RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Consider a right circular cone of base radius 4 and height 10 cm. A cylinder is to be placed inside the cone with one of the flat surface resting on the base of the cone. Find the largest possible total surface area (in sq cm) of the cylinder.
A.100π/3
B.80π/3
C.120π/7
D.130π/9
Answer: A.100π/3
Explanation: Explanation :
Let the radius of cylinder be r and its height is h.
So, the height remained above cylinder is 10-h
Also, triangles ABC and ADE are similar. so ratio of corresponding sides must be equal
i.e AB/AD = BC/DE.
i.e. (10-h)/10 = r/4.
so 40 - 4h = 10r (by cross multiply)
h = (40-10r)/4 = 10-2.5r
Now we have total surface area of cyl = 2*π*r*h + 2*π*r2.
Putting value of h = 10 - 2.5r here, we get S = 2*π*r*(10-2.5r) + 2*π*r2.
S = 20*π*r- 5 * π * r2 + 2 * π * r2 .
S = 20 *π*r- 3*π*r .
Now, we have to maximize S, so differentiate it w.r.t r, we get
S = 20*π - 6 * π * r setting it to zero, we get
=> 20*π - 6 * π * r= 0
=> r = 20/6 = 10/3.
So, h = 10 - 2.5r = 10 - 2.5*10/3 = 5/3
So,
=> S = 2 * π * r * h + 2 * π * r2.
=> S = 2 * π * 10/3 * 5/3 + 2 * π* 100/9.
=> S = 2 * π * 50/9 + 2 * π* 100/9.
=> S = 2π150/9.
=> S = 100π/3.
Answer : A
Question: An article is bought for Rs.675 and sold for Rs.1100, find the gain percent?
A.65%
B.64%
C.63%
D.62%
Answer: C.63%
Explanation: 675 ---- 425
100 ---- ? =>
=63%
Answer:C
Question: A two digit no is 18 less than square of the sum of its digit.how many such no are there?
A.2
B.3
C.4
D.5
Answer: A.2
Explanation: 63=(6+3)^2-18=81-18
82=(8+2)^2-18=100-18
ANSWER:A
Question: If a/b = 5/2, b/c = 1/2, c/d = 1, d/e = 3/2 and e/f = 4/3, then what is the value of abc/def ?
A. 15/8
B. 14/3
C. 41/7
D. 3/18
Answer: A. 15/8
Explanation: Say a = 2. Then:
a/b = 5/2 --> b = 2/5;
b/c = 1/2 --> c = 4/5;
c/d = 1 --> d = 4/5;
d/e = 3/2 --> e = 8/15;
e/f = 4/3 --> f = 2/5.
abc/def = (1*2/5*4/5)/(4/5*8/15*2/5) = 15/8.
Answer: A.
Question: If 3x < 2y < 0, which of the following must be the greatest?
A.2y - 3x
B.3x - 2y
C.-(3x - 2y)
D.-(3x + 2y)
Answer: D.-(3x + 2y)
Explanation: Plugging in -1 for both x and y we get
A. 2y - 3x = 2
B. 3x - 2y = -1
C. -(3x - 2y) = 3
D. -(3x + 2y) = 15
E. 0
Answer: D
Question: TOM traveled the entire 60 miles trip. If he did the first 15 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 45 miles per hour, what is the his average speed, in miles per hour?
A.35.62mph
B.25.45mph
C.34.52mph
D.36.92mph
Answer: D.36.92mph
Explanation: avg speed = total distance/ total time = (d1+d2)/(t1+t2) = (15+45) / ((15/24)+(45/45)) = 60*2/3 = 36.92mph
D
Question: There are X persons and Y chocolates. If each person is given 1 chocolate then 1 chocolate is left, if each person is given 2 chocolates then 1 person will be left. So how many persons and chocolates are there??
