mathewhe/aqua_rat huggingface dataset:
Question: At 3:00 pm, a car has driven 10 miles east. It will continue to drive east at 0.8 minutes per mile and then turn around and drive at 0.8 minutes per mile back to its original starting point. How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm?
(A) a) 10
(B) b) 11
(C) c) 12
(D) d) 20
(E) e) 14
Rationale: 0.8 minutes --> 1 mile
1 minute --> 1/0.8 = 10/8 = 1.25 miles/minute
Distance covered in 40 minutes = 1.25 * 40 = 12.5 * 4 = 50 miles
Distance covered in the current direction = Distance covered from the opposite direction (since car returns back to starting point)
Let x be the miles driven before turning
10 + x = 50 - x
2x = 40
x = 20
Answer: D
Answer: (D) d) 20
Question: The prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 20% and that of tea dropped by 20%. if in july , a mixture containing equal quantities of tea and coffee costs 60/kg. how much did a kg of coffee cost in june ?
(A) 50
(B) 60
(C) 80
(D) 100
(E) 120
Rationale: Let the price of tea and coffee be x per kg in June.
Price of tea in July = 1.2x
Price of coffee in July = 0.8x .
In July the price of 1/2 kg (600gm) of tea and 1/2 kg (600gm) of coffee (equal quantities) = 60
1.2x(1/2) + 0.8x(1/2) = 60
=> x =60
Thus proved...option B.
Answer: (B) 60
Question: A women buys an article and sells it at a profit of 20%. If she had bought it at 20% less and sold it for $75 less, she could have gained 25%. What is the cost price?
(A) 392
(B) 424
(C) 375
(D) 273
(E) 429
Rationale: C
375
CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
75 ----- ? => 375
Answer: (C) 375
Question: If two resistors, A(R1) and B(R2) stand in parallel with each other in electrical wire, the total resistor appears as R1R2/(R1+R2). If three resistors, A(R1), B(R2), and C(2R2) stand in parallel in electrical wire, what is the ratio W of the resistors’ sum of A and C to the resistors’ sum of A and B?
(A) 2(R1+R2):(R1+2R2)
(B) (R1+R2):(R1+2R2)
(C) (2R1+R2):(R1+2R2)
(D) 2(R1+R2):(2R1+R2)
(E) 2(R1-R2):(R1+2R2)
Rationale: two resistors A (r1) and B (r2).
total or sum of two resistors appear as
r1r2/r1+r2. It is looks like inversion of sum of rates.
1/r1+1/r2= r1+r2/r1r2.
same way sum of A(r1) and c(2r2)=1/r1+1/2r2
=2r2+r1/r12r2.
inversion rate = r12r2/2r2+r1.
ratio W of sum of a and c/sum of a and b=2r2r1/2r2+r1*r1+r2/r1r2
=2(r1+r2)/2r2+r1.A
Answer: (A) 2(R1+R2):(R1+2R2)
Question: A and B start from Opladen and Cologne respectively at the same time and travel towards each other at constant speeds along the same route. After meeting at a point between Opladen and Cologne, A and B proceed to their destinations of Cologne and Opladen respectively. A reaches Cologne 40 minutes after the two meet and B reaches Opladen 50 minutes after their meeting. How long did A take to cover the distance between Opladen and Cologne?
(A) 1 hour
(B) 1 hour 20 minutes
(C) 2 hours 30 minutes
(D) 1 hour 40 minutes
(E) 2 hours 10 minutes
Rationale: v1 and V2 are speeds.
v1.t /50 = v2
v2.t/40 = v1
v1/v2 = 5/4
which train A would 50. 4/5 mins to cover the same distance
40 + 40 = 80 mins (ANS B)
Answer: (B) 1 hour 20 minutes
Question: A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?
(A) 5 mins
(B) 3 mins
(C) 7 mins
(D) 9 mins
(E) 2 mins
Rationale: D = 25 * 60 + 1500 = 3000 m
T = 3000/60 * 18/5 = 180 sec = 3 mins
Answer: B
Answer: (B) 3 mins
Question: The area of a circular field is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 4 per metre approximately
(A) 4457
(B) 4567
(C) 5943
(D) 4547
(E) 4675
Rationale: Explanation:
Area = (17.56 x 10000) m2= 175600 m2.
