RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Mr. Karthik drives to work at an average speed of 48 km/hr. Time taken to cover the first 60% of the distance is 20 minutes more than the time taken to cover the remaining distance. Then how far is his office ?
A.23
B.98
C.28
D.80
Answer: D.80
Explanation: Explanation:
Let the total distance be 'x' km.
Time taken to cover remaining 40% of x distance is
But given time taken to cover first 60% of x distance is
\Rightarrow
\small \Rightarrow x=80 km.
Answer: D
Question: The number of arrangements that can be made with the letters of the word PETER so that the vowels occupy the even places?
A.14
B.18
C.12
D.15
Answer: B.18
Explanation: The word PETER has 5 letters of which 2 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 2 even places in 2! i.e., 2 ways. While the consonants can be arranged among themselves in the remaining 3 places in 3! i.e., 6 ways.
Hence the total ways are 6 * 2 = 18.
Answer:B
Question: What is the sum of the different positive prime factors of 720?
A.5
B.10
C.15
D.17
Answer: B.10
Explanation: Prime factorization of 720
=72 * 10
=6*12 * 10
=2*3 * 2*6 * 2*5
=2*3 * 2 * 2*3 * 2*5
=2^4 * 3^2 * 5
Sum of the different positive prime factors of 720 = 2+3+5
=10
Answer B
Question: College T has 1000 students. Of the 250 students majoring in one or more of the sciences,140 are majoring in Chemistry and 170 are majoring in Biology. If at least 50 of the students are not majoring in either Chemistry or Biology, then the number of students majoring in both Chemistry and Biology could be any number from?
A.110 to 150
B.110 to 140
C.110 to 130
D.120
Answer: B.110 to 140
Explanation: Total = Chemistry + Biology - Both + Neither
250 = 140 + 170 - Both + N
We know that N (Neither) must be at least 30, so set N=30 and solve:
250 = 140 + 170 - Both + 50
250 = 360 - Both
Both = 110
Even if you're not sure whether 110 is the highest or lowest Both could possibly be, it doesn't matter, because you know it's a boundary point of the range,
Both can not be greater than 140, because even if every chemistry major was also a biology major, there are only 140 chemistry majors total. B the solution.
Question: A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 5 hours. Working alone, the outlet pipe can empty out the tank in 10 hours. If it is desired that the tank should be filled, from empty, exactly 8 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?
A.11:30am
B.10:30am
C.9:30am
D.8:30am
Answer: A.11:30am
Explanation: In 8 hours the inlet pipe will pump in water equal to 8*1/5 = 8/5 of the pool. So, 3/5 more than necessary, which should be compensated by the outlet pipe. To pump out 3/5 of the water the outlet pipe needs 30/5 = 6 hours.
Therefore, the outlet pipe should be opened at 9:30am + 8 hours - 6 hours = 11:30am.
Answer: A
Question: If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station?
A.4/5 km
B.2/3 km
C.8/2 km
D.1/3 km
Answer: A.4/5 km
Explanation: x/3 – x/4 = 4/60
x = 4/5 km
Answer:A
Question: Question: What is the remainder when R=(1!)!^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144?
A. 0
B. 25
C. 49
D. 81
Answer: D. 81
Explanation: 144 =12 *12
(1!)^3=1
2!=2, therefore (2!)^3=2*2*2=8
3!=6, therefore (3!)^3=6*6*6=216
4!=24 therefore (4!)^3= 24*24*24 which is completely divisible by 144
thus from 4! onwards each term will be divisible by 144 and will leave the remainder of 0
now the remainder when R=(1!)^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144 is same as, when 1+8+216 =225 is divided by 144
now remainder when 225 is divided by 144 is 81. hence answer should be D
Question: Alex deposited x dollars into a new account that earned 9 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?
A.w/(1+1.08)
B.w/(1.08+1.16)
C.w/(1.16+1.24)
D.w/(1.09+1.09^2)
Answer: D.w/(1.09+1.09^2)
Explanation: Account at the end of the first year would be 1.09x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.09x+x) dollars. Account at the end of the second year would be (1.09x+x)*1.09=w --> x(1.09^2+1.09)=w --> x=w/(1.09+1.09^2).
Answer: D.
Question: The diagonals of the two squares are in the ratio of 2:5 find the ratio of their area .
A.5:89
B.7:96
C.4:25
D.5:84
Answer: C.4:25
Explanation: Let the diagonals of the square be 2x and 5x respectively .
ratio of their areas =1/2(2x)^2:1/2(5x)
= 4x^2:25x^2=4:25
Answer(C)
Question: A worker's daily wage is increased by 50% and the new wage is $30 per day. What was the worker's daily wage before the increase?