A.3,2
B.3,3
C.3,4
D.4,5
Answer: C.3,4
Explanation: X person, Y chocolates
1st equation ==> (Y-1)/x = 1
2nd equation ==> Y/(X-1) = 2
Solving we get x = 3 , Y =4
ANSWER:C
Question: 23 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
A.None of these
B.506
C.512
D.524
Answer: B.506
Explanation: Explanation :
He can go in any bus out of the 23 buses.
Hence He can go in 23 ways.
Since he can not come back in the same bus that he used for travelling,
He can return in 22 ways.
Total number of ways = 23 x 22 = 506. Answer : Option B
Question: (x-2) men can do a piece of work in x days and (x+7) men can do 75% of the same work in (x-10)days. Then in how many days can (x+10) men finish the work?
A.27 days
B.12 days
C.25 days
D.18 days
Answer: B.12 days
Explanation: Explanation:
(3/4) × (x - 2)x = (x + 7)(x - 10)
=> x2 - 6x - 280 = 0
=> x= 20 and x=-14
so, the acceptable values is x=20
Total work = (x - 2) × x = 18 × 20 = 360 unit
Now 360 = 30 × k (30 = 20 + 10)
k = 12 days
Answer: B
Question: If 20,374 + x is a multiple of 5, which of the following could be the value of x?
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: Sum of the digits of 20,374 is 2+0+3+7+4 = 16
Now 16 is not a multiple of 5, the next multiple of 5 close to 16 is 20, which is 4 added to 16.
So the least number to be added to 20,374 is 4.
D
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.2 : 3
C.3 : 5
D.4 : 7
Answer: A.1 : 2
Explanation: 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
Question: Pat, kate and mark charged a total of 198 hours to a certain project . If pat charged twice as much time to the project as kate and 1/3 as much times as mark, how many more hours did mark charge to the project than kate.
A.18
B.36
C.72
D.110
Answer: D.110
Explanation: Let Kate charge for x hours,
then Pat charged for 2x and Mat - for 6x.
So, 2x+6x+x = 198 -total hours charged for,
x= 22.
Mat charged 6x-x or 5x for more hours than kate, or for 110 hours .
D is correct
Question: is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 47, then how old is B?
A.7
B.8
C.9
D.18
Answer: D.18
Explanation: Let C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.
(2x + 2) + 2x + x = 47
5x = 45 => x = 9
Hence, B's age = 2x = 18 years.
ANSWER:D
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1215 as rent for parking his cars, what is the total rent paid by all the four agencies?
A.6642
B.2778
C.1279
D.6150
Answer: A.6642
Explanation: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1215
45k = 1215 => k = 27
246k = 246(27) = Rs. 6642
Thus the total rent paid by all the four agencies is Rs. 6642.
Answer: A
Question: Last year the range of the annual bonus of the 100 employees at Company X was $20,000. If the annual bonus of each of the 100 employees this year is 10 percent greater than it was last year, what is the range of the annual bonus of the 100 employees this year?
A. $27,000
B. $22,000
C. $33,000
D. $16,000
Answer: B. $22,000
Explanation: let the lowest bonus be x.
Therefore, highest bonus is x +20000.
Now bonus of each employee is increased by 10%.
Therefore the bonus will remain arranged in the same order as before.
or Lowest bonus = 1.1x and Highest = 1.1 * (x+20000)
or Range = highest - lowest = 1.1 * (x+20000) - 1.1x
= 22000, Hence, B
Question: (150% of 1265) ÷ 7 = ?
A.A)125
B.B)175
C.C)271
D.D)375
Answer: C.C)271
Explanation: Explanation :
? = (150 x 1265/100) ÷ 7 = 189750/700 = 271
Answer : Option C
Question: A fruit seller had some apples. He sells 40% and still has 420 apples. Originally, he had ?
A.588 apples
B.600 apples
C.672 apples
D.700 apples
Answer: D.700 apples
Explanation: Answer
∵ 60% of N = 420
∴ N = (420 x 100)/60 = 700
Correct Option: D
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
A.40 sec
B.11 sec
C.88 sec
D.19 sec
Answer: A.40 sec
Explanation: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
Answer: A
Question: After running a series of television advertisements, a leading beverage producer saw its sales increase by 25% to $3 million dollars per month. Prior to the advertising campaign, about how many dollars in sales did the company average per day?
