RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
A.20/89
B.20/9
C.20/7
D.20/6
Answer: C.20/7
Explanation: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.
The time required = d/s = 100/35 = 20/7 sec.
Answer:C
Question: A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 1/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?
A.1/3
B.2/9
C.9/46
D.7/19
Answer: C.9/46
Explanation: The first thing to notice is that A is faster than B and B is faster than C.
Since work is proportional to time, in 1 day lets say if A does 2 works, B does 1 work and C does 2/3rd of a work.
If A works for 2 days, B works for 1 day and C works for only 2/3 of the day.
Therefore total work done = (2*2) + (1*1) + (1/3*1/3) = 46/9
Proportion of work done by B = (1*1) / (46/9) = 9/46
Hence Answer C.
Question: The ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers is 17:325. the value of n is
A.15
B.25
C.35
D.30
Answer: B.25
Explanation: sum of 1st n natural no.s is n(n+1)/2,
sum of sqaures of 1st n natural no.s is n(n+1)(2n+1)/6,
The ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers=n(n+1)(2n+1)*2*2/(n*n*(n+1)*(n+1))
=2(2n+1)/(3n(n+1))
now by hit and trial for the given options,if we put 25 then this will give 17/325
therefore the answer is 25
ANSWER:B
Question: A man’s speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr.The man’s speed against the current is :
A.8.5 km/hr
B.9 km/hr
C.10 km/hr
D.12.5 km/hr
Answer: C.10 km/hr
Explanation: Solution
Man’s rate in still water =(15-2.5) km/hr = 12.5 km/hr.
Man’s rate against the current = (12.5-2.5)km/hr = 10 km/hr. Answer C
Question: If the sum and the difference of two numbers are 20 and 8 respectively, then the difference of their square is
A.12
B.28
C.160
D.180
Answer: C.160
Explanation: Solution
Let the numbers be x and y.
Then, x + y = 20 and x - y = 8.
Therefore,x2 - y2 = (x + y)(x - y)
‹=› 20 x 8
‹=› 160.
Answer C
Question: Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 9 meters, and the interior of tank B has a height of 9 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
A.75%
B.90%
C.100%
D.120%
Answer: B.90%
Explanation: The radius of tank A is 9/(2*pi).
The capacity of tank A is 10*pi*81 / (4*pi^2) = 405 / (2*pi)
The radius of tank B is 10 / (2*pi).
The capacity of tank B is 9*pi*100 / (4*pi^2) = 450 / (2*pi)
Tank A / Tank B = 405/450 = 9/10 = 90%
The answer is B.
Question: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
A.19 1/7 min
B.15 1/7 min
C.17 1/7 min
D.7 1/7 min
Answer: C.17 1/7 min
Explanation: Explanation:
1/20 + 1/30 - 1/40 = 7/120
120/7 = 17 1/7
Answer: Option C
Question: Which of the following number will completely divide (49^15)-1?
A.8
B.6
C.22
D.12
Answer: A.8
Explanation: x^n - 1 will be divisible by x+1 only when n is even.
49^15 - 1 = (7^2)^15 - 1 = 7^30 - 1 which is divisible by 7+1 i.e. 8
Answer is A
Question: A’s speed is 16/15 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?
A.1/8
B.1/16
C.1/15
D.1/32
Answer: B.1/16
Explanation: Let x be the fraction of the distance that B runs.
Let v be the speed at which B runs.
The time should be the same for both runners.
Time = D / (16v/15) = xD/v
(15/16)*D/v = x*D/v
x = 15/16
B should have a head start of 1/16 of the full distance.
The answer is B.
Question: Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 4/7 and that of Ravi is 1/5. Find the probability that both of them are selected.
A.4/35
B.2/3
C.7/35
D.5/7
Answer: A.4/35
Explanation: Let A be the event that Ram is selected and B is the event that Ravi is selected.
P(A) = 4/7
P(B) = 1/5
Let C be the event that both are selected.
