RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A large tanker can be filled by two pipes A and B in 30 and 15 hours respectively. How many hours will it take to fill the tanker from empty state if A and B fill it together?
A.8hr
B.10hr
C.12hr
D.9hr
Answer: B.10hr
Explanation: Part filled by A in 1hr = 1/30
Part filled by B in 1hr = 1/15
part filled by A+B = 1/30 + 1/15 = 1/10
Both the pipes can fill the tank in = 10 hours
Answer is B
Question: In the fifth grade at Parkway elementary school there are 450 students. 320 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?
A.69.
B.73.
C.81.
D.95.
Answer: D.95.
Explanation: Total students = 450
Boys = 320, Girls = 130
Total playing soccer = 250
86%of 250 = 215 are boys who play soccer.
Girls who play soccer = 35.
Total girls who do not play soccer = 130 - 35 = 95.
Correct option: D
Question: 8 is 4% of a, and 4 is 8% of b. c equals b/a. What is the value of c?
A.1/32
B.1/4
C.1
D.4
Answer: B.1/4
Explanation: Explanation :
Given,
=>4a/100=8.
=>a=8×(100/4)=200. ---------(i)
And,
=>(8/100)×b=4.
=>b=50. ---------(ii)
Now, c=b/a ( from (i) and (ii) )
=>50/200.
=>1/4.
Answer : B
Question: A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 2, 3, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following ?
A.1/625
B.2/625
C.4/625
D.50/625
Answer: D.50/625
Explanation: I think most of the answers are missing a point. Let me try to put it across:
Total number of possible numbers are : 5x5 = 25
Correct number =1
Case 1: When he gets it right in first attempt: P(E1) = 1/25
Case 2: He gets 1st attempt wrong and second right:
When he gets it wrong then the probability of getting wrong is 24/25.
Now there are 24 cases with him and he chooses the right one this time.
Probability of right case is 1/24
Thus, P(E2) = 24/25 x 1/24
=1/25
Probability of getting it right in at most two cases = P(E1) + P(E2)
= 1/25 + 1/25
= 2/25
= 50/625
Option (D) is therefore right as most of you mentioned but the method employed was wrong.
Question: If b=4p where p is a prime number greater than 2, how many different positive even divisors does b have, including b?
A.two
B.three
C.four
D.six
Answer: C.four
Explanation: b=2, 2, p (p is in the prime factorization since were told it is a prime number in the question)
2
4 (because of 2*2)
2p (because of 2 * p)
4p (because of 2 * 2 * p)=C
Question: A watch was sold at a loss of 10%. If the watch was sold for $20 more, there would have been a gain of 6%. What is the cost price?
A.$95
B.$105
C.$115
D.$125
Answer: D.$125
Explanation: 0.9x + 20 = 1.06x
0.16x = 20
x = 125
The answer is D.
Question: a goes to place x and b goes to place y.
after a travelled 180 km more than b they together meet at a point between xy. they together had their lunch for half an hour. after that a took 2 hrs to reach x and b took 4.5 hrs to reach y. find distance between x and y?
A.900km
B.540km
C.720km
D.820km
Answer: A.900km
Explanation: let speed of A be-------Sa
let speed of B be--------Sb
let the distance covered by B while going to position XY be-----------x
so distance covered by A in same time while going to XY is----------180 +x(it's given in the question)
so total distance b/w X and Y is=x+(x+180)
while going to position XY :-
time taken by A = time taken by B
(x+180)/Sa= x/Sb
Sa/Sb=(x+180)/x---------------------1
After lunch:-
A.C.T(according to question)
Sa=x/2
Sb=(x+180)/4.5
dividing Sa/Sb=(x*4.5) / ((x+180)*2)--------------------2
equating equations 1 and 2
9/4 = (x+180)^2 / x^2
now taking square root on both sides we get
3/2 = (x+180) / x
x=360
therefore distance between x and y =x+(x+180)=900km
ANSWER:A
Question: The length of the bridge, which a train 180 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
A.195 m
B.156 m
C.245 m
D.156 m
Answer: A.195 m
Explanation: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time
= 30 sec. Let the length of bridge be x meters. Then, (180 + X)/30 = 25/2
==> 2(180 + X) = 750 ==> X
= 195 m.
Answer: A
Question: A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1.2 cm when a man gets on it. The mass of man is
A.72 kg
B.60 kg
C.72 kg
D.96 kg
Answer: A.72 kg
Explanation: Solution
Volume of water displaced	= (3 x 2 x 0.012)m3
= 0.072 m3.
Mass of man	=Volume of water displaced ×Density of water
= (0.072×1000) kg
= 72 kg.