A.$15
B.$18
C.$20
D.$22
Answer: C.$20
Explanation: Let x be the daily wage before the increase.
1.5x = $30
x = $20
The answer is C.
Question: If six persons sit in a row, then the probability that three particular persons are always together is ?
A.1/3
B.1/9
C.1/5
D.1/7
Answer: C.1/5
Explanation: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5
Answer:C
Question: A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 355 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?
A. 90
B. 115
C. 120
D. 130
Answer: B. 115
Explanation: Orchestra Seats - a
Balcony Seats - b
a+b = 355
and 12a + 8b = 3320
Solving equations simultaneously (Multiply Equation 1 with 8 and subtract from second equation)
4a = 3320 - 8*355 = 3320 - 2840 = 480
i.e. a = 120
and b = 355-120 = 235
More seats in balcony than orchestra = b-a = 235 - 120 = 115
Answer: option B
Question: A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.
A.2997
B.1900
C.2887
D.2898
Answer: B.1900
Explanation: 65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74 => 1900.Answer: B
Question: he population of a city is 120,000. If it increases at the rate of 6% per annum, then what will be its population 2 years hence?
A.137787
B.134832
C.139776
D.139728
Answer: B.134832
Explanation: Population after n years = P [1 + (R/100)]2
Population after 2 years = 120000 * [1 + 6/100]2 = (120000 x 53/50 x 53/50) = 134832
ANSWER: B
Question: Three seventh of a number is 12 more than 40% of that number. What will be the 90% of that number?
A.A)148
B.B)210
C.C)189
D.D)248
Answer: C.C)189
Explanation: 3/7 x – 40/100 x = 12
x = 35 * 12
35 * 12 * 90/100 = 378/2 = 189
ANSWER:C
Question: Bob finishes the first half of an exam in one-fifth the time it takes him to finish the second half. If the whole exam takes him an hour, how many minutes does he spend on the first half of the exam?
A.20
B.24
C.27
D.36
Answer: A.20
Explanation: Many times, it is easiest to think of problems like this conceptually (as opposed to formulaically). Conceptually, if the first half of the exam takes 1/5's the time of the second half (6/6's), we can see that the hour the entire exam took to finish can be broken down into sixth's. (Another way to look at this problem is via ratio's - first half is 1:6 and the second half is 5:6). With each sixth of an hour being 10 minutes (60/6), the first half of the exam would have taken 20 minutes. Correct answer is A.
Question: Josh and Dan have a 12 apples each. Together they flip a coin 6 times. For every heads, Josh receives an apple from Dan, and for every tails Dan receives an apple from Josh. After the coin has been flipped 6 times, what is the probability that Josh has more than 12 apples but fewer than 18?
A.1/64
B.15/64
C.21/64
D.21/32
Answer: C.21/64
Explanation: minimum number of times to win is 4 to have more than 12 apples .
coz: if he wins 3 times => he gets 3 apples and give 3 apples ; no change
so he needs to win 4 times OR 5 times
Not 6 times because ,
if he wins 6 times => he gets 6 apples and he will have 18 apples
Now number of ways to win 4 times out of 6 times 6C4
Now number of ways to win 5 times out of 6 times 6C5
Total number of ways 2626 ways
Probability =(6C4) + (6C5)/2^6
=21/64
Answer :C
Question: Bruce and Bhishma are running on a circular track of length 600m. Speed of Bruce is 30 m/s and that of Bhishma is 20 m/s .They start fro the same point at the same time in the same direction. When will they meet again for the first time?
A.30
B.40
C.50
D.60
Answer: D.60
Explanation: Actually Arjun has to make a lead of 600 m, because when Arjun will be 600m ahead of Bhishma, they will be together again as a person when completes the total length it starts retracing he same path and thus Arjun and Bhishma can be together again.
Since , they make a difference of 10 m in 1 second. so, he will create 600m difference in 60 second.
D
Question: 20 marbles were pulled out of a bag of only white marbles, painted black, and then put back in. Then, another 20 marbles were pulled out, of which 1 was black, afterwhich they were all returned to the bag. If the percentage of black marbles pulled out the second time represents their percentage in the bag, how many marbles in total does the bag currently hold?
A.40
B.200
C.380
D.400
Answer: D.400
Explanation: We know that there are 20 black marbles in the bag and this number represent 1/20 th of the number of all marbles in the bag, thus there are total of 20*20=400 marbles.
Answer: D.
Question: In an engineering class that contained 100 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly?
