mathewhe/aqua_rat huggingface dataset:
Question: The average of runs of a cricket player of 10 innings was 18. 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) 62
(D) 76
(E) 17
Rationale: Average after 11 innings = 22
Required number of runs
= (33* 11) - (18* 10) = 242 - 180
= 62.
Answer: C
Answer: (C) 62
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 3520 cm is?
(A) 22
(B) 28
(C) 17
(D) 12
(E) 40
Rationale: 2 * 22/7 * 14 * x = 3520 => x = 40
Answer: E
Answer: (E) 40
Question: A certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 5:3. The ratio of economy cars to sport utility vehicles is 4:3. What is the ratio of luxury cars to sport utility vehicles?
(A) 12:15
(B) 8:9
(C) 3:2
(D) 2:3
(E) 1:2
Rationale: The ratio of economy to luxury cars is 5:3 --> E:L = 5:3 = 20:12.
The ratio of economy cars to sport utility vehicles is 4:3 --> E:S = 4:3 = 20:15.
Thus, L:S = 12:15.
Answer: A.
Answer: (A) 12:15
Question: Graph G has a line of symmetry of x = –2. Graph G passes through the point (3, 3). What is the x-coordinate of another point that must have a y-coordinate of 3?
(A)  –8
(B)  –7
(C)  –5
(D)  –4
(E)  2
Rationale: Line of symmetry is X=-2; one point is (3,3)
Right side distance =2+3(distance from origin) = 5; therefore Left side distance should be same from line of symmetry =5;
therefore left side co-ordinate=5+ 2(distance from origin) = 7; as the X coordinate is in 2nd quadrant hence -7
Therefore answer is B
Answer: (B)  –7
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 44 kg, then the weight of B is:
(A) 31 kg
(B) 32 kg
(C) 33 kg
(D) 34 kg
(E) None of these
Rationale: Explanation:
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 …. (i)
A + B = (40 x 2) = 80 …. (ii)
B + C = (44 x 2) = 88 ….(iii)
Adding (ii) and (iii), we get: A + 2B + C = 168 …. (iv)
Subtracting (i) from (iv), we get : B = 33.
B’s weight = 33 kg.
Answer: C
Answer: (C) 33 kg
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $46. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
(A) xy/360
(B) 9xy/40
(C) 40xy/9
(D) 414xy
(E) 414/(xy)
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 46 / (xy/9) = 414/(xy).
The answer is E.
Answer: (E) 414/(xy)
Question: Find the L.C.M of 16,24,36,54
(A) 528
(B) 432
(C) 528
(D) 456
(E) 741
Rationale: The l.c.m of 16,24,36,54=2^4*3^3=432
Answer(B)
Answer: (B) 432
Question: A man wears socks of two colours - Black and brown. He has altogether 20 black socks and 20 brown socks in a drawer. Supposing he has to take out the socks in the dark, how many must he take out to be sure that he has a matching pair ?
(A) 3
(B) 20
(C) 39
(D) 45
(E) None of these
Rationale: Explanation:
Since there are socks of only two colours, so two out of any three socks must always be of the same colour.
Answer: A
Answer: (A) 3
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
(A) 31/32
(B) 31/39
(C) 31/31
(D) 61/32
(E) 32/39
Rationale: Explanation:
Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
Answer:A
Answer: (A) 31/32
Question: A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 6 minutes?
(A) 36
(B) 54
(C) 108
(D) 216
(E) 324
Rationale: Direct Relationship:-
1 standard Veggiematik machine - 36 Carrots - 4 minutes,
1 standard Veggiematik machine - 9 Carrots - 1 minute,
Now
6 standard Veggiematik machine - ? Carrots - 6 minutes,
Hence = 9X6X6 =324 Carrots
Answer E
Answer: (E) 324
Question: In Township K, 1/5 of the housing units are equiped with cable Tv. If 1/15 of the housing units, including 1/3 of those that are equiped with cable tv, are equipped with videocassette recorders, what fraction of the housing units have neither cable tv nor videocassette recorders?
