RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: 20 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.380
C.312
D.324
Answer: B.380
Explanation: Explanation :
He can go in any bus out of the 20 buses.
Hence He can go in 20 ways.
Since he can not come back in the same bus that he used for travelling,
He can return in 19 ways.
Total number of ways = 20 x 19 = 380. Answer : Option B
Question: A man sitting in a train which is traveling at 30 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.?
A.50 kmph
B.82 kmph
C.62 kmph
D.65 kmph
Answer: B.82 kmph
Explanation: Relative speed = 280/9 m / sec = ((280/9)*(18/5)) kmph = 112 kmph.
Speed of goods train = (112 - 30) kmph = 82 kmph.
Answer : B.
Question: The average age of 3 boys is 30 years and their ages are in the proportion 1:2:3. The age of the youngest boy is?
A.15years
B.20years
C.22years
D.25years
Answer: A.15years
Explanation: Total age of 3 boys = 30*3 = 90
ratio of their ages = 1:2:3
Age of the youngest = 90*1/6 = 15 years
Answer is A
Question: In the series 0, 3, 8, 15,__ What is the next number?
A.22
B.23
C.24
D.25
Answer: C.24
Explanation: 3-0=3
8-3=5
15-8=7
difference increasing by 2 every time
next difference 9
15+9=24
ANSWER:C
Question: Machine–A produces 40% of the total output and Machine-B produces 60% of the total output. An average of nine units out of a thousand goods manufactured by Machine-A and one unit of 50 units produced by Machine-B prove to be defective. What is the probability that a unit chosen at random from the total daily output of the factory is defective?
A.a. 0.156
B.b. 0.01506
C.c. 0.0156
D.d. 0.0001566
Answer: C.c. 0.0156
Explanation: Let total Production be 10000 units....
A produces 4000 units and 36 units are defective
B produces 6000 units and 120 units are defective
So, Out of total 10,000 units 156 units are defective...
So the required probability = 156/10000 => 0.0156
Answer will be (C)
Question: In the first hour of a two-hour trip, a car traveled d kilometers, and in the second hour of the trip, the car traveled one that distance. What is the average rate at which the car traveled during the trip, in kilometers per hour?
A. d
B. 1/3*d
C. 1/2*d
D. 3/4*d
Answer: A. d
Explanation: Solution:
Lets look at the information given in the question...
Total time travelled = 2 hrs
Distance travelled first hour = d
Distance travelled second hour = d
The question is asking for the avg speed at which the car travels for 2 hrs
We know that avg speed = total distance/total time
Lets place the information given in the question to the formula above = (d+d)/2
=d
We find that option A is the answer as it gives the same expression as found in our calculation above. Answer option A.
Question: City A and City B are 140 miles apart. Train C departs City A, heading towards City B, at 4:00 and travels at 40 miles per hour. Train D departs City B, heading towards City A, at 4:20 and travels at 20 miles per hour. The trains travel on parallel tracks. At what time do the two trains meet?
A.5:00
B.5:30
C.6:00
D.6:20
Answer: D.6:20
Explanation: Train C has traveled 20 mi in the half hour before Train D has started its journey.
140-20=120
40+20 =60 mph
120 mi/ 60 mph = 2 hrs
4:20pm + 2 hrs = 6:20pm
Answer:
D. 6:20
Question: The rate at which a sum becomes four times of itself in 15 years at S.I., will be :
A.10 %
B.15 %
C.20 %
D.40 %
Answer: C.20 %
Explanation: Sol.
Let sum = x. Then, S.I. = 3x
∴ Rate = [100 * S.I. / P*T] = [100 * 3x / x * 15]% = 20%.
Answer C
Question: Consider a quarter of a circle of radius 25. Let r be the radius of the circle inscribed in this quarter of a circle. Find r.
A.16*(sqr2 -1)
B.8*(sqr3 -1)
C.25*(sqr2 - 1)
D.12* (sqr7 -1)
Answer: C.25*(sqr2 - 1)
Explanation: I got 16/(sqr2 +1) and just forgot to multiply by (sqr2 -1).