P(C) = P(A) x P(B) as A and B are independent events:
= 4/7 x 1/5 = 4/35
ANSWER:A
Question: Express 45 mps in kmph?
A.170
B.160
C.162
D.130
Answer: C.162
Explanation: 45 * 18/5 = 162 kmph
Answer:C
Question: In how many ways, a committee of 5 members can be selected from
6 men and 5 ladies, consisting of 3 men and 2 ladies?
A.100
B.200
C.300
D.400
Answer: B.200
Explanation: (3 men out 6) and (2 ladies out of 5) are to be chosen.
Required number of ways = (6c3x5c2) = [6x5x4/3x2x1] x [5x4/2x1] = 200.
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.4687
B.3899
C.7815
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: Option D
Question: In the xy-coordinate system, line k passes through points (-9m, 0) and (0, 3m). Which of the following is a possible equation of line k?
A.y = -3x + 3m
B.y = 1/3*x - 9m
C.y = 3x + 3m
D.y = 1/3*x + 3m
Answer: D.y = 1/3*x + 3m
Explanation: The slope of the line is 3m/9m=1/3.
The y-intercept is 3m.
the equation of the line is: y = 1/3*x +3m
The answer is D.
Question: Six years ago, the ratio of ages of Kunal and Sagar was 6:5. Four years hence, the ratio of their ages will be 11:10. What is Sagar's age at present?
A.16
B.17
C.8
D.12
Answer: A.16
Explanation: Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.
Then, [(6x + 6) + 4] / [(5x + 6) + 4] = 11/10
10(6x + 10) = 11(5x + 10) => x = 2
Sagar's present age = (5x + 6) = 16 years.Answer: A
Question: Three friends (Sam, Jerry and Guy) are employees of a company. Their respective salaries are in the ratio of 2 : 5 : 7. Jerry and Guy's salaries together is Rs. 6600. By what percent is Guy's salary than that of Sam?
A.250%
B.200%
C.150%
D.350%
Answer: A.250%
Explanation: Explanation:
Let the salaries of A, B, C be 2x, 5x and 7x respectively.
Then,5x + 7x = 6600 => x = 550.
Sam's salary = Rs. 1100, , Jerry's salary = Rs. 2750, and Guy's salary Rs. 3850.
Excess of Guy's salary over Sam's=[ (2750 /1100) x 100] = 250%.
Answer: A
Question: Solve the equation:
A) 16x + 10 – 32 = 35 – 10x - 5,
B) y + 3/2y + 25 = 1/2y + 3/4y – 5/2y + y + 37,
C) 7u – 9 – 3u + 5 = 11u – 6 – 4u
A.2, 48/11, 2/3
B.3, 48/11, 2/3
C.2, 48/11, 2/4
D.4, 48/11, 2/3
Answer: A.2, 48/11, 2/3
Explanation: Solution:
A)We do some of the makred actions and we get
16x – 22 = 30 – 10x
After using rule 2 we find 16x + 10x = 30 + 22
After doing the addition 26x = 52
We find unknown multiplier by dividing the product by the other multiplier.
That is why x = 52/26
Therefore x = 2
B) By analogy with A) we find:
y(1 + 3/2) + 25 = y(1/2 + 3/4 – 5/2 + 1) + 37 <=>
5/2y + 25 = -1/4y + 37 <=> 5/2y + 1/4y = 37 - 25 <=>
11/4y = 12 <=> y = 12.4/11 <=> y = 48/11
C) 4u – 4 = 7u – 6 <=> 6 – 4 = 7u – 4u <=> 2 = 3u <=> u = 2/3
Answer A
Question: A person walks from one end to the other of a 80-meter long moving walkway at a constant rate in 40 seconds, assisted by the walkway. When this person reaches the end, they reverse direction and continue walking with the same speed, but this time it takes 120 seconds because the person is traveling against the direction of the moving walkway. If the walkway were to stop moving, how many seconds would it take this person to walk from one end of the walkway to the other?
A.56
B.60
C.64
D.68
Answer: B.60
Explanation: Let v be the speed of the person and let x be the speed of the walkway.