ΠR2 = 175600 ⇔ (R)2 = (175600 x (7/22)) ⇔ R = 236.37 m.
Circumference = 2ΠR = (2 x (22/7) x 236.37) m =1485.78 m.
Cost of fencing = Rs. (1485.78 x 4) = Rs. 5943.
Answer: Option C
Answer: (C) 5943
Question: If n is a natural number, then (6n2 + 6n) is always divisible by:
(A) Both 6 and 12
(B) 6 only
(C) 12 only
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
6n2 + 6n = 6n(n + 1)
Hence 6n2 + 6n is always divisible by 6 and 12 (∵ remember that n(n + 1) is always even) Answer : Option A
Answer: (A) Both 6 and 12
Question: A train 150 m long is running at a speed of 62 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?
(A) 5 sec
(B) 10 sec
(C) 12 sec
(D) 18 sec
(E) 15 sec
Rationale: Answer : B.
Speed of the train relative to man = (62 - 8) kmph
= (54* 5/18) m/sec = 15m/sec
Time taken by the train to cross the man
= Time taken by It to cover 150 m at 15 m / sec = 150 *1/ 15 sec = 10sec
Answer: (B) 10 sec
Question: There are how many hours between x minutes past 12 noon and 8:10 p.m. of the same day, where x < 60?
(A)  (490-x)/60
(B)  (480-x)/60
(C)  (470-x)/60
(D)  60 (60 – x + 7)
(E)  60 (60 – x + 17)
Rationale: Let's just say that X is equal to 10 so we will have that the number of hours will be 8, this is our target value. Now plug 10 in the answer choices to see which gives 8.
A is correct here.
Answer: (A)  (490-x)/60
Question: P is three times as fast as Q and working together, they can complete a work in 12 days. In how many days can Q alone complete the work?
(A) 16
(B) 88
(C) 29
(D) 14
(E) 12
Rationale: P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 12 days, which means Q can do the work in 48 days.
Hence, P can do the work in 16 days. Answer: A
Answer: (A) 16
Question: If a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster, he would have covered 60 more miles than he actually did. How many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day?
(A)  100
(B)  120
(C)  140
(D)  150
(E)  160
Rationale: Case 1:
let rate = R, Time = T, and Distance =D
so D=RT
Case 2:
(D+60)=(R+5)(T+1)
Case 3:
(D+X)=(R+10)(T+2)
X=120
Ans B
Answer: (B)  120
Question: A BISCUIT manufacturer produces 300 units of a certain model each month at a cost to the manufacturer of £30 per unit and all of the produced units are sold each month. What is the minimum selling price per unit that will ensure that the monthly profit (revenue from sales minus production costs) on the sales of these units will be at least £30,000?
(A) 110
(B) 330
(C) 220
(D) 440
(E) 550
Rationale: 300(x-30)≥30,000
x-30≥300
x≥330
Answer: Option B
Answer: (B) 330
Question: 210 college students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?
(A) 25
(B) 40
(C) 50
(D) 60
(E) 75
Rationale: 120 = 60(Mac) + x(Window) + 20(both) => x=40
ANSWER:B
Answer: (B) 40
Question: Magnabulk Corp sells boxes holding d magnets each. The boxes are shipped in crates, each holding b boxes. What is the price charged per magnet, if Magnabulk charges m dollars for each crate?
(A) 100bd/m
(B) 100m/(bd)
(C) bd/(100m)
(D) m/(bd)
(E) bd/m
Rationale: crate has = bd magnates
C crate cost = m dollars = 100 m cents
each magnate cost for each crate = m / bd
Ans; D
Answer: (D) m/(bd)
Question: The overall age of X and Y is 12 year greater than the overall age of Y and Z. Z is how many decades younger that X?