Answer A
Question: The average of runs of a cricket player of 10 innings was 40. How many runs must he make in his next innings so as to increase his average of runs by 4?
A.87
B.16
C.10
D.84
Answer: D.84
Explanation: Average after 11 innings = 44
Required number of runs
= (44* 11) - (40* 10) = 484- 400
= 84.
Answer: D
Question: The average age of the district level hockey team of eleven is 26 years.The average age gets increased by 2 year when the coach age is also included.what is the age of the coach ?
A.40 yrs.
B.50 yrs.
C.45 yrs.
D.48 yrs.
Answer: B.50 yrs.
Explanation: Explanation:
Total age of players in team = 26 x 11 = 286
When coach is included, total members = 12, Avg age increases by two becomes 28
Total age when coach is included = 28x12 = 336
Age of coach = 336-286 = 50 yrs.
Answer: B
Question: A glucose solution contains 20 grams of glucose per 1000 cubic centimeters of solution. If 500 cubic centimeters of the solution were poured into an empty container, how many grams of glucose would be in the container?
A. 10.00
B. 15.00
C. 11.50
D. 10.50
Answer: A. 10.00
Explanation: We are given that a glucose solution contains 20 grams of glucose per 1000 cubic centimeters of solution. Since we are dealing with a solution, we know that the grams of glucose is proportional to the number of cubic centimeters of solution. Thus, to determine how many grams of glucose would be in the container when we have 500 cubic centimeters of solution, we can set up a proportion.
We can say: “20 grams of glucose is to 1000 cubic centimeters of solution as x grams of glucose is to 500 cubic centimeters of solution.” Let’s now set up the proportion and solve for x.
20/1000 = x/500
When we cross multiply we obtain:
(20)(500) = 1000x
10000 = 1000x
10 = x
There are 10.00 grams of glucose in the solution in the container.
The answer is A.
Question: The area of a triangle is with base 3m and height 4m?
A.4 m2
B.6 m2
C.18 m2
D.19 m2
Answer: B.6 m2
Explanation: 1/2 * 3 * 4
= 6 m2
Answer: B
Question: .01 x .3 ÷ .4 x .5 = ?
A..015
B..0375
C..00375
D..1
Answer: C..00375
Explanation: Answer
Given expression = .01 x .3 ÷ .4 x .5
= .0015 ÷ .4
= .00375
Option: C
Question: Which of the following is divisible by the first six positive integer multiples of 19?
(i) 52440
(ii) 114600
(iii) 19038
A.None
B.i only
C.iii only
D.ii and iii only
Answer: B.i only
Explanation: A positive integer x is divisible by 19, 2*19,...,6*19 if and only if it is divisible by their least common multiple, which in this case is 3*4*5*19. In particular, x is divisible by 10, so iii is not divisible by the first six positive integer multiples of 19.
3*4*5*19=60*(20-1)=1140. 1140*100=114000, so clearly (ii) is not divisible by the first six positive integer multiples of 19.
It remains to verify (i). 52440-40*1140=52440-45600=6840=6*1140, so (i) is divisible by 1140.
Answer B.
Question: Machine A and machine W are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine W. Machine W produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?
A.6
B.6.6
C.60
D.100
Answer: A.6
Explanation: [Reveal]Spoiler:
TimeW: 660/x
TimeA: [660/x+10]
660/x = [660/x+10] *110/100
660/x =66*11/x+10
660x+10= 66*11*x
660x +6600 = 66*11*x
x= 100
plug in back to timeA
660/100+10 => 660/110 = 6=A
Question: A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B ?
A.160 km
B.180 km
C.200 km
D.220 km
Answer: B.180 km
Explanation: Down Stream Speed :(14+4)km/hr =18 km/hr
Up Stream Speed:(14-4)km/hr=10km/hr
(x/18)+(x/2/20)=19
x=180km
ANSWER:B
Question: A cube has a volume of 27 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is?
A.216
B.48
C.64
D.80
Answer: A.216
Explanation: Volume = 27 = side^3
i.e. Side of Cube = 3
New Cube has dimensions 6, 6, and 6 as all sides are twice of teh side of first cube
Volume = 6*6*6 = 216 square feet
Answer: option A
Question: Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion. In 16 years from now, Lyn the circus Lion will be exactly half as old as Ele, the circus Elephant. How old is Ele today?
A.47
B.48
C.43
D.42
Answer: B.48
Explanation: Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion.
Ele = 3*Lyn
Usually, ages are integers so there is a good possibility that the age of Ele is 48 (the only option that is a multiple of 3).