Answer is C
Question: 78, 64, 48, 30, 10, (...)
A.-12 number
B.-14
C.2
D.8
Answer: A.-12 number
Explanation: Explanation :
78 - 14 = 64
64 - 16 = 48
48 - 18 = 30
30 - 20 = 10
10 - 22 = -12
Answer : Option A
Question: Find large number from below question The difference of two numbers is 1000. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
A.1345
B.1197
C.1540
D.1600
Answer: B.1197
Explanation: Let the smaller number be x. Then larger number = (x + 1365).
x + 1000 = 6x + 15
5x = 985
x = 197
Large number = 197 +1365 = 1197
B
Question: From the starting point in a boat race, one competitor started to sail north at a speed of 1.3 Km/h, the other competitor started to sail west at a speed of 1.2 Km/h. What is the distance in Km between the two competitors after 5 hours?
A.8.8
B.12.
C.12.5.
D.14.
Answer: A.8.8
Explanation: Both competitors are sailing making angle of 90 degrees.
After 5 hrs one competitor will cover a distance of = 1.3 *5= 6.5 KM
And, other competitor will cover a distance of = 1.2*5= 6KM
distance between them after 5 hrs = (6.5^2+ 6^2)^1/2= 8.8KM
A is the answer
Question: What inequality represents the condition 1<x<5?
A.|x|<3
B.|x+5|<4
C.|x-3|<2
D.|-5+x|<4
Answer: C.|x-3|<2
Explanation: 1<x<5 represents segment with
length: 5-1 = 4
center: (5+1)/2 = 3
For any |x-a|<b a is a center and b is a half of length. So, |x-3|<4/2 represents our inequality (answer C)
Question: The ratio of two quantities is 5 to 6. If each of the quantities is increased by 3, what is the ratio of these two new quantities?
A.2/15
B.7/5
C.9/5
D.It cannot be determined from the information given.
Answer: D.It cannot be determined from the information given.
Explanation: let the actual ratio be 5k/6k, increase numerator and denominator by 4=> 5k+3/6k+3
Until the value of k is unknown we can not determine the actual ratio.
OR
let the actual be 3/4. After increasing 3 => 6/7
let the actual be 6/8. After increasing 3 => 9/11
Therefore without actual quantities we cannot determine the actual ratio.
Answer : D
Question: How many different subsets of the set {0, 1, 2, 3, 4, 5,6,7} do not contain 0?
A.A.16
B.B.72
C.C.93
D.D.32
Answer: C.C.93
Explanation: Number of subset
Since we have 7 digits other than 0, we can take any numbers from the set of 7 to make a subset. Also it is a matter of selection and not arrangement.So we will consider combinations.
7c1+7c2+7c3+7c4+7c5+7c6+7c7=92
And one set is the NULL set having no elements in it so
92+1=93.
ANSWER C.
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
A.4538
B.4529
C.4528
D.4530
Answer: D.4530
Explanation: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls
= 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5
= Rs. 4530
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.09:20p.m
B.04:40p.m
C.10.30p.m
D.02.32p.m
Answer: C.10.30p.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: Two positive integers differ by 4, and sum of their reciprocals is 4. Then one of the numbers is
A.a) 3
B.b) 1
C.2
D.d) 21
Answer: C.2
Explanation: Algebraic approach:
Let n be the smaller integer => 1/n + 1/(n+4) = 4
or ((n+4)+n)/n(n+4) =4 or (n^2+4n)*4 =2n+4 or n=2 as n cannot be -negative
Solve for n => n=2. Hence,
C
Question: C and D started a business investing Rs. 49,000 and Rs. 35,000 respectively. In what ratio the profit earned after 4 years be divided between C and D respectively?
A.7:4
B.7:5
C.6:4
D.5:5
Answer: B.7:5
Explanation: C:D= 49000 : 35000 = 7:5.