A.$1.25 million
B.$80,000
C.$750,000
D.$27,000
Answer: B.$80,000
Explanation: Let sales in previous month = X
1.25 X=2,000,000
5/4 X= 2,000,000 ..........> X=2,400,000
sales per day= 2,400,000/30= less than 80,000
Answer:B
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform.
A.310 meter
B.335 meter
C.345 meter
D.350 meter
Answer: D.350 meter
Explanation: Explanation:
Speed = Distance/time = 300/18 = 50/3 m/sec
Let the length of the platform be x meters
then
Distance=Speed∗Time
x+300=50/3∗39
=>3(x+300)=1950
=>x=350 meters
Option D
Question: By selling 45 lemons for Rs 40, a man loses 20 %. How many should he sell for Rs 24 to gain 20 % in the transaction ?
A.33
B.18
C.99
D.27
Answer: B.18
Explanation: Explanation:
Let S.P. of 45 lemons be Rs. x.
Then, 80 : 40 = 120 : x or x = = 60
For Rs.60, lemons sold = 45
For Rs.24, lemons sold == 18.
Answer: B
Question: I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I have to pack and distribute ?
A.25
B.37
C.54
D.65
Answer: A.25
Explanation: Explanation:
Clearly, the required number would be such that it leaves a remainder of 1 when divided by 2, 3 or 4 and no remainder when divided by 5. Such a number is 25.
Answer: A
Question: A work as fast as B. If B can complete a work in 36days independently,the number of days in which A and B can together finish the work in?
A.12days
B.3days
C.4days
D.5days
Answer: A.12days
Explanation: Ratio of rates of working of A and B = 2:1
ratio of times taken = 1:2
A's 1day work = 1/18
B's 1day work = 1/36
A+B 1day work = 1/18 + 1/36 = 3/36 = 1/12
A and B can finish the work in 12days
Answer is A
Question: If an object travels at six feet per second, how many feet does it travel in one hour?
A.21600
B.3778
C.12788
D.18000
Answer: A.21600
Explanation: Explanation:
If an object travels at 6 feet per second it covers 6x60 feet in one minute, and 6x60x60 feet in one hour.
Answer = 21600
Answer: A) 21600
Question: A certain restaurant offers 7 different salads, 4 different main courses, and 6 different desserts. If customers choose one salad, one main course, and two different desserts for their meal, how many different meals are possible?
A.340
B.380
C.420
D.460
Answer: C.420
Explanation: The number of possible choices for desserts is 6C2 = 15
The number of possible meals is 7*4*15 = 420
The answer is C.
Question: A profit of Rs. 20000 is to be distributed among A, B, C in the proportion 2 : 3 : 5. What will be the difference between B’s and C’s shares
A.4000
B.3000
C.5500
D.4500
Answer: A.4000
Explanation: Explanation :
B's share = Rs 20000 *(3/10) = Rs 6000
C's share = Rs 20000 * (5/10) = Rs 10000
Difference in B's and C's shares = Rs 4000
Answer : A
Question: Tom, working alone, can paint a room in 20 hours. Peter and John, working independently, can paint the same room in 10 hours and 5 hours, respectively. Tom starts painting the room and works on his own for two hour. He is then joined by Peter and they work together for two hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?
A.5/7
B.7/8
C.2/5
D.3/5
Answer: C.2/5
Explanation: Let the time when all three were working together be t hours. Then:
Tom worked for t+4 hour and has done 1/20*(t+4) part of the job;
Peter worked for t+2 hour and has done 1/10*(t+2) part of the job;
John worked for t hours and has done 1/5*t part of the job:
1/20*(t+4)+1/10*(t+2)+1/5*t=1 --> multiply by 20 --> (t+4)+(2t+2)+4t=20 --> t=2;
Hence Peter has done 1/10*(2+2)=4/10 =2/5
Answer: C
Question: A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is frozen if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently nine spaces behind player B, what is the probability that player B will be frozen after player A rolls?