(A) 23/30
(B) 11/15
(C) 7/10
(D) 4/5
(E) 2/15
Rationale: 1/5 -- cable TV (This includes some data from video cassette recorder)
1/15 -- video cassette recorder including 1/3(equiped with cable tv) i.e. 1/3(1/5) = 1/15
therefore only video cassette recorder = 1/15 - 1/15 = 0
Total = 1/5+0+neither cable tv nor videocassette recorders
1 = 1/5 + neither cable tv nor videocassette recorders
therefore neither cable tv nor videocassette recorders = 1-1/5 = 4/5
Hence D.
Answer: (D) 4/5
Question: Harry started a 7-mile hike with a full 9-cup canteen of water and finished the hike in 2 hours with 3 cup of water remaining in the canteen. If the canteen leaked at the rate of 1 cup per hour and Harry drank 2 cups of water during the last mile, how many cups did he drink per mile during the first 6 miles of the hike?
(A) 1/6
(B) 2/6
(C) 3/6
(D) 4/6
(E) 5/6
Rationale: No of cups leaked during the trip = 2 cups.
No of cups Harry drank = 6 cups.
No of cups harry drank during the first 6 miles = 4.
drink / mile = 4/6
Answer D
Answer: (D) 4/6
Question: If a cloth merchant sells ‘a’ metres of cloth for Rs.x, then what is the selling price of ‘b’ metres of cloth?
(A) Rs.(b*x)
(B) Rs.{(b*x)/a}
(C) Rs.{(a*b)/x}
(D) None of these
(E) Cannot be determined
Rationale: Explanation:
Cost of ‘a’ metres of cloth = Rs.x. Therefore, each metre of cloth costs Rs. (x/a).
The cost of ‘b’ metres of cloth = Rs. b*(x/a) = Rs. {(b*x)/a}
ANSWER B
Answer: (B) Rs.{(b*x)/a}
Question: In how many different ways can three letters be posted from seven different postboxes assuming no two letters can be posted from the same postbox?
(A) 110
(B) 210
(C) 310
(D) 410
(E) 510
Rationale: First letter could be sent from ANY of the seven postboxes - 7 (7 options);
Second letter could be sent from the SIX postboxes left - 6 (6 options);
Third letter could be sent from the FIVE postboxes left - 5 (5 options);
Total # of ways =7*6*5=210
ANSWER:B
Answer: (B) 210
Question: A boat can travel with a speed of 12 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.
(A) 4.25 hr
(B) 5.25 hr
(C) 8.25 hr
(D) 2.25 hr
(E) 2.50 hr
Rationale: speed of boat in still water = 12 km/hr
speed of the stream = 4 km/hr
Speed downstream = (12+4) = 16 km/hr
Time taken to travel 68 km downstream = 68⁄16 = 17⁄4 = 4.25 hours
Answer is A
Answer: (A) 4.25 hr
Question: what is a percent of b divided by b percent of a?
(a) a (b) b (c) 1 (d) 10 (d) 100
(A) 1
(B) 7
(C) 19
(D) 2
(E) 3
Rationale: a percent of b : (a/100) * b
b percent of a : (b/100) * a
a percent of b divided by b percent of a : ((a / 100 )*b) / (b/100) * a )) = 1
Answer:A
Answer: (A) 1
Question: At what time between 5.30 and 6 will the hands of a clock be at right angles?
(A) 40 min. past 5
(B) 42 min. past 5
(C) 43 4/11 min past 5
(D) 43 7/11 min. past 5
(E) None
Rationale: Sol.
At 5 o’clock, the hands are 24 min. spaces apart.
To be at right angles and that too between 5.30 and 6, the minute hand hasto gain (25 + 15) = 40 min. spaces.
55 min. spaces are gained in 60 min.