ANSWER:B
Question: A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?
A.18 days
B.20 days
C.24 days
D.30 days
Answer: C.24 days
Explanation: Explanation:
2c = ¼ + 1/6 – 1/3 = 1/12
c = 1/24 => 24 days
Answer: C
Question: Look at this series: 97, 97, 97, 87, 87, 87, 77, 77, 77 ... What number should come next?
A.66
B.67
C.68
D.69
Answer: B.67
Explanation: Explanation:
In this series, each number is repeated, then 10 is subtracted to arrive at the next number.
Answer: Option B
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
A.80
B.100
C.25
D.206
Answer: D.206
Explanation: We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).
Required number
of ways	= (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4)
= (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2)
= (24 + 90 + 80 + 15)
= 209.
ANSWER D
Question: The sum of all the integers d such that -26 < d < 24 is
A.0
B.-2
C.-25
D.-49
Answer: D.-49
Explanation: Easy one -
-25, -24, -23,-22,...... -1,0, 1, 2...., 22, 23
Cancel everyhitng and we're left with - -25 and -24 d= -49.
D is the answer.
Question: Of the four numbers, whose average is 80, the first is one-fourth of the sum of the last three. The first number is ?
A.28
B.64
C.11
D.48
Answer: B.64
Explanation: Explanation:
Let the first number be x,
Then, sum of the four numbers = x + 4x = 5x.
so, 5x/4 = 80 or x = (80 * 4) / 5 = 64
Answer: B
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
A.Rs.4532
B.Rs.4526
C.Rs.4598
D.Rs.4530
Answer: D.Rs.4530
Explanation: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls
= 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5
= Rs.4530
Answer:D
Question: In how many different number of ways 4 boys and 2 girls can sit on a bench?
A.700
B.720
C.780
D.800
Answer: B.720
Explanation: npn = n!
6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720
B
Question: The length of a rectangle is three - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 2500 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 15 units?
A.440 sq.units
B.550 sq.units
C.455 sq.units
D.450 sq.units
Answer: D.450 sq.units
Explanation: Given that the area of the square = 2500 sq.units
=> Side of square = âˆš2500 = 50 units
The radius of the circle = side of the square = 50units.
Length of the rectangle = 3/5 * 50 = 30 units
Given that breadth = 15 units
Area of the rectangle = lb = 30 * 15= 450 sq.units
Answer:D
Question: Ramu bought an old car for Rs. 34000. He spent Rs. 12000 on repairs and sold it for Rs. 65000. What is his profit percent?
A.16%
B.17%
C.18%
D.41%
Answer: D.41%
Explanation: Total CP = Rs. 34000 + Rs. 12000
= Rs. 46000 and SP = Rs. 65000
Profit(%)
= (65000 - 46000)/46000 * 100
= 41%
Answer: D
Question: When a plot is sold Rs. 18,700, the owner loses 15%. At what price must the plot be sold in order to gain 15%?
A.Rs. 21,000
B.Rs. 22,500
C.Rs. 25,300
D.Rs. 25,800
Answer: C.Rs. 25,300
Explanation: Solution
85 : 18700 = 115 : x or	x = (18700 x 115 / 85)
= 25300.
Hence, S.P. = Rs. 25300.
Answer C
Question: In a certificate by mistake a candidate gave his height as 25% more than actual height. In the interview panel, he clarified that his height was 5 feet 8 nches. Find the % correction made by the candidate from his stated height to his actual height?
A.10
B.20
C.30
D.17
Answer: D.17
Explanation: His height was = 5 feet 8 inch = 8 + 60 = 68 inch. Required % correction =68*(1.25-1) = 17
D
Question: Three candidates contested an election and received 1136, 7636 and 13628 votes respectively. What percentage of the total votes did the winning candidate got?