Then age of Lyn would be 16. In 16 yrs, Ele would be 64 and Lyn would be 32 - so Lyn would be half as old as Ele.
Answer (B)
Question: What is the smallest number which when increased by 3 is divisible by 18, 70, 100 and 21?
A.5037
B.5447
C.5867
D.6297
Answer: D.6297
Explanation: When increased by 3, the number must include at least 2^2*3^2*5^2*7 = 6300
The answer is D.
Question: What is the probability of flipping a fair coin four times and the coin landing on heads on exactly three flips?
A.1/3
B.1/4
C.2/3
D.2/5
Answer: B.1/4
Explanation: Probability = (Favorable combination)/(Total combination)
Favorable combination = (HHHT, HHTH, HTHH,THHH) ==> 4
Total combination = 8 (2^4)
Probability = (4)/(16) = 1/4
(B)
Question: There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability W that the number of men is equal to that of women?
A.W=18/35
B.W=16/35
C.14/35
D.13/35
Answer: A.W=18/35
Explanation: METHOD-1:
Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36
Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70
Probability = 36/70 = 18/35
A
METHOD-2:Also see the mistake done by the person who posted this question
Probability of First selected person being Man = 4/8
Probability of Second selected person being Man = 3/7
Probability of First selected person being Woman = 4/6
Probability of Second selected person being Woman = 3/5
i.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) *[4!/(2!*2!)]= 18/35
The important part for the readers is to understand the reason of multiplying[4!/(2!*2!)]here
When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well
The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2!
A
Question: If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many Z such committees are possible?
A.20
B.40
C.50
D.Z=80
Answer: D.Z=80
Explanation: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 5C3=10.
But these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.
Total # of ways: 5C3*2^3=80.
Answer: D.
Question: A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
A.09:30 p.m
B.11:23 p.m
C.10:30 p.m
D.07:30 p.m
Answer: C.10:30 p.m
Explanation: D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
3.30 + 7 h = 10.30 p.m.
Answer: C
Question: 4, 5, 7, 11, 19, (...)
A.32
B.22
C.35
D.27
Answer: C.35
Explanation: 4
4 × 2 - 3 = 5
5 × 2 - 3 = 7
7 × 2 - 3 = 11
11 × 2 - 3 = 19
19 × 2 - 3 = 35
Answer is C
Question: Two pyramids are thrown with faces 1,2,4,6. Find the probability to get a sum of even number on an their faces?
A.5/8
B.3/4
C.1/4
D.7/4
Answer: A.5/8
Explanation: 1 pyramid can show 4 different kind of arrangements
1,2,4=7
1,2,6=9
1,4,6=11
2,4,6=12
So, out of 4 outcomes
3 are odd and 1 is even.
In question given two pyramids are thrown.
So, to make some of their faces as even
Condition 1: some of both individual faces of each pyramid is odd
3/4 * 3/4
=9/16
Condition 2: some of both individual faces of pyramid is even
1/4 + 1/4
=1/16
Total such conditions = 9/16 + 1/16
= 10/16
= 5/8
ANSWER:A
Question: Average of all prime numbers between 30 to 50
A.37
B.37.8
C.39
D.39.8
Answer: D.39.8
Explanation: Explanation:
Prime numbers between 30 and 50 are:
31, 37, 41, 43, 47
Average of prime numbers between 30 to 50 will be
(31+37+41+43+47 / 5)=199 / 5=39.8
Option D
Question: A snail, climbing a 42 feet high wall, climbs up 4 feet on the first day but slides down 2 feet on the second. It climbs 4 feet on the third day and slides down again 2 feet on the fourth day. If this pattern continues, how many days will it take the snail to reach the top of the wall?
A.20
B.26
C.32
D.39
Answer: D.39
Explanation: total transaction in two days = 4-2 = 2 feet
in 38 days it will climb 38 feet
on the 39th day , the snail will climb 4 feet , thus reaching the top
therefore , total no of days required =39
D
Question: Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then
A.XB > CD
B.XB < YD
C.AX > XB
D.AX < CD
Answer: D.AX < CD
Explanation: A--X------B
C-----Y---D
AX < CD.
Answer: D.
Question: The letters D, G, I, I , and T can be used to form 5-letter strings as DIGIT or DGIIT. Using these letters, how many 5-letter strings can be formed in which the two occurrences of the letter I are separated by at least one other letter?