(A) 11
(B) 15
(C) 12
(D) 17
(E) 19
Rationale: C
12
(X + Y) – (Y + Z) = 12
X – Z = 12
Answer: (C) 12
Question: In the formula V = (4r)^2, if r is halved, then V is multiplied by
(A) 64
(B) 8
(C) 1/4
(D) 1/8
(E) 1/64
Rationale: Say r=2 => V1 = 16
when r=1; V2 = 4
V2 = 1/4*V1.
Answer : C
Answer: (C) 1/4
Question: Find √? /11= 4 ?
(A) 76
(B) 1936
(C) 1304
(D) 1296
(E) None
Rationale: Answer
Let √N/11= 4
Then √N = 11 x 4 = 44
∴ N = 44 x 44= 1936.
Correct Option: B
Answer: (B) 1936
Question: An gun can take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the 1st, 2nd, third and 4th shots are 1.4, 1.3, 1.2 & 1.1 respectively. What is the probability that the plane is hit when all the four shots are fired?
(A) 0.6976
(B) 0.7013
(C) 0.789
(D) 0.8356
(E) 0.8666
Rationale: Required probability:
=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)
=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002
=0.6976=0.6976
Edit: Thank you Vaibhav for providing an alternative method.
Alternate Method:
probability that the plane is hit when all the four shots are fired,
P=1−probability of not hitting the targetP=1−probability of not hitting the target
=1−(0.6×0.7×0.8×0.9)=1−(0.6×0.7×0.8×0.9)
=1−0.3024=1−0.3024
=0.6976
A
Answer: (A) 0.6976
Question: Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 1/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
(A) 3/140
(B) 1/280
(C) 27/280
(D) 3/35
(E) 7/56
Rationale: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*1/8*5/7 + 1/5*7/8*2/7 + 4/5*1/8*2/7 = 27/280.
Answer: C
Answer: (C) 27/280
Question: From a group of 3 MEN and 3 WOMEN, 4 ADULTS are to be randomly selected. What is the probability that equal numbers of men and women will be selected?
(A) 1/5
(B) 2/5
(C) 3/5
(D) 4/5
(E) 1
Rationale: Using the first example, here is the probability of THAT EXACT sequence occurring:
MMWW = (3/6)(2/5)(3/4)(2/3) = 36/360 = 1/10
Each of the other 5 options will yield the exact SAME probability....
eg
MWMW = (3/6)(3/5)(2/4)(2/3) = 36/360 = 1/10
So we have 6 different options that each produce a 1/10 chance of occurring.
6(1/10) = 6/10 = 3/5
Final Answer:
C
Answer: (C) 3/5
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get ?
(A) 57%
(B) 60%
(C) 65%
(D) 90%
(E) None of these
Rationale: Solution
Total number of votes polled= (1136 + 7636 + 11628) = 20400.
∴ Required percentage= ( 11628/20400x 100)%= 57%
Answer A
Answer: (A) 57%
Question: (160)^2 - (161)^2 =
(A) 1
(B) 100
(C) 229
(D) 323
(E) 349
Rationale: Using the formula:
(a+1)^2 - a^2 = 2a+1
So, Answer = 161*2 + 1
= 322+1 = 323 = Answer = D
Answer: (D) 323
Question: Find the area of a parallelogram with base 28 cm and height 32 cm.
(A) 200
(B) 384
(C) 345
(D) 244
(E) 896
Rationale: Area of a parallelogram = base * height = 28 * 32 = 896 cm2
Answer: Option E
Answer: (E) 896
Question: At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 400-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $200?
(A) 1,108
(B) 3,300
(C) 2,108
(D) 2,124
(E) 2,256
Rationale: We have $200 and we have to maximize the number of hot dogs that we can buy with this amount.
Let's try to find out what is the maximum number of hot dogs that we can buy for a lesser amount of money, which in this case is 400 for $22.95.
For the sake of calculation, let's take $23. 23x8 gives 184 ,i.e. a total of 400x8 = 3200 hot dogs . We are left with ~$16. Similarly, let's use $3 for calculation. We can buy 5 20-pack hot dogs (3x5), a total of 20x5 = 100 hot dogs. So we have 3300 hot dogs.
2108 looks far-fetched (since we are not likely to be left with > $1.55). Hence, (b) 3300 (ANSWER B)
Answer: (B) 3,300
Question: A bike covers a certain distance at the speed of 62km/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?