A.55%
B.56%
C.57%
D.60.8%
Answer: D.60.8%
Explanation: Total number of votes polled = (1136 + 7636 + 13628) = 22400
So, Required percentage = 13628/22400 * 100 = 60.8%
ANSWER : D
Question: Suppose 8 monkeys take 8 minutes to eat 8 banana's.How many minutes would it take 3 monkeys to eat 3 banana's?
A.5 min
B.6 min
C.7 min
D.8 min
Answer: D.8 min
Explanation: there are equal no. of monkeys and equal no. of bananas and they take equal time and the time is 8 mint to eat a banana so each monkey take 8 mints to eat a banana's so 3 monkeys will take 8 mints to eat 3 banana's.
ANSWER:D
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 6360, what is the length of the plot in metres?
A.333
B.200
C.240
D.276
Answer: C.240
Explanation: Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 6360
[4L - 40] = 6360 / 26.50 = 240
4L = 280
L = 280/4= 70 meters.
Answer: C
Question: A charitable association sold an average of 66 raffle tickets per member. Among the female members, the average was 70 raffle tickets. The male to female ratio of the association is 1:2. What was the average number T of tickets sold by the male members of the association
A.50
B.56
C.58
D.62
Answer: C.58
Explanation: Given that, Total average T sold is 66, Male/Female = 1/2 and Female average is 70. Average of Male members isX.
(70*F+X*M)/(M+F) = 66 -> Solving this equation after substituting 2M=F, X = 58. ANS C.
Question: What is the simplified result of following the steps below in order?
(1)	add 5y to 2w
(2)	multiply the sum by 3
(3)	subtract w + y from the product
A.5w + 14y
B.5x + 16y
C.5x + 5y
D.6x + 4y
Answer: A.5w + 14y
Explanation: 3(5Y+2W) -W-Y= 14Y+5W
'A' is the answer
Question: The length of the bridge, which a train 120 m long and traveling at 45 km/hr can cross in 30 sec is?
A.377
B.367
C.237
D.255
Answer: D.255
Explanation: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (120 + x)/30 = 25/2
x = 255 m.
Answer: D
Question: Paul's income is 20% less than Rex's income, Quentin's income is 20% less than Paul's income, and Sam's income is 40% less than Paul's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?
A.	26/27
B.	13/17
C.	13/19
D.	12/19
Answer: A.	26/27
Explanation: MAKE R = 10
P = 0.8R = 8
Q = 0.8P = 6.4
S= 0.6P = 4.8
FOR THAT WE GET S = 10.8
AND Q 10.4
SO 10.4/10.8= 2.6/2.7
Ans:A
Question: Mercury travels around the Sun at an approximate speed of 28.8 miles per second. This speed is how many kilometers per hour? (1 km = 0.6 miles)
A.172,800
B.124,600
C.93,400
D.72,200
Answer: A.172,800
Explanation: The speed is 28.8 miles/s. Then 28.8/0.6 = 48 km/s
48*3600 = 172,800 kph
The answer is A.
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
A.75%
B.25%
C.28%
D.85%
Answer: B.25%
Explanation: 800 --- 200
100 --- ? => 25%
Answer: B
Question: A man can do a job in 15 days. His father takes 10 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together?
A.6.3
B.6.9
C.7.1
D.6.1
Answer: C.7.1
Explanation: 1 day work of the three persons = (1/15 + 1/10 + 1/25) = 21/150
So, all three together will complete the work in 150/21 = 7.1 days.
Answer:C
Question: A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of B in the profit.
A.2660
B.1000
C.2300
D.4000
Answer: A.2660
Explanation: Explanation :
A is a working member and for that, he receive 5% of the profit
= 5% of 7400 = 5*7400/100 = 370
Remaining amount = 7400-370 = 7030
Ratio of their investments = 6500*6 : 8400*5 : 10000*3
= 65*6 : 84*5 : 100*3 = 13*6 : 84 : 20*3 = 13*2 : 28 : 20
= 13 : 14 : 10
Share of B in the profit = 7030 * (14/37) = 190*14 = 2660. Answer : Option A
Question: Two trains are traveling on a collision course. If train A is traveling at a speed of 350 mph and train B is traveling 28% slower, how much time will it take the trains to collide if the initial distance between the two is 3010 miles?
