 dollars each determine his gain.
A.$ 20
B.$ 10
C.$ 30
D.$ 5
Answer: B.$ 10
Explanation: Cost of 40 purse = $110
Sold each purse for $3
So he sold 40 purse for $(40 × 3) = $120
Loss = $(120 – 110) = $10
Therefore, gain = $ 10.
Answer:B
Question: A rectangular field is 72 yards long and 33 yards wide. A fence is needed for the perimeter of the
field. Fencing is also needed to divide the field into three square sections. How many feet of fencing
are needed? (It is a good idea to make a drawing for this one.)
A.630 ft
B.830 ft
C.430 ft
D.828 ft
Answer: D.828 ft
Explanation: 72 + 33 + 72 + 33 = 210 yds. for
outside of field.
33 + 33 = 66 yds. for dividing sections
210+ 66 = 276 yds. of fencing
276 x 3 = 828 ft. of fencing
correct answer D
Question: Winson leaves home everyday at 4 p.m to pick his son from school and returns home at 6 p.m. One day, the school was over at 4 p.m and the son started walking home from school. Winson, unaware of this, starts from home as usual and meets his son on the way and returns home with him 15 minutes early. If the speed of Winson is 30 km\hr, find the speed of his son.
A.15km/hr
B.6 km/hr
C.4.28 km/hr
D.9 km/hr
Answer: C.4.28 km/hr
Explanation: Winson leaves home everyday at 4 p.m to pick his son from school and returns home at 6 p.m. One day, the school was over at 4 p.m and the son started walking home from school. Winson, unaware of this, starts from home as usual and meets his son on the way and returns home with him 15 minutes early. If the speed of Winson is 30 km\hr, find the speed of his son.
The distance from home to school is 30 km. The round trip distance = 60 km. Because he returns home 15 minutes early, I thought it might be easier to break his trip up into 8 identical 15 minute blocks, each of which he traveled at 7.5 km/hour.
Because we are dealing with a round trip here, Winson would have stopped 7.5 minutes short of the school. This means he traveled Distance=rate* time .5Km/hour*52.5 minutes or 26.25 KM. His son therefore traveled 3.75km/hour by the time he met his dad at 4:52.5. It took the son 52.5 minutes to travel 3.75 km. Because we are trying to find the son's rate per hour (i.e. 60 minutes) and we have his speed for 52.5 minutes it's best to convert to km/minute then multiply by 60 to get km/hour
3.75km/52.5 = .07 km/minute
.07km/minute*60 minutes = 4.28 km/hour.
Answer: C. 4.28 km/hr
Question: In a factory, there are 40% technicians and 60% non-technicians. If the 60% of the technicians and 40% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
A.82%
B.58%
C.52%
D.22%
Answer: C.52%
Explanation: Total = 100
T= 40 NT= 60
40*(60/100)=24 60*(40/100)=24
24 + 24 = 48 => 100 - 48 = 52%
Answer: C