A.4
B.6
C.8
D.12
Answer: C.8
Explanation: 1st Question : Three fifths of the students answered the first question correctly - so 3/5âˆ—100=60
2nd Question : four fifths of the remainder answered the second question correctly so 4/5âˆ—(100âˆ’60)=4/5âˆ—40=32
total students who answered at least one Q correct =60+32=92
so students who answered BOTH incorrectly = 100âˆ’92=8
ANSWER:C
Question: How many multiples of 5 are there between 0 and 358?
A.54
B.75
C.76
D.71
Answer: D.71
Explanation: 5 * 1 = 5
5 * 71 = 355
Total number of multiples = (71 + 1)
= 72
Answer D
Question: Sachin is older than Rahul by 7 years. If the ratio of their ages is 11:9, find the age of Sachin
A.24.5
B.24.8
C.38.5
D.24.88
Answer: C.38.5
Explanation: Explanation:
If Rahul age is x, then Sachin age is x + 7,
so,
9x + 63 = 11x
2x = 63
x = 31.5
So Sachin age is 31.5 + 7 = 38.5
Answer: C) 38.5
Question: A certain company has budgeted $1320 for entertainment expenses for the year, divided into 12 equal monthly allocations. If by the end of the third month, the total amount spent on entertainment was $300, how much was the company under budget or over budget?
A.$60 under budget
B.$30 under budget
C.$30 over budget
D.$60 over budget
Answer: B.$30 under budget
Explanation: The budget for 3 months is (3/12)*$1320 = $330
The company is $30 under budget.
The answer is B.
Question: If Rs.460 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
A.Rs.575
B.Rs.595
C.Rs.590
D.Rs.580
Answer: D.Rs.580
Explanation: 80 = (460*4*R)/100
R = 4.34%
I = (460*6*4.34)/100 = 120
460 + 120 = 580
ANSWER:D
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12200 after a year?
A.3660
B.2881
C.2887
D.9977
Answer: A.3660
Explanation: 6300:4200:10500
3:2:5
3/10 * 12200 = 3660.Answer: A
Question: When N is divided by T, the quotient is S and the remainder is Q. Which of the following expressions is equal to N?
A.ST
B.S + V
C.ST + Q
D.T(S+V)
Answer: C.ST + Q
Explanation: Using the rule dividend = Quotient * divisor + remainder =>ST + Q C is correct
Question: If n divided by 3 has a remainder of 2, what is the remainder when 2 times n is divided by 3?
A.1
B.2
C.3
D.5
Answer: A.1
Explanation: As per question => N=3P+2 for some integer p
hence 2N => 6Q + 4 => remainder => 1 for some integer Q
hence A
Question: If among 5 children there are 2 siblings, in how many ways can the children be seated in a row so that the siblings do not sit together?
A. 38
B. 46
C. 72
D. 86
E. 102
A.38
B.46
C.72
D.86
Answer: C.72
Explanation: Without limitations, 5 children can be seated in 5!=120 ways. Find the number of ways to seat the 5 children so that the siblings DO sit together. The siblings can be regarded as one unit so there are 4! combinations. But within this unit the siblings can sit in two different ways. So the number of ways to seat the 5 children so that the siblings DO sit together is 4!∗2=48. Thus, the number of combinations in which the siblings DO NOT sit together is 120 - 48 = 72.
Answer: C
Question: If the seller selling his goods with the profit of 200 and profit percentage of the good is 50%, then what is the Cost price of that goods.
A.200
B.300
C.400
D.500
Answer: C.400
Explanation: Explanation:
Profit = 200
Profit% = 50% = (Profit/C.P)*100
C.P = (200*100) / 50 = 400. Answer: C
Question: A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the least number you would have to pick, without looking, to be sure of selecting 3 red balls?
A.59
B.33
C.52
D.68
Answer: A.59
Explanation: A
59
The first 56 balls could be of all colours except red. This would leave 8 balls, all of which are red. so any three chosen would be red.
Question: In a school of 300 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
A.54
B.63
C.70
D.42
Answer: A.54
Explanation: 44 + 28 + 10 = 82%
100 – 82 = 18%
300 * 18/100 = 54
ANSWER:A
Question: What percent of 50 is 80?
A.133 1⁄3
B.75
C.160
D.33 1⁄3
Answer: C.160
Explanation: To find out the % of 80 in 50
Do 80/50 = 160%
Answer C)
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
A.1/455
B.1/459
C.1/458
D.1/451
Answer: A.1/455
Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue = ³C₃/¹⁵C₃ = (1 * 3 * 2 * 1)/(15 * 14 * 13) = 1/455
Answer:A
Question: A, B, C hired a car for Rs. 520 and used it for 7, 8 and 11 hours respectively. Hire charges paid by B were?