40(v+x)=80 then 120(v+x)=240
120(v-x)=80
When we add the two equations:
240v=320
v=4/3
time = 80 / (4/3) = 60 seconds
The answer is B.
Question: A group consists of 8 men, 8 women and 4 children. In how many ways can 2 men , 2 women and 1 child selected from the given group?
A.3236
B.3336
C.3436
D.3136
Answer: D.3136
Explanation: Two men, two women and one child can be selected in 8C₂ * 8C2 * 4C₁ ways
8*7/2*1*8*7/2*1*4
=3136 ways
Answer : D
Question: A man can swim in still water at 7.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
A.3
B.2.5
C.2.25
D.1.5
Answer: B.2.5
Explanation: M = 7.5
S = x
DS = 7.5 + x
US = 7.5 - x
7.5 + x = (7.5 - x)2
7.5 + x = 15 -2x
3x = 7.5
x = 2.5
ANSWER:B
Question: The inverse ratio of 3: 5: 1 is?
A.2:3:7
B.5:3:15
C.2:3:2
D.2:3:6
Answer: B.5:3:15
Explanation: 1/3: 1/5: 1/1 = 5:3:15
Answer:B
Question: If a and b are positive numbers, and a^3 + b^3 = 100, then the greatest possible value of a is between:
A.0 and 3
B.3 and 4
C.4 and 5
D.5 and 7
Answer: C.4 and 5
Explanation: If a = 4.5 and b is a bit more than 2, then a^3 + b^3 can equal 100.
If a > 5, then a^3 + b^3 > 100.
The answer is C.
Question: a and b can do a piece of work in 28 days. with the help of c, they can finish it in 21 days .how long will c take to finish it
A.84 days
B.74 days
C.64 days
D.82 days
Answer: A.84 days
Explanation: A + B 's 1 day work = 1/28
A + B + C 's 1 day work = 1/21
1/28 + C= 1/21
C = 1/21 - 1/28
C = 1/84
So C ll finish the work alone in 84 days
ANSWER:A
Question: An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?
A.Rs.4086.40
B.Rs.4882.40
C.Rs.4089.40
D.Rs.4082.40
Answer: D.Rs.4082.40
Explanation: Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04)
= 4095 - 12.6
= Rs.4082.40
Answer:D
Question: A recipe for a large batch of fruit juice at a factory calls for 10% oranges, 20% lemons, and 70% limes. if 35 limes are used, how many oranges are needed?
A.2
B.5
C.10
D.40
Answer: B.5
Explanation: 70%= 35 fruit
100%=50 fruit
10% of 50 fruit=5 fruit
5 oranges
ANSWER:B
Question: {-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number will be a solution to the equation (x-9)(x+8)(2X+5) = 0?
A.1/12
B.1/6
C.1/4
D.1/3
Answer: A.1/12
Explanation: x = -1
Prob = 1/12
Answer - A
Question: 193,194,207,.....?
A.340
B.341
C.342
D.343
Answer: C.342
Explanation: first increment is by 1 which is the first odd number second increment is by 13 in this 2nd term is 3 which is second odd number the next increment should be by 135 in this the third term is 5 which is third odd number .Thus 342 is the answer.
ANSWER:C
Question: A, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1480?
A.228
B.217
C.100
D.288
Answer: C.100
Explanation: 3x 4x 5x
6 9 4
18x + 36x + 20x = 1480
74x = 1480 => x = 20
5x = 100 Rs.
Answer: C
Question: A man complete a journey in 10 hours. 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.121 KM
B.242 KM
C.224 KM
D.112 KM
Answer: B.242 KM
Explanation: AVERAGE SPEED = 2*21*24/21+24 = 22.4 KM/HR
TOTAL DIST = 22.4 * 10 =224 KM
DIST = SPEED * TIME
LET TIME TO TRAVEL THE FIRST HALF = X HR
THEN TIME = (10-X) HR
DIST COVERED IN FIRST HALF = 21X
DISTANCE COVERED IN SECOND HALF = 24(10-X)
BUT DISTANCE COVERED BOTH EQUAL
21X = 24(10-X)
X=16/3
HENCE 21X = 21 * 16/3 = 7 * 16 = 112 KM TOTAL DIST = 2 * 112 = 224 KM
ANSWER B
Question: A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start at same point at 7:30 am. They shall first cross each other at ?