A.12
B.18
C.24
D.36
Answer: D.36
Explanation: Total no of ways arranging 5 letter with one letter redundant is 5!/2!=60
No of ways two I's can be together 4!=24
no of ways at least one alpha is between two I's =60-24=36
ANS:D
Question: A 8% stock yields 20%. The market value of the stock is:
A.Rs 48
B.Rs 45
C.Rs 40
D.Rs 50
Answer: C.Rs 40
Explanation: Explanation:
For an income of Rs. 20, investment = Rs. 100.
For an income of Rs 8, investment =Rs.100/20 X8 =Rs 40
Market value of Rs. 100 stock = Rs 40
Answer is C
Question: At what rate percent on simple interest will Rs.750 amount to Rs.825 in 5 years?
A.2
B.3
C.4
D.5
Answer: A.2
Explanation: 75 = (750*5*R)/100
R = 2%.Answer: A
Question: In the formula V = 1/(2r)^3, if r is halved, then V is multiplied by?
A.16
B.8
C.1
D.1/8
Answer: B.8
Explanation: Say r=1 => V1 = 1/8
when r=1/2; V2 = 1
V2 = 1*V1.
Answer : B
Question: If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:
A.0
B.1
C.2
D.3
Answer: C.2
Explanation: Explanation:
Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3.
x = 2.
ANSWER IS C
Question: A vending machine randomly dispenses four different types of fruit candy. There are twice as many apple candies as orange candies, twice as many strawberry candies as grape candies, and twice as many apple candies as strawberry candies. If each candy cost $0.4, and there are exactly 90 candies, what is the minimum amount of money required to guarantee that you would buy at least three of each type of candy?
A.$3.00
B.$20.75
C.$33.20
D.$42.75
Answer: C.$33.20
Explanation: Let number of Apple , Orange , strawberry and grape candies be A, O ,S and G respectively .
A= 2O
S= 2G
A= 2S
A= 4G
A+O+S+G = 90
=>A + A/2 + A/2 +A/4 = 90
=> 9A/4 = 90
=> A = 40
O = 20
S = 20
G = 10
Cost of each candy = .25 $
Mininum amount of money required to guarantee that you would buy at least three of each type of candy
We can buy 40 Apple candies , 20 orange candies , 20 strawberry candies and 3 grape candies to ensure atleast 3 of each type of candies .
Total = 83 candies
Amount required = 83 * .4 = 33.20 $
Answer C
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
A.277 m
B.240 m
C.627 m
D.892 m
Answer: B.240 m
Explanation: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x
= 240 m.
Answer: B
Question: If two positive numbers are in the ratio 1/9 : 1/5, then by what percent is the second number more than the first?
A.80%
B.90%
C.60%
D.50%
Answer: A.80%
Explanation: Given ratio = 1/9 : 1/5 = 5 : 10
Let first number be 5x and the second number be 9x.
The second number is more than first number by 4x.
Required percentage = 4x/5x * 100 = 80%.
Answer:A
Question: A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 8:00 a.m., at what time was it one-eighth full?
A.9:00 a.m.
B.7:00 a.m.
C.6:00 a.m.
D.4:00 a.m.
Answer: B.7:00 a.m.
Explanation: To go from one-eighth (1/8) full to half (1/2) full culture of bacteria should quadruple: 1/8*4=1/2, as it quadruples every hour then container was one-eighth full at 8:00 a.m -1 hour = 7:00 a.m.
Answer: B.
Question: C and D enter into partnership with capital as 7:9. At the end of 8 months, C withdraws. If they receive the profits in the ratio of 8:9 find how long D's capital was used?
A.months
B.months
C.months
D.months
Answer: D.months
Explanation: 7 * 8 : 9 * x = 8:9 => x= 7
ANSWER:D
Question: The product of two successive numbers is 4160. Which is the smaller of the two numbers?
A.78
B.64
C.88
D.67
Answer: B.64
Explanation: B
4160
From the given alternatives,
64 × 65 = 4160
∴ Smaller number = 64
Question: A basket has 6 apples and 4 oranges. FOUR fruits are picked at random. The probability that at least 3 apples are picked is
A.25/42
B.25/48
C.19/42
D.25/47
Answer: C.19/42
Explanation: Total fruits = 10Since there must be at least two apples,(6C3 * 4C1)/10C4 + 6C4/10C4 = 19/42.Answer:C
Question: A man complete a journey in 10 hrs. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km?
A.271 km
B.224 km
C.243 km
D.222 km
Answer: B.224 km
Explanation: B
224 km
Let the total distance be x km.
Then, [(1/2 x) / 21 + (1/2 x) / 24] = 10
15x = 168 * 20 => x = 224 km.