(A) 85 km/h
(B) 82.66 km/h
(C) 87.67 km/h
(D) 90.25 km/h
(E) 90.64 km/h
Rationale: Ans.(B)
Sol. Total distance = 62 × 8 = 496 km
Now speed = 496/6 = 82.66 km/h
Answer: (B) 82.66 km/h
Question: A restaurant meal cost $75 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then the total amount paid must have been between
(A)  $75 and $80
(B)  $85 and $90
(C)  $83 and $87
(D)  $82 and $87
(E)  $81 and $87
Rationale: Hence it will be between 75 * (1+10/100) and 75 * (1+15/100).
i.e b/w 82.5 and 86.25. Hence the answer E (b/w 81 and 87).
Answer: (E)  $81 and $87
Question: Cindy paddles her kayak upstream at c kilometers per hour, and then returns downstream the same distance at n kilometers per hour. How many kilometers upstream did she travel if she spent a total of p hours for the round trip?
(A) cnp
(B) cn/p
(C) (c + n)/p
(D) cnp/(c + n)
(E) pm/n- pn/m
Rationale: let t1 and t2 be the time taken to row upstream and downstream respectively
now,
t1=distance/speed=d/c
similarly,
t2=d/n (as same distance has to be rowed)
also,
t1+t2=p
therefore,
p=(d/c)+(d/n)
=d(c+n)/cn
d=pcn/(c+n)=D
Answer: (D) cnp/(c + n)
Question: Three workers have a productivity ratio of 2 to 4 to 8. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?
(A) 20 to 3
(B) 6 to 1
(C) 5 to 1
(D) 1 to 6
(E) 1 to 5
Rationale: The fastest worker who does 8 units of job worked for all 10 hours, so he did 8*10=80 units of job;
The slowest worker who does 2 unit of job worked for only 4+2=6 hours (first 4 hours and last 2 hours), so he did 2*6=12 units of job;
The ratio thus is 80 to 12, or 20 to 3.
Answer: A.
Answer: (A) 20 to 3
Question: There are 3 numbers A, B and C. If A:B = 3/4, B:C = 4/5, C:D = 5/6, then A:D will be?
(A) 1 : 2
(B) 3 : 5
(C) 5 : 7
(D) 6 : 11
(E) 5 : 3
Rationale: Sol. A : B = 3 : 4, B : C = 4 : 5, C : D = 5 : 6
∴A∶B∶C∶D= 3 : 4 : 5 : 6.
Thus, A : D = 3 : 6 or, 1 : 2
A
Answer: (A) 1 : 2
Question: If (y - 1)(z - 3) + 5(y - 1) = 0, then which of the following must be true?
(A)  y = -4 and z = -3
(B)  y = 4 or z = -3
(C)  y = -4 or z = 3
(D)  y = 1 and z = 3
(E)  y = -1 or z = 3
Rationale: factor out:
(y-1)(z-3+5)=0
(y-1) (z+2) = 0
So by checking options we get ,
Ans - D
Answer: (D)  y = 1 and z = 3
Question: Ravi's brother is 3 years senior to him. His father was 28 years of age when his sister was born while his mother was 26 years of age when he was born. If his sister was 4 years of age when his brother was born, what were the ages of Ravi's father and mother respectively when his brother was born ?
(A) 32 years, 23 years
(B) 32 years, 29 years
(C) 35 years, 29 years
(D) 35 years, 33 years
(E) 35 years, 34 years
Rationale: Explanation:
When Ravi's brother was born, let Ravi's father's age = x years and mother's age = y years.
Then, sister's age = (x - 28) years. So, x - 28 = 4 or x = 32.
Ravi's age = (y - 26) years. Age of Ravi's brother = (y - 26 + 3) years = (y - 23) years.
Now, when Ravi's brother was born, his age = 0 i.e. y - 23 = 0 or y = 23.