A.Five hours and 0 minutes.
B.One hour and 10 minutes.
C.Two hours and 25 minutes.
D.Three hours and 15 minutes.
Answer: A.Five hours and 0 minutes.
Explanation: Answer is A. Five hours and 0 minutes.
Since they are racing towards each other, the speed is accumulative, ie. 350 mph + 350*0.72 = 602 (0.72 because the second train is 28% slower)
So time before collision is total distance / total speed = 3010/602 = 5 hours
Question: A and B go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?
A.120 sec
B.176 sec
C.178 sec
D.187 sec
Answer: A.120 sec
Explanation: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 600/ (36 * 5/18) , 600/ (54 * 5 /18) }
= LCM (60, 40) = 120 sec.
Answer: A
Question: When all the students in a school are made to stand in rows of 50, 25 such rows are formed. If the students are made to stand in rows of 30, how many such rows will be formed ?
A.41
B.36
C.38
D.19
Answer: A.41
Explanation: Explanation:
Total number of students = 50 x 25
When arranged in rows of 30, number of rows formed are,
= 41.
Answer: A
Question: A cement mixture is composed of 3 elements. By weight, 1/3 of the mixture is sand, 1/4 of the mixture is water, and the remaining 10 pounds of the mixture is gravel. What is the weight of the entire mixture in pounds?
A.24
B.26
C.28
D.30
Answer: A.24
Explanation: Let the total weight be x.
Sand content= (1/3)x
Water content= (1/4)x
Gravel=x-(1/3)x-(1/4)x=(5/12)x=10
x=24
Then answer will be A=24
Question: Find the least number of 5 digits, which is exactly divisible by 89.
A.27
B.37
C.932
D.12
Answer: A.27
Explanation: ANSWER:A
Question: If a sequence of 8 consecutive odd integers with increasing values has 5 as its 7th term, what is the sum of the terms of the sequence?
A.-8
B.-4
C.0
D.4
Answer: C.0
Explanation: Let x be the first term.
Then x + 12 = 5 and x = -7
The sum is: x + (x+2) +...+ (x+14) =
8x + 2(1+2+...+7) = 8x + 2(7)(8) / 2 = 8(-7) +56 = 0
The answer is C.
Question: A clock store sold a certain clock to a collector for 25 percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at 55 percent of what the collector had paid. The shop then sold the clock again at a profit of 70 percent on its buy-back price. If the difference between the clock's original cost to the shop and the clock's buy-back price was $125, for how much did the shop sell the clock the second time?
A.$500
B.$467.5
C.$935
D.$525.5
Answer: B.$467.5
Explanation: Now, in the question above, lets say the original cost of the clock to store was C$ and then it sold the same to the collector at 25% profit.
This means the clocks' selling price was C (1.25) and this becomes cost price for the collector.
Now, when the collector tries to sell the same clock to the store, the store buys it for 55% the price at which the collector bought it.
Thus, you get = 1.25*0.55*C = 0.6875 C
Furthermore, the store sells the clock for the second time for 70% profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy-back * 1.7 = 1.7 * 0.6875 C
Finally given that C - 0.6875 C = 125 ----> C = 400$
Thus, the cost of the clock the second time around = 1.7*0.6875 C = 1.7 * 0.6875 * 400 = 467.5$. Hence B is the correct answer.
Question: Which one of the following is equal to 3.14×10(6)?
A.314
B.3140
C.3140000
D.None of these
Answer: C.3140000
Explanation: Solution
Given, 3.14 ×106	=3.140000×1000000
= 3140000.
Answer C
Question: Marts income is 60 percent more than Tims income and Tims income is 40 percent less than Juans income. What percentage of Juans income is Marts income
A.124%
B.120 %
C.96 %
D.80 %
Answer: C.96 %
Explanation: Tim=100
Mary's income is 60 percent more than tims income;
Mary's Income = T+0.6T = 1.6T = 1.6*100=160
Tims income is 40 percent less than juans income .