Question: The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
A.16 2/3% loss
B.16 8/3% loss
C.19 2/3% loss
D.13 2/3% loss
Answer: A.16 2/3% loss
Explanation: 15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
Answer: A
Question: A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
A.288
B.286
C.298
D.2776
Answer: D.2776
Explanation: 2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400
Answer:D
Question: On Saturday morning, John will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.6, what is the probability that Malachi will return home at the end of the day on the following Monday?
A.0.096
B.0.125
C.0.128
D.0.512
Answer: A.0.096
Explanation: Re-phrasing the question:
What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain
Probability of rain = 0.6
Therefore, probability of no rain = 0.4
0.6*0.6*0.4 = 0.096
Hence A
Question: How many combinations of three letters taken from letters (a, b, b, c, c, d) are possible?
A.10
B.13
C.35
D.36
Answer: A.10
Explanation: So 4C3 for abcd - 4 choices
3 more for bb(a,c or d)
3 more for cc(a,b or d)
total 10
Ans :A
Question: A part-time employee’s hourly wage was increased by 25%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased?
A.9%
B.15%
C.20%
D.50%
Answer: C.20%
Explanation: Let's plug in somenicenumbers and see what's needed.
Let's say the employee used to make $1/hour and worked 100 hours/week
So, the TOTAL weekly income was $100/week
After the 25% wage increase, the employee makes $1.25/hour
We want the employee's income to remain at $100/week.
So, we want ($1.25/hour)(new # of hours) = $100
Divide both sides by 1.25 to get:
new # of hours = 100/1.25
≈ 80 hours
So, the number of hours decreases from 100 hours to (approximately) 80 hours.
This represents a 20% decrease (approximately) .
Answer : C
Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother three years younger to her was born. What is the difference between the ages of her parents?
A.2 years
B.4 years
C.5 years
D.7 years
Answer: C.5 years
Explanation: Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 3) years = 41 years.
Required difference = (41 - 36) years = 5 years.
Answer: Option C
Question: A batch of cookies was divided among three tins: 2/3 of all the cookies were placed in either the blue tin or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction E of the cookies that were placed in the other tins were placed in the green tin?
A.15/2
B.9/4
C.5/9
D.7/5
Answer: C.5/9
Explanation: Blue tin or red tin: 2/3 (N)
Red tin: (1/3)N
Blue tin: (1/4)N
What the last statment meant, is it wants this fraction: (# of cookies in green tin)/(# of cookies in red and green tin)
# of cookies in green tin = 2N/3 - N/4 = 8N- 3N/12 = 5N/12
# of cookies in red and green tin = N/3 + 5N/12 = 9N/12
Fraction E= 5N/12 * 12/9N = 5/9 (C)
Question: If the cost price is 96% of the selling price, then what is the profit percent?
A.4.17%
B.5%
C.6.12%
D.3.25%
Answer: A.4.17%
Explanation: Let S.P. = $100
C.P. = $96
Profit = $4
Profit% = 4/96 * 100 = 25/6 = 4.17%
Answer is A
Question: It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is?
A.2:9
B.3:1
C.3:4
D.3:9
Answer: C.3:4
Explanation: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120/x + 480/y = 8 or 1/x + 4/y
= 1/15 --- (i)
And, 200/x + 400/y = 25/3 or 1/x + 2/y
= 1/24 --- (ii)
Solving (i) and (ii), we get x = 60 and y
= 80
Ratio of speeds = 60:80 = 3:4
Answer:C
Question: A train running at the speed of 48 km/hr crosses a pole in 9 seconds. Find the length of the train?
A.120 meter
B.299 meter
C.666 meter
D.155 meter
Answer: A.120 meter
Explanation: Speed = 48*(5/18) m/sec = 40/3 m/sec
Length of Train (Distance) = Speed * Time
(40/3) * 9
= 120 meter
Answer: A
Question: John distributes his pencil among his 4friends Rose, Mary, Ranjan, and Rohit in the ratio 1/2 : 1/3 :1/4:1/5 . What is the minimum no. of pencils that the person should have?
A.45
B.65
C.70
D.77
Answer: D.77
Explanation: Rakesh : Rahul : Ranjan : Rohit = 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5
Step 1: At First we need to do is LCM of 2,3,4 and 5 is 60.
Step 2: Then pencil are distributed in ratio among friends,
Rakesh = ( 1 / 2 x 60 ) = 30.
Rahul = ( 1 / 3 x 60 ) = 20.
Ranjan = ( 1 / 4 x 60 ) = 15.
Rohit = ( 1 / 5 x 60 ) = 12.
Step 3: Total number of pencils are ( 30 x + 20 x + 15 x + 12 x) = 77 x.
For minimum number of pencils x = 1 .
The person should have atleast 77 pencils.
D)