A.1/12
B.5/36
C.1/9
D.1/3
Answer: C.1/9
Explanation: no. of possible outcomes = 6*6 = 36
no. of outcomes that result a total of 9 (as A is 9 spaces behind B) = 4 ( (3,6), (4,5), (5,4), (6,3) )
So, the probability = 4/36=1/9 (Option C)
Question: 9 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 48 cm height. What is the diameter of each sphere?
A.4 cm
B.6 cm
C.8 cm
D.10 cm
Answer: C.8 cm
Explanation: Volume of cylinder = pi*r^2*h
Volume of a sphere = 4*pi*R^3 / 3
9*4*pi*R^3 / 3 = pi*r^2*h
R^3 = r^2*h / 12 = 64 cm^3
R = 4 cm
D = 8 cm
The answer is C.
Question: A can do a work in 7 days. B is 20% more efficient than A. How many days does B alone take to do the same job?
A.28/6
B.25/6
C.35/6
D.33/6
Answer: C.35/6
Explanation: Ratio of times taken by A and B = 120:100 = 6:5
suppose B alone to take x days to do the work
then, 6:5::7:x
6x= 5*7
x=35/6 days
correct option is C
Question: The average (arithmetic mean) of the even integers from 0 to 60 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 30 inclusive?
A.10
B.15
C.20
D.25
Answer: B.15
Explanation: The sum of even numbers from 0 to N is 2 + 4 +...+ N
= 2(1 + 2 + ...+ N/2)
= 2(N/2)(N/2+1)/2 = (N/2)(N/2+1)
The average is (N/2)(N/2+1)/(N/2+1) = N/2
The average of the even numbers from 0 to 60 is 60/2 = 30
The average of the even numbers from 0 to 30 is 30/2 = 15
The answer is B.
Question: What is the are of an equilateral triangle of side 8 cm?
A.64√5
B.64√9
C.16√3
D.64√3
Answer: C.16√3
Explanation: Area of an equilateral triangle = √3/4 S2
If S = 8, Area of triangle = √3/4 * 8 * 8 = 16√3 cm2;
Answer: C
Question: Soymilk are sold in packages of two or three only. If Hannah bought 17 Soymilk exactly, what could be the number of large packs Hannah bought?
A.1
B.4
C.3
D.5
Answer: C.3
Explanation: Let number of packs of three = t
let number of packs of two = w
3t + 2w = 17
Now , we need to test for values of w .
Since sum 17 is odd and 2w will always be even, therefore w can't be even .
Now , we can test for values w = 1 , 3 and 5
2*4 + 3*3 = 8 + 9 = 17
Answer C
Question: Robert ate 10 chocolates, Nickel ate 5 chocolates. How many more chocolates did Robert ate than nickel?
A.A)4
B.B)7
C.C)9
D.D)5
Answer: D.D)5
Explanation: 10-5=5. Answer is D
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
A.776
B.298
C.245
D.266
Answer: C.245
Explanation: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time
= 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X)
= 750 ==> X
= 245 m.
Answer: C
Question: Virginia, Adrienne, and Dennis have taught history for a combined total of 87 years. If Virginia has taught for 9 more years than Adrienne and for 9 fewer years than Dennis, for how many years has Dennis taught?
A. 23
B. 32
C. 38
D. 41
Answer: C. 38
Explanation: Let number of years taught by Virginia = V
number of years taught by Adrienne = A
number of years taught by Dennis = D
V+A+D = 96
V= A+9
=>A = V-9
V= D-9
=> A = (D-9)-9 = D-18
D-9 + D-18 + D = 87
=> 3D = 87+ 27 = 114
=> D = 38
Answer C
Question: Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
A.478
B.476
C.472
D.471
Answer: B.476
Explanation: 3 1/2 * 8 1/2 = 1/4 * 1/4 * x => x
= 476
Answer:B
Question: In a cricket team, the average of eleven players is 28 years. Out of these, the average ages of three groups of three players each are 25 years, 28 years and 32 years respectively. If in these groups, the captain and the youngest player are not included, and the captain is eleven years older than the youngest player, what is the age of the captain ?