40 min. spaces are gained in [60/55 * 40] min. = 43 7/11 min.
∴ Required time = 43 7/11 min. past 5.
Answer D
Answer: (D) 43 7/11 min. past 5
Question: Pipe A can fill a tank in 15 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes?
(A) 18
(B) 27
(C) 98
(D) 27
(E) 24
Rationale: Let the pipe B be closed after x minutes.
30/15 - x/24 = 1 => x/24 = 30/15 - 1 = 1
=> x = 1* 24
= 24.
Answer:E
Answer: (E) 24
Question: A box contains four light out of which 2 are defective. If two light are chosen at random, find the probability that all the two light are defective?
(A) 2/7
(B) 3/8
(C) 1/9
(D) 3/7
(E) 1/6
Rationale: Out of nine light , five are good and four are defective.
Required probability = 2C2/4C2 = 1/6
E
Answer: (E) 1/6
Question: a car runs 10,000 miles using 5 tyres interchangably. to have equal wornout by all tyres, how many miles each tyre should have run?
(A) 7000 miles
(B) 8000 miles
(C) 9000 miles
(D) 6000 miles
(E) 5000 miles
Rationale: simply 10000*4/5=8000
or
take a,b,c,d,e are tyres then each tyre travells 8000 miles first car runs with
a,b,c,d for 2000 miles
b,c,d,e for 2000 miles
a,c,d,e for 2000 miles
a,b,d,e for 2000 miles
a,b,c,e for 2000 miles
so total distance travelled is 10000 miles and each tyre travells 8000 miles
ANSWER:B
Answer: (B) 8000 miles
Question: The rate of Interest on a sum of money is 9% p.a. for the first 3 years, 4% p.a. for the next 4 years, and 5% for the period beyond 7 years. If the S.I, Occured on the sum for the total period of 8 years is Rs. 540/-, the sum is
(A) 1,125
(B) 2,000
(C) 2,100
(D) 2,250
(E) 2,540
Rationale: Explanation:
I1 = (P x 3 x 9)/100 = 10P/37
I2 = (P x 4 x 4)/100 = 4P/25
I3 = (P x 1 x 5)/100 = P/20
10P/37 + 4P/25 + P/20 = 540
12P/25 = 540
P = 1125
Answer: Option A
Answer: (A) 1,125
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 140 marks, the no of questions he attempts correctly is :
(A) A)35
(B) B)38
(C) C)90
(D) D)88
(E) E)40
Rationale: Let the number of correct answers be X.
Number of incorrect answers = (60 – X).
4x – (60 – x) = 140
=> 5x = 200
=> x = 40
Answer:E
Answer: (E) E)40
Question: If there are 4 peanuts in a box and Mary puts 8 more peanuts inside, how many peanuts are in the box?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: 8+4=12
correct answer is E)12
Answer: (E) 12
Question: The cost of an item was reduced from its usual selling price of $23.99 to $15.99. Which of the following is closest to the percent decrease in the price of the item?
(A) 17%
(B) 21%
(C) 24%
(D) 25%
(E) 33%
Rationale: The price decreased by 23.99 - 15.99 = $8.
$8 is a bit more than 33% of original price of $24.
Answer: E.
Answer: (E) 33%
Question: If x^3 + y^3 = 200, then the greatest possible value of x is between
(A) 2 and 3
(B) 3 and 4
(C) 4 and 5
(D) 5 and 6
(E) 7 and 8
Rationale: for the greatest possible value of x^3, we must minimize the value of y^3 i.e. lets say y^3 = 0
then we need to find a number x such that x^3 < 200. 5^3 = 125 and 6^3 = 216 so we can say that the maximum possible value of x can be a little more than 5 hence answer = between 5 and 6
hence D
Answer: (D) 5 and 6
Question: Mixture W is 20% oil and 80% material B by weight. If 2 more kilograms of oil are added to the 8 kilograms mixture W, how many kilograms of mixture W must be added to make a 70% material B in the new mixture?