A.7:15 am
B.7:30 am
C.7: 42 am
D.7:50 am
Answer: C.7: 42 am
Explanation: Explanation:
Relative speed between two = 6-1 = 5 round per hour
They will cross when one round will complete with relative speed,
which is 1/5 hour = 12 mins.
So 7:30 + 12 mins = 7:42
Option C
Question: Pipes A and B can fill a tank in 6 and 8 hours. Pipe C can empty it in 4 hours. If all pipes are opened together, then the tank will be filled in?
A.3/2hr
B.24hr
C.22hr
D.20hr
Answer: B.24hr
Explanation: Net part filled in 1 hour = 1/6 + 1/8 - 1/4 = 1/24
The tank will be full in 24 hr
Answer is B
Question: John purchased a fridge and a mobile for Rs. 15000 &Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit.
A.Rs. 100
B.Rs. 130
C.Rs. 200
D.Rs. 230
Answer: C.Rs. 200
Explanation: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200
As this is positive, an overall profit of Rs. 200 was made.
C
Question: The side of a square is increased by 25% then how much % does its area increases?
A.56.25 %
B.56.25 %
C.56.85 %
D.52.25 %
Answer: B.56.25 %
Explanation: a = 100 a2 = 10000
a = 125 a2 = 15625
----------------
10000 --------- 5625
100 -------? => 56.25 %
Answer:B
Question: (X)+3612+16125-6149=90189. Calculate the value of X
A.76601
B.76600
C.76655
D.76313
Answer: A.76601
Explanation: x+3612+16125-6149=90189
=x+3612+16125=90189+6149
=x+19737=96338
=x=96338-19737
=76601
Answer is A
Question: There are 10 magazines lying on a table; 5 are fashion magazines and the other 5 are sports magzines. If 4 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazine will be selected?
A.60/61
B.40/42
C.41/42
D.45/46
Answer: C.41/42
Explanation: 1- (5c4/10c4) = 1-1/42 = 41/42
Answer : C
Question: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 60. What is the total number of students in the school?
A.72
B.80
C.125
D.150
Answer: C.125
Explanation: Explanation: Let the number of students be x.
Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x.
80% of x = 60 + 2/3 of 60
80/100x = 100
x = 125.
Answer: Option C
Question: On an order of 9 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of:
A.10%
B.15%
C.20%
D.25%
Answer: A.10%
Explanation: Clearly, the retailer gets 1 dozen out of 10 dozens free.
Equivalent discount = 1/10 * 100 = 10%.
Answer A) 10%
Question: How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest ?
A.3.5 years
B.4 years
C.4.5 years
D.5 years
Answer: B.4 years
Explanation: Solution
Time =(100*81/450*4.5) years =4 years
Answer B
Question: For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 100?
A.30
B.28
C.27
D.25
Answer: D.25
Explanation: 4n+7 > 1
4n> -6
n > -(3/2)
n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity)
From second constraint
4n+7 < 100
4n< 93
n < 23. 25
n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 23)
Combining the two
-1.5 < n<23.25
n = 1 to 23 (23 integers)
and n = -1 and 0
so 25 integers.
D is the answer
Question: A cricket player whose bowling average was 22.5 runs per wicket, takes 5 wicket for 52 runs in a match. Due to this his average decreases by 0.5. What will be the number of wickets taken by him till the last match?
A.64
B.72
C.121
D.984
Answer: C.121
Explanation: Average = Total Runs / Total wickets
Total runs after last match = 22.5w + 52
Total wickets after last match = w + 5
(22.5w + 52) / (w + 5) = 22.5 - 0.5 = 22
w = 116
so total wickets aftr last match = w+5 = 121
ANSWER:C
Question: There has been a successive increase of 25% and 20% in the price of petrol from the previous month. By how much %age a man should reduce his consumption so that his expenditure does not change?