A.32 years
B.34 years
C.35 years
D.36 years
Answer: A.32 years
Explanation: Explanation :
Let the age of youngest player be x.
Then, age of the captain = (x + 11).
=> 3*25 + 3*28 + 3*32 + x + x + 11 = 11*28.
=> 75+84+96+2x+11=308
so 2x = 42
so x = 21.
Age of the captain = (x+11)
= 32 years.
Answer : A
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 100 m and they cross each other in 12 sec, then the speed of each train is?
A.30
B.35
C.36
D.37
Answer: A.30
Explanation: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (100 + 100)/12 => x = 8.33
Speed of each train = 10 m/sec.
= 8.33 * 18/5 = 30 km/hr.
Answer: Option A
Question: In a school of 850 boys, 34% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
A.A)125
B.B)627
C.C)153
D.D)238
Answer: D.D)238
Explanation: 34 + 28 + 10 = 72%
100 – 72 = 28%
850 * 28/100 = 238
Answer:D
Question: If a farmer wants to plough a farm field on time, he must plough 120 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?
A.334
B.720
C.667
D.261
Answer: B.720
Explanation: Let xx be the number of days in the initial plan. Therefore, the whole field is 120⋅x120⋅x hectares. The farmer had to work for x+2x+2 days, and he ploughed 85(x+2)85(x+2) hectares, leaving 4040 hectares unploughed. Then we have the equation:
120x=85(x+2)+40120x=85(x+2)+40
35x=21035x=210
x=6x=6
So the farmer planned to have the work done in 6 days, and the area of the farm field is 120⋅6=720120⋅6=720 hectares
Answer:B
Question: David works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate, and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 600 and then he left the lab. He returned in time to take a reading at 4 p.m., by which point the population had grown to 4,800. Now he has to fill in the missing data for 2 p.m. and 3 p.m. What was the population at 3 p.m.?
A.2400
B.3600
C.3000
D.2800
Answer: A.2400
Explanation: let the rate be x, then population of the bacteria after each hour can be given as 600,600x, 600(x^2), 600(x^3)
now population at 4pm =4800
thus we have 600(x^3) = 4800 =8
thus x=2
therefore population at 3pm = 600(4) = 2400
Answer : A
Question: What is the sum of the 1st 6 prime numbers greater than 10?
A.112
B.111
C.212
D.115
Answer: A.112
Explanation: Required numbers are= (11 + 13 + 17 + 19 + 23+ 29) = 112
Note: 1 is not a prime number
Answer A
Question: A train travels from station A to station B. If it travels at a speed of 80 miles per hour, it ends up reaching the station 30 minutes late. If it travels at 120 miles per hour, it reaches the station 15 minutes early. What is the amount of time that the train is scheduled to take for the journey and what is the distance between the stations?
A.	2 hours, 225 miles
B.	3 hours, 350 miles
C.	1.75 hours, 180 miles
D.	5 hours, 550 miles
Answer: C.	1.75 hours, 180 miles
Explanation: Let t be the usual time and x be the distance between AB. So we need to find t and Distance x. The question gives us 2 combinations of speedtime, but the distance remains the same for both condition.
Equation 1 - x= 80 (t+.5) (converted 30 mins into hr) added .5 hrs because it is late or took more time than usual.
Equation 2 - x= 120 (t-.25) subtracted .25 hrs because it is early or took less time than usual.
Now equating 12 we get 100(t+.5)=120(t-.25)
=> 8t +4 = 12t - 3
=> 4t=7 => t= 1.75 hrs.
Hence x= 80(1.75+.5) =>80 X 2.25 => 180 miles.
Hence correct answer C.
Question: Dawson is going with 14 friends on a trip to Washington D.C for spring break. Airfare and hotel costs a total of $13500.00 for the group of 15 friends. How much does each person have to pay for their hotel and airfare?