A.127
B.160
C.287
D.237
Answer: B.160
Explanation: A : B : C = 7 : 8 : 11.
Hire charges paid by B = Rs. (520 * 8/26) = Rs. 160.
Answer: B
Question: A train running at certain speed crosses a stationary engine in 20 seconds. To find out the speed of the train, which of the following information is necessary:
A.Only the length of the train
B.Only the length of the engine
C.Either the length of the train or the length of the engine.
D.Both the length of the train and the length of the engine.
Answer: D.Both the length of the train and the length of the engine.
Explanation: Explanation:
Since the sum of the length of the train and the length of the engine is needed, so both the lengths must be known.
Correct Option : D
Question: what is the compound interest on rs:50,000 for 4 months at the rate of 5% per annum
A.1058.24
B.2006.24
C.838.55
D.848.55
Answer: C.838.55
Explanation: it is monthly compound
rate=5/12% per month
50000*(1+5/1200)^4-50000=838.55
ANSWER:C
Question: Diana picked a number of pears, each of which she sold, canned, or poached. If she canned 60 percent more than she poached, and she poached 50 percent less than she sold. If there were a total of 115 pears, then how many pears did she sell?
A.41
B.44
C.47
D.50
Answer: D.50
Explanation: Let x be the amount of pears that she sold.
Then she poached 0.5x.
Then she canned 1.6*0.5x=0.8x.
The total amount of pears is x+0.5x+0.8x=2.3x
The fraction of pears that she sold is 1/2.3=10/23.
The number of pears she sold is (10/23)*115=50.
The answer is D.
Question: Find a number such that when 15 is subtracted from 7 times the number, the result is 10 more than twice the number.
A.1
B.3
C.5
D.7
Answer: C.5
Explanation: 7x-15=10+2x
7x-2x=25
x=5
ANSWER:C
Question: A and B together can do a work in 6 days. If A alone can do it in 15 days. In how many days can B alone do it?
A.10
B.99
C.77
D.55
Answer: A.10
Explanation: 1/6 – 1/15 = 1/10
=> 10
Answer: A
Question: x =3 4 5
y= 27 36 9 then what is the relation between x and y
A.1*X)^2
B.1*X)^3
C.1*X)^4
D.1*X)^5
Answer: A.1*X)^2
Explanation: Y=(1*X)^2
9=(1*3)^2
9=9
ANSWER:A
Question: Mohan's salary was first increased by 20% and then decreased by 20%. If his present salary is Rs. 7200, then what was his original salary?
A.8789
B.7500
C.8392
D.8390
Answer: B.7500
Explanation: Let Mohan's salary be Rs.100.
When increased by 20%, Mohan's salary = Rs.120
Again when decreased by 20%, Mohan's salary = 120 - 24 = Rs. 96.
But present salary is Rs. 7200
for, 96 ---> 100 ; 7200 ---> ?
Required salary is 7200/96 * 100 = Rs. 7500
Answer:B
Question: How many prime numbers between 100 to 150?
A.10
B.11
C.15
D.14
Answer: B.11
Explanation: primes are of the form 6n+1 or 6n-1
Put n=25 ==> 151
for n=26 ==> 157
for n=27 , ==>163
for n=28 , ==> 167
for n =29 ==> 173
for n =30 ==> 179 and 181
for n =31 ==> no prime no.
for n= 32 ==> 191
for n =33 ==> 199
therefore total number of prime numbers = 11
Ans - B
Question: The ratio of a to b is 4 to 5, where a and b are positive. If x equals a increased by 25 percent of a, and m equals b decreased by 20 percent of b, what is the value of m/x?
A.2/5
B.3/4
C.4/5
D.5/4
Answer: C.4/5
Explanation: x equals a increased by 25 percent of a => x = a + 25%a = 1.25a
m equals b decreased by 20 percent of b => m = b - 20%b = 0.8b
m/x = 0.8b/1.25a
Putting the value of b/a = 5/4 we get m/x = 4/5
ANSWER:C
Question: 2 is what percent of 50
A.2%
B.4%
C.6%
D.8%
Answer: B.4%
Explanation: Explanation:
2/50 * 100 = 1/25 * 100 = 4 %
Option B
Question: If Y = 2Z+1 where Y is an Integer then which of the following is true?
A.Y is always Odd
B.Y is always Even
C.Y is even if Z is a non integer and a multiple of 0.5
D.Y= 1
Answer: C.Y is even if Z is a non integer and a multiple of 0.5
Explanation: C
Question: If 2^z is a factor of 27!, which of the following could be the value of z?