100 is 40% less than Juan's Income
100=J-0.4J
100=0.6J
J = 100/0.6=1000/6
What percentage of juans income is marts income
(160/(1000/6))*100 = (160*6*100)/1000 = 96%
ANSWER:C
Question: 4, 9, 13, 22, 35, ?
A.57
B.70
C.63
D.75
Answer: A.57
Explanation: Sum of two consecutive numbers of the series gives the next number.
Answer : A.
Question: A does 4/5th of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
A.23 days
B.37 days
C.37 ½ days
D.40 days
Answer: C.37 ½ days
Explanation: Explanation:
A can finish the whole work in 20 × 5/4 days = 25 days
A and B together finish the whole work in 5 × 3 days = 15 days
Therefore, B can finish the whole work in 25 B/ 25 + B = 15
25 B = 15 ( 25 + B)= 375 + 15B
10B = 375 and B = 375/10 = 37 ½ days.
Answer: Option C
Question: Two dogsled teams raced across a 500-mile course in Alaska. Team A finished the course in 5 fewer hours than team B. If team A’s average speed was 5 miles per hour greater than that of team B, what was team B’s average speed, in miles per hour?
A.12
B.15
C.18
D.20
Answer: D.20
Explanation: Let v be team B's average speed.
Time = Distance/Rate and the time difference was 5 hours.
500/v - 500/(v+5)= 5
500v + 2500 - 500v = 5(v)(v+5)
500 = (v)(v+5)
(20)(25) = (v)(v+5)
v = 20 mph
The answer is D.
Question: Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15kmph. At what speed must he travel to reach A at 1 PM?
A.10 kmph
B.11 kmph
C.12 kmph
D.14 kmph
Answer: C.12 kmph
Explanation: Let the distance travelled by x km.
Then, x - x = 2
10 15
3x - 2x = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.
10
So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
Required speed = 60 kmph. = 12 kmph.
5
C
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
A.152600m2
B.153500m2
C.153600m2
D.153800m2
Answer: C.153600m2
Explanation: Explanation:
Question seems to be typical, but trust me it is too easy to solve, before solving this, lets analyse how we can solve this.
We are having speed and time so we can calculate the distance or perimeter in this question.
Then by applying the formula of perimeter of rectangle we can get value of length and breadth, So finally can get the area. Lets solve it:
Perimeter = Distance travelled in 8 minutes,
=> Perimeter = 12000/60 * 8 = 1600 meter. [because Distance = Speed * Time]
As per question length is 3x and width is 2x
We know perimeter of rectangle is 2(L+B)
So, 2(3x+2x) = 1600
=> x = 160
So Length = 160*3 = 480 meter
and Width = 160*2 = 320 meter
Finally, Area = length * breadth
= 480 * 320 = 153600
ANSWER IS C
Question: In how many different number of ways 4 boys and 4 girls can sit on a bench?
A.40320
B.42345
C.23456
D.40567
Answer: A.40320
Explanation: npn = n!
8p8 = 8 x 7 x 6 × 5 × 4 × 3 × 2 × 1 = 40320
A)
Question: A can finish a work in 18 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day
A.1/6
B.1/9
C.1/11
D.1/3
Answer: A.1/6
Explanation: A's 1 day work = 1/18
B's 1 day work = 1/9
(A+B)'s one day work = (1/18+1/9)=1/6
Answer: A
Question: If x ≠ 0 and (−y^2 + xy)/x=y+x, which of the following expressions is equal to its opposite?
A.x^2
B.x^2 + y^2
C.y^2
D.(y + x)^2
Answer: B.x^2 + y^2
Explanation: (−y^2 + xy)/x=y+x
=> −y^2 + xy = xy +x^2
=> x^2 + y^2 = 0
Answer B