(A) A)6
(B) B)7
(C) C)8
(D) D)9
(E) E)10
Rationale: Can be done with weighted avg method.
if 2 kg more of oil is added to 20% oil of 8 kg mix,then a 10kg of mix will have 3.6kg (or 36%) of oil .
W1=20(initial mix.)
Avg. is what we need..ie 70% of material B means 30% of oil
W2=36(36% of 10 kg mix)
w1/w2=(W2-Avg)/(Avg-W1)
(36-30)/(30-20)
6/10
means for every 10 kg of new mix. we need 6 kg of mix W
Ans A
Answer: (A) A)6
Question: A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 126.Find the number of notes of Rs.50 denomination.
(A) 115
(B) 121
(C) 117
(D) 119
(E) 121
Rationale: Total Money = Rs. 10350.
Let 50 rupees note was X.
Then 500 rupees note = 126 - X
Now,
50*X + 500 * (126 - X) = 10350
50X + 63000 - 500X = 10350
- 450X = - 52650
X = 117.
No. of 50 rupees note = 117.
Answer: Option C
Answer: (C) 117
Question: Eight friends go to see a movie at the local movie theater and sit in a row together. If there are two friends who refuse to sit next to each other, how many 8-person seating arrangements are possible?
(A) 5040
(B) 15,120
(C) 30,240
(D) 35,280
(E) 40,320
Rationale: The number of ways to arrange 8 people in a row is 8!
From this we want to subtract all the arrangements where the two friends are next to each other. If we consider them as one unit, then the number of arrangements of this 2-person unit and the 6 other friends is 7! And the number of arrangements of the two friends within this unit are 2 because the two friends can switch places. So the total number of arrangements of the 8 friends with the 2-person unit together is 7!*2
The total number of permutations where these two friends are not seated next to each other is 8! - 7!*2 = 6*7! = 30,240
The answer is C.
Answer: (C) 30,240
Question: A baseball pitcher won 80% of the games he pitched. If he pitched 35
ballgames, how many games did he win?
(A) 21
(B) 23
(C) 25
(D) 28
(E) 30
Rationale: 80% of 35 is what?
80/100=/35
100)28/2800
28 games
correct answer D
Answer: (D) 28
Question: some money is distributed among A,B,C,D in the proportion of 1:3:4:2. If C gets $50 more than D, What is B's share?
(A) 50
(B) 100
(C) 75
(D) 27
(E) 30
Rationale: Let the share of A,B,C,D be 1x, 3x, 4x, 2x
then 4x-2x =50
2x=50
x= 25
B's share = 3*25 = $75
Answer is C
Answer: (C) 75
Question: If ghi < 0 and hi > 0, which of the following must be positive?
(A)  xy
(B)  xz
(C)  (g^2)hi
(D)  g(h^2)i
(E)  xy(z^2)
Rationale: Given that hi is positive and ghi is negative, you can say that g MUST be negative. As for h and i either they are both positive or both negative.
Option (C) has g^2 which is positive and hi which is positive. So (C) must be positive.
Answer: (C)  (g^2)hi
Question: If x is 20 percent greater than 52, then x =
(A) 68
(B) 62.4
(C) 86
(D) 72.8
(E) 108
Rationale: X is 20% greater than 52 means X is 1.2 times 52 (in other words 52 + 20/100 * 52 = 1.2 * 52)
Therefore, X = 1.2 * 88 = 62.4
ANSWER:B
Answer: (B) 62.4
Question: If a coin is tossed 7 times what is the probability that it will land either heads 7 times or tails 7 times?
(A) 1/4
(B) 1/8
(C) 1/16
(D) 1/32
(E) 1/64
Rationale: The probability of 7 heads is (1/2)^7 = 1/128
The probability of 7 tails is (1/2)^7 = 1/128
The probability of 7 heads or 7 tails is 1/128 + 1/128 = 1/64
The answer is E.