I. 22
II. 23
III. 24
A.I ​ only
B.II only
C.I​ and II
D.I, II, and III
Answer: C.I​ and II
Explanation: 27! contains all numbers from 1 to 27. To find the factor with the highest power of 2, we count the number of multiples of 2, 4, 8 and 16.
Multiples of 2 = 13
Multiples of 4 = 6
Multiples of 8 = 3
Multiples of 16 = 1
Total count = 23
The answer is C.
Question: The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum?
A.640
B.500
C.3000
D.1000
Answer: A.640
Explanation: (P*5*15)/100 - (P*3.5*15)/100 = 144
75P/100 â€“ 52.5P/100 = 144
22.5P = 144 * 100
=> P = Rs.640
ANSWER A
Question: A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 200km less in time. Find his speed?
A.20km/hr
B.30km/hr
C.40km/hr
D.50km/hr
Answer: C.40km/hr
Explanation: Let the speed be x km/hr
50x-50* 9/10 *x = 200
50x - 45x = 200
5x = 200
x = 40km/hr
Answer is C
Question: Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following numbers could be the sum of G and H?
A.153
B.150
C.143
D.141
Answer: D.141
Explanation: Let x be the original 2-digit number.
If each digit is halved, then the sum of G and H is 3x/2.
Note the sum must be a multiple of 3 and less than 150.
Of these five choices, only 141 satisfies these two conditions.
The answer is D.
Question: In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examination?
A.30,000
B.35,000
C.37,000
D.None of these
Answer: A.30,000
Explanation: Solution
Let the number of applicants be x.Number of eligible candidates	= 95% of x.
Eligible candidates of each other categories	= 15% of (95% of x).
=(15/100×95/100×x)
= 57/400×x.
Therefore, 57/400×x	= 4275
‹=› x =(4275×400 / 57)
‹=› 30000
Answer A
Question: The compound and the simple interests on a certain sum at the same rate of interest for two years are Rs.11730 and Rs.10200 respectively. Find the sum
A.Rs.17037
B.Rs.17000
C.Rs.17276
D.Rs.170287
Answer: B.Rs.17000
Explanation: Explanation:
The simple interest for the first year is 10200/2 is Rs.5100 and compound interest for first year also is Rs.5100. The compound interest for second year on Rs.5100 for one year
So rate of the interest = (100 * 1530)/ (5100 * 1) = 30% p.a.
So P = (100 * 10200)/ (30 * 2) = Rs.17000
Answer:B
Question: A sum of money at simple interest amounts to Rs. 820 in 3 years and to Rs. 854 in 4 years. The sum is:
A.647
B.718
C.654
D.847
Answer: B.718
Explanation: S.I. for 1 year = Rs. (854 - 820) = Rs. 34.
S.I. for 3 years = Rs.(34 x 3) = Rs. 102.
Principal = Rs. (820 - 102) = Rs. 718.
Answer:B
Question: On day one, a store sold 86 cups. On each of the next d days, the company sold 50 cups. If the average daily sales of cups over this time period (including day one) is 53 cups, what is the value of d?
A.9
B.10
C.11
D.12
Answer: C.11
Explanation: 86 + 50d = 53(d+1).
3d = 33.
d = 11.
The answer is C.
Question: Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is
A.12
B.13
C.15
D.17
Answer: C.15
Explanation: Explanation:
Let the three integers be x, x+2 and x+4.
Then, 3x = 2(x+4)+3,
x= 11
Therefore, third integer x+4 = 15
Answer: Option C
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
A.6.25
B.7.25
C.7.75
D.7.35
Answer: A.6.25
Explanation: Runs scored in the first 10 overs = 10 × 3.2 = 32
Total runs = 282
Remaining runs to be scored = 282 - 32 = 250
Remaining overs = 40
Run rate needed = 25040=6.25
ANSWER:A
Question: 85 litres of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 800 km using 1200 cc engine?
A.80 litres
B.90 litres
C.120 litres
D.170 litres
Answer: D.170 litres
Explanation: Explanatory Answer
To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 800/600*85= 113.33 litres.
However, the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity.
i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too.
Therefore, with a 1200 cc engine, quantity of diesel required = 1200/800*113.33 = 170 litres.
Answer D
Question: How many ways can 5 friends be arranged around a circular dinner table?
A.A)24
B.B)48
C.C)96
D.D)120
Answer: A.A)24
Explanation: The number of arrangements of n distinct objects in a row is given by n!n!.
The number of arrangements of n distinct objects in a circle is given by (n−1)!(n−1)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
n!n=(n−1)!n!n=(n−1)!.
So, the answer is (5 - 1)! = 4! = 24.
Answer: A.