A.$900
B.$800
C.$850
D.$950
Answer: A.$900
Explanation: Answer= A
The total cost of the trip ($13500.00) divided by 15 equals $900.00.
Question: What is the average of first 21 multiples of 7 ?
A.70
B.77
C.79
D.81
Answer: B.77
Explanation: Required average = 7(1+2+....+21) / 21
(7/21)X ( (21x22) / 2 ) (because sum of first 21 natural numbers)
= 77
B
Question: A train 275 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
A.7 sec
B.5 sec
C.15 sec
D.6 sec
Answer: C.15 sec
Explanation: Speed of train relative to man
= (60 + 6) km/hr
= 66 km/hr
[66 * 5/18] m/sec
= [55/3] m/sec.
Time taken to pass the man
= [275* 3/55] sec
= 15 sec
Answer:C
Question: 3th/4 of 1th/5 of a number is 60. The number is
A.300
B.400
C.450
D.1200
Answer: B.400
Explanation: Explanation:
Let the number be N. Then
3/4×1/5×N=60⇒3N=1200⇒N=400
Correct Option: B
Question: A clothing store originally bought 100 jackets at a total cost of j dollars. If each jacket was sold for 60 percent more than its original cost, what was the individual price, in terms of j, of each jacket sold?
A.j/62
B.7j/500
C.140j
D.j/100+40
Answer: A.j/62
Explanation: lets take j=1000, as decided by you..
now 60% increase makes it 1600..
this is the price for 100 jackets, so selling price for each jacket=1600/100=$16..
j/62
so ans is correct as A..
Question: What is the sum of all possible 3-digit numbers that can be constructed using the digits 2, 3, and 5 if each digit can be used only once in each number?
A.2210
B.2220
C.2230
D.2240
Answer: B.2220
Explanation: There are 6 possible arrangements of the three numbers.
Then each number will be in the hundreds, tens, and ones place two times each.
The sum is 2(222) + 2(333) + 2(555) = 2220
The answer is B.
Question: At a certain organisation, the number of male members went up by 13% in the year 2001 from year 2000, and the number of females members went down by 6% in the same time period. If the total membership at the organisation went up by 1.2% from the year 2000 to 2001, what was the ratio of male members to female members in the year 2000?
A.1:2
B.1:3
C.2:3
D.3:5
Answer: D.3:5
Explanation: men increase by 13% ==> 1.13M = males in 2001
women decrease by 6% ==> 0.94F = women in 2001
total employees increase by 1.2% ==> 1.012*(M + F) = total number of employees in 2001
Obviously
(males in 2001) + (females in 2001) = total number of employees in 2001
1.13M + 0.94F = 1.012*(M + F)
1.13M + 0.94F = 1.012M + 1.012F
1.13M - 1.012M = 1.012F - 0.94F
0.108M = 0.072F
M/F = (0.072)/(0.118) = 72/118 = 3/5
Answer =(D)
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 320 m long platform?
A.44 min
B.55 min
C.47 min
D.67 min
Answer: A.44 min
Explanation: A
44 min
Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +320)/ 36 * 5/18 = 44 min.
Question: Two goods trains each 400 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
A.38.4
B.32.6
C.48
D.27.4
Answer: A.38.4
Explanation: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 400 + 400 = 800 m.
Required time = 800 * 6/125 = 38.40 sec.
Answer:A
Question: The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. The present worth is:
A.480
B.520
C.600
D.960
Answer: C.600
Explanation: T.D. = B.G. x 100 / Rate x Time
= Rs.(24 x 100/10 x 2)= Rs. 120.
P.W. =(100 x T.D./Rate x Time)
= Rs.(100 x 120/10 x 2)= Rs. 600.
Correct answer is C.
Question: In the rectangular coordinate system, what is the area of triangle CDE with points
C=(5,8)
D=(4,2)
E=(8,0)
A.13
B.12
C.12.8
D.14
Answer: A.13
Explanation: Use the formula of the distance formula
square root (x2-x1)^2+(y2-y1)^2
Do this for each of the sides and then the value is given as A.