Answer: Option A
Answer: (A) 32 years, 23 years
Question: In expressing a length of 81.472 km as nearly as possible with the three significant digits, find the percentage error
(A) 0.35%
(B) 0.34%
(C) 0.034%
(D) 0.035%
(E) None of these
Rationale: Explanation:
Error = (81.5 - 81.472) = 0.028
Required percentage =
0.028/ 81.472×100=0.034
Option C
Answer: (C) 0.034%
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10 kmph
(B) 13 kmph
(C) 65 kmph
(D) 55 kmph
(E) 14 kmph
Rationale: Speed of the boat in still water
= (60+80)/2
= 70 kmph. Speed of the stream
= (80-60)/2
= 10 kmph.
Answer: A
Answer: (A) 10 kmph
Question: Excluding stoppages, the speed of a bus is 60 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
(A) 10 min
(B) 12 min
(C) 18 min
(D) 20 min
(E) 15 min
Rationale: Due to stoppages, it covers 15 km less.
Time taken to cover 15 km = (15/60x 60) min = 15 min
Answer :E
Answer: (E) 15 min
Question: There are 400 wolfs at a large zoo. The number of wolfs is 4 times the number of all the other animals combined. How many more wolfs are there than non wolfs animals at the zoo?
(A) 450
(B) 420
(C) 400
(D) 390
(E) 350
Rationale: Answer is D.
Total wolfs= 400 = 4 * Other Animals (X)
or X = 10.
So, Difference in wolfs and X = 400-10 = 390.
Answer: (D) 390
Question: Which of the following is not a leap year?
(A) 1200
(B) 800
(C) 700
(D) 2000
(E) None of these
Rationale: Explanation :
1. Every year divisible by 4 is a leap year, if it is not a century.
2. Every 4th century is a leap year, but no other century is a leap year.
800,1200 and 2000 comes in the category of 4th century (such as 400,800,1200,1600,2000 etc).
Hence 800,1200 and 2000 are leap years
700 is not a 4th century, but it is a century. Hence it is not a leap year
Answer : Option C
Answer: (C) 700
Question: In a simultaneous throw of 2 dice what is the probability of getting a total of 11?
(A) 1/4
(B) 1/18
(C) 2/11
(D) 3/13
(E) 1/5
Rationale: n(S) = 6*6 = 36
E = {(5,6),(6,5)}
Probability = 2/36 = 1/18
Answer is B
Answer: (B) 1/18
Question: Find the odd man out. 1, 3, 9, 12, 19, 29
(A) 12
(B) 9
(C) 1
(D) 3
(E) 19
Rationale: 12 is an even number. All other given numbers are odd
Answer : Option A
Answer: (A) 12
Question: A certain number of men can do a work in 65 days working 6 hours a day. If the number of men are decreased by one-fourth, then for how many hours per day should they work in order to complete the work in 40 days?
(A) 11
(B) 12
(C) 14
(D) 13
(E) 15
Rationale: D
13
Let the number of men initially be x. we have M1 D1 H1= M2 D2 H2
So, x * 65 * 6 = (3x)/4 * 40 * h2
=> h2 = (65 * 6 * 4)/(3 * 40) = 13.
Answer: (D) 13
Question: In a certain college, 20% of the boys and 40% of the girls attended the annual college outing. If 35% of all the students are boys, what percent of all the employees went to the outing?
(A) 33%
(B) 34%
(C) 35%
(D) 36%
(E) 37%
Rationale: assume total students =100 in that 35 students are boys ,remaining 65 are girls........
20% of boys(35) =7
40% of girls(65) =26
totally (26+7)=33 mens went to outing...... 33 is 33% in 100
so, the answer is 33%
ANSWER:A
Answer: (A) 33%
Question: A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:
(A) 7 4/5
(B) 9 3/5
(C) 4 1/6
(D) 7 7/12
(E) 8 6/7
Rationale: A + B + C's 1 day's work = 1/4
A's 1 day's work = 1/16
B's 1 day's work = 1/12
Therefore C's 1 day's work = 1/4	- ( A's 1 day's work + B's 1 day's work )
=> C's 1 day's work = 1/4 - ( 1/16 + 1/12 )
=> C's 1 day's work = (12-3-4)/48 = 5/48
So, C alone can do the work in 48/5 = 9 3/5 days.