A.33.33%
B.50%
C.66.66%
D.15%
Answer: A.33.33%
Explanation: Earlier price of petrol = x
Current price of petrol = (5/4) * (6/5) * x = 1.5x
Let earlier Consumption = 100 gallons
Earlier: x dollars --> 100 gallons
Now: 1.5x dollars --> 100 gallons --> x dollars --> 100*2/3 = 66.66 gallons
Therefore the person should reduce his consumption by 100 - 66.66 = 33.33 gallons if his expenditure has to remain same.
Answer: A
Question: In an office, totally there are 5200 employees and 45% of the total employees are males. 50% of the males in the office are at-least 50 years old. Find the number of males aged below 50 years?
A.1040
B.1170
C.1150
D.4160
Answer: B.1170
Explanation: Number of male employees = 5200* 45/100 = 2340
Required number of male employees who are less than 50 years old = 4160 * (100 - 50)%
= 2340* 50/100 = 1170.
ANSWER:B
Question: In how many different ways can 4 physics, 2 math and 3 chemistry books be arranged in a row so that all books of the same branch are together?
A.1242
B.1728
C.1484
D.1734
Answer: B.1728
Explanation: Soln:
= 3! * 4! * 2! * 3!
= 1728
Ans is B
Question: In the floor of a particular kitchen owned by an abstract artist, each row of tiles to the right of the first row contains two fewer tiles than the row directly to its left. If there are nine rows in all and a total of 405 tiles in the floor, how many tiles does the leftmost row contain?
A.53
B.56
C.60
D.64
Answer: A.53
Explanation: This question can be solved in a variety of ways: with algebra, by TESTing THE ANSWERS and by using a great Number Property shortcut involving consecutive integers.
We're given a few facts to work with:
1) There are 9 rows of tiles.
2) When going from 'left to right', each row contains TWO FEWER tiles than the one next to it.
3) There are a total of 405 tiles
We're asked how many tiles the left-most most row holds (meaning the one with the MOST tiles).
To start, 405 is divisible by 9, so we can figure out the AVERAGE number of tiles per row. That is 405/9 = 45. Since we're dealing with a set of 9 consecutive integers that differ by 2 each, we know that the '5th row' will have 45 tiles (the average). Then we just have to 'add 2s' until we get to the first row...
45 +2 +2 +2 +2 = 53.
Final Answer:
A
Question: A train runs at the speed of 72 kmph and crosses a 250 metre long platform in 26 seconds. What is the length of the train?
A.270 m
B.200 m
C.400 m
D.340 m
Answer: A.270 m
Explanation: speed = 72 * 5/18 = 20 m/s
length of the train - x m
distance covered = 250 + x
time = 26 s
250+x/26=20
250+x=26*20=520
x=520-250=270
ANSWER A
Question: Three numbers are in the ratio 3:5:7. The largest number value is 42. Find difference between Smallest & largest number is?
A.20
B.24
C.26
D.28
Answer: B.24
Explanation: == 3:5:7
Total parts = 15
= The largest number value is 42
= The largest number is = 7
= Then 7 parts -----> 42 ( 7 * 6 = 42 )
= smallest number = 3 & Largest number = 7
= Difference between smallest number & largest number is = 7 - 3 = 4
= Then 4 parts -----> 24 (4 * 6 = 24)
B
Question: Speed of a boat in standing water is 8kmph and speed of the stream is 0.5kmph. A man can rows to a place at a distance of 105km and comes back to the starting point. The total time taken by him is?
A.27.35hours
B.26.35hours
C.25.35hours
D.24.35hours
Answer: B.26.35hours
Explanation: Speed upstream = 7.5kmph
Speed downstream = 8.5kmph
Total time taken = 105/7.5 + 105/8.5 = 26.35 hours
Answer is B
Question: A teacher will pick a group of 4 students from a group of 8 students that includes Lisa. If one of all the possible four-student groups is picked at random, what is the probability of picking a group that includes Lisa?