So correct answer is B
Answer: (B) 9 3/5
Question: If |4x+6| = 46, what is the sum of all the possible values of x?
(A) 2
(B) -2
(C) 4
(D) -5
(E) 6
Rationale: There will be two cases
4x+6= 46 or 4x+6 = -46
=> x =10 or x= -12
sum of both the values will be -12 +10 = -2
Answer is B
Answer: (B) -2
Question: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 60 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
(A) 17 1/4 min
(B) 28 1/7 min
(C) 15 min
(D) 17 1/8 min
(E) 17 5/7 min
Rationale: 1/20 + 1/30 - 1/60 = 4/60 = 1/15
15/1 = 15
Answer:C
Answer: (C) 15 min
Question: Mr. David manufactures and sells a single product at a fixed price in a niche market. The selling price of each unit is Rs. 30. On the other hand, the cost, in rupees, of producing x units is 240 + bx + cx2, where b and c are some constants. Mr. David noticed that doubling the daily production from 20 to 40 units increases the daily production cost by 66.66%. However, an increase in daily production from 40 to 60 units results in an increase of only 50% in the daily production cost. Assume that demand is unlimited and that Mr. David can sell as much as he can produce. His objective is to maximize the profit.
How many units should Mr. David produce daily ?
(A) 130
(B) 100
(C) 70
(D) 150
(E) None of these
Rationale: Explanation :
Cost price function f(x) = cx2 + bx + 240.
When x = 20, f(20) = 400c + 20b + 240.
=> f(40) = 1600c + 40b + 240
66.67% is 2/3.
=> f(40) – f(20) = 2/3 * f(20).
Substituting f(40) and f(20), we get, 1200c+ 20b =(2/3) * (400c + 20b + 240)
Solving, we get 20b + 2800c = 480.
Now, f(60) = 3600c + 60b + 240.
f(60) – f(40) = ½ * f(40)
Substituting, and solving, we get, 360 + 60b + 2400c = 240 + 60b + 3600c
c = 1/10.
Substituting we get, b = 10.
So, the cost function f(x) = 0.1x2 + 10x + 240.
Selling price = 30 * x. ( Each unit SP is 30)
So, profit = SP – CP = 30x – (0.1x2 + 10x + 240) = -x2/10 + 20x – 240.
For maximum profit, differentiating this should give 0.
dp/dt = 0, dp/dt = -x/5 + 20
20 – x/5 = 0. x= 100.
Also double differentiating d2p / dt2, we get a negative number, so profit is maximum.
So, profit is maximum when 100 units are produced daily.
Answer : B
Answer: (B) 100
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1234
(B) 1356
(C) 1567
(D) 1546
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: (E) 1635
Question: In a building there are 5 rooms.Each having a equal area .The length of the room is 4m and breadht is 5 m.The height of the rooms are 2m. If 17 bricks are needed to make a square meter then how many bricks are needed to make the floor of a particular room ?
(A) 320
(B) 340
(C) 300
(D) 310
(E) 330
Rationale: Area of the floor = 4m x 5m = 20 m2
17 bricks are needed to make 1 m2 area.
So to make 20 m2 no of bricks needed = 17 x 20 = 340 Answer : B
Answer: (B) 340
Question: A boy & a girl appear for an interview against 2 vacant posts in an office. The probability of the boy's selection is 1/5 and that of the girl's selection is 1/3. What is the probability that only 1 of them is selected?
(A) 1/3
(B) 2/5
(C) 2/7
(D) 3/8
(E) 4/9
Rationale: Probability that only one of them is selected = (prob. that brother is selected) × (prob. that sister is not selected) + (Prob. that brother is not selected) × (Prob. that sister is selected)
= = 2/5
B
Answer: (B) 2/5
Question: Find the no.of ways of arranging the boy and 9 guests at a circular table so that the boy always sits in a particular seat?
(A) 3!
(B) 8!
(C) 7!
(D) 9!
(E) 11!
Rationale: Ans.(D)
Sol. Total number of persons = 10 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 9 places in 9P9 = 9! Ways ... The number of required arrangements = 9! x 1= 9! = 9! ways
Answer: (D) 9!