A.1/7
B.3/14
C.1/2
D.1/3
Answer: C.1/2
Explanation: Probability = Favorable Outcomes / Total Outcomes
Total Outcomes= Total No. of ways of Picking Group of 4 out of 8 = 8C4 = 8! / (4! * 4!) = 70
Favorable Outcomes= Total No. of ways of Picking Group of 4 out of 8 such that L is always in the group (i.e. we only have to pick remaining 3 out of remaining 7 as L must be there in group) = 7C3 = 35
Hence,Probability=35/70=1/2
Answer: Option C
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. What is the duration of the flight ?
A.3 hours
B.2.4 hours
C.1.4 hours
D.1 hour
Answer: D.1 hour
Explanation: Explanation:
Let the duration of the flight be x hours.
Then
600/x−600 /x+1/2=200
600/x−1200 /2x+1=200
x(2x+1)=3
2x2+x−3=0
=>(2x+3)(x−1)=0
Neglecting the negative value for x we get x = 1
Option D
Question: The average monthly income of P and Q is Rs. 2050. The average monthly income of Q and R is Rs. 5250 and the average monthly income of P and R is Rs. 6200. The monthly income ofQ is:
A.1100
B.2100
C.1200
D.3100
Answer: A.1100
Explanation: Explanation:
Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (2050 x 2) = 4100 .... (i)
Q + R = (5250 x 2) = 10500 .... (ii)
P + R = (6200 x 2) = 12400 .... (iii)
Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 27000 or P + Q + R = 13500 .... (iv)
Subtracting (iii) from (iv), we get P = 1100.
P's monthly income = Rs. 1100.
Answer: A
Question: A man sitting in a train which is traveling at 50 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.52 kmph
B.56 kmph
C.58 kmph
D.62 kmph
Answer: D.62 kmph
Explanation: Explanation:
Relative speed = 280/9 m / sec = ((280/9)×(18/5)) kmph = 112 kmph.
Speed of goods train = (112 - 50) kmph = 62 kmph
Answer: Option D
Question: If 2994 Ã· 14.5 = 177, then 29.94 Ã· 1.45 = ?
A.17.1
B.17.3
C.17.5
D.17.7
Answer: D.17.7
Explanation: 29.94/ 1.45 = 299.4/14.5
= (2994/14.5) x 1/10) [ Here, Substitute 177 in the place of 2994/14.5 ]
= 177/10
= 17.7
Answer is D.
Question: A certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour. If the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end, then what percent of the tank was used to travel 80 miles at 60 mph?
A.15%
B.20%
C.25%
D.30%
Answer: B.20%
Explanation: otal time for travelling 80 miles @ 60 mph = 80/60 = 4/3 hour = 80 minutes.
Given, the car uses 1 gallon for every 40 minutes of driving @ 60 mph. Thus in 80 minutes it will use = 2 gallons. Thus, full tank = 2+8 = 10 gallons ---> 2/10 = 20% of the fuel used. B is the correct answer.
Question: In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors C?
A.2
B.3
C.5
D.6
Answer: B.3
Explanation: I like to put the numbers in prime factors so it is easier and faster to visualize.
14*n/60
If we write the factors of 14 --> 2, 7, and the factors of 60 --> 2, 2, 3, 5, we have
(2*7*n)/(2^2*3*5)
Simplifying
7*n/(2*3*5)
The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7.
The number could be 2*3*5, or 2*3*5*2, or 2*3*5*.....
However to be less than 200 we can not add any prime number.
2*3*5 = 120
If we added the next prime factor 7, we would have C=2*3*5*7 = 840
Thus, answer B
Question: The area of a triangle will be when a = 1m, b = 4m, c = 5m, a, b, c being lengths of respective sides?
A.2
B.7
C.5
D.3
Answer: C.5
Explanation: S = (1 + 4 + 5)/2
= 5
Answer: C