Answer: (E) 1/64
Question: A rectangular courtyard 3.78 meters long 5.25 meters wide is to be paved exactly with square tiles, all of the same size. what is the largest size of the tile which could be used for the purpose?
(A) 14 cms
(B) 21 cms
(C) 42 cms
(D) None of these
(E) 56 cms
Rationale: Explanation:
3.78 meters =378 cm = 2 × 3 × 3 × 3 × 7
5.25 meters=525 cm = 5 × 5 × 3 × 7
Hence common factors are 3 and 7
Hence LCM = 3 × 7 = 21
Hence largest size of square tiles that can be paved exactly with square tiles is 21 cm. Answer: B
Answer: (B) 21 cms
Question: If there are 9 horizontal lines and 9 vertical lines in a chess board, how many rectangles can be formed in the chess board?
(A) 1200
(B) 1245
(C) 1296
(D) 1340
(E) 1450
Rationale: Number of rectangles that can be formed by using m horizontal lines and n vertical lines
= mC2 × nC2
Here m = 9, n = 9
Hence, number of rectangles that can be formed
= mC2 × nC2
= 9C2 × 9C2 = (9C2)2
=(9×82×1)2=362=1296=(9×82×1)2=362=1296
ANSWER C 1296
Answer: (C) 1296
Question: The perimeter of a triangle is 39 cm and the inradius of the triangle is 1.5 cm. What is the area of the triangle?
(A) 22
(B) 35
(C) 77
(D) 54
(E) 29
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 1.5 * 39/2
= 29 cm2
Answer:E
Answer: (E) 29
Question: Approximately what percentage of the world’s forested area is represented by Finland given that Finland has 53.42 million hectares of forested land of the world’s 8.076 billion hectares of forested land.
(A) 0.0066%
(B) 0.066%
(C) 0.66%
(D) 6.6%
(E) 66%
Rationale: Since 1 billion is 1000 million
Soc changing all quantities to million
Finland forest area =53.42 million hect.
Worlds's forest area =8.076 billion hect.
% =53.42*100/8.076*1000 =0.66%
Answer C
Answer: (C) 0.66%
Question: Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 8 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?
(A) 22 km
(B) 20 km
(C) 44 km
(D) 18 km
(E) 16 km
Rationale: Distance = Relative Speed * Time
= (8 + 3) * 4 = 44 km
[ They are travelling in the opposite direction, relative speed
= sum of the speeds].
Answer: C
Answer: (C) 44 km
Question: 8 men can dig a pit in 20 days.If a men work half as much again as a boy,then 4 men and 9 boys can dig a similar pit.Fint the days for 15 boys can dig?
(A) 17
(B) 10
(C) 15
(D) 20
(E) 16
Rationale: 1 man=3/2 boys
(4 men+9 boys)=15 boys
8 men=[(3/2)+8]=12 boys
now, 12 boys can dig the pit in 20 days.
15 boys can dig=16 days.
Answer is option E
Answer: (E) 16
Question: the average monthly salary of 12 workers and 3 managers in a factory was Rs. 600. When one of the manager whose salary was Rs. 720, was replaced with a new manager, then the average salary of the team went down to 580. What is the salary of the new manager?
(A) 640
(B) 690
(C) 420
(D) 570
(E) None
Rationale: Solution:
The total salary amount = 15 � 600 = 9000
The salary of the exiting manager = 720.
Therefore, the salary of 12 workers and the remaining 2 managers,
= 9000−720 = 8280
When a new manager joins, the new average salary drops to Rs.580 for the total team of 15 of them.
The total salary for the 15 people i.e., 12 workers, 2 old managers and 1 new manager =580�15 =8700
Therefore, the salary of the new manager is,
9000 - 8700 = 300 less than that of the old manager who left the company, which is equal to 720 - 300 = 420.
Answer: Option C
Answer: (C) 420
Question: A train passes a station platform in 34 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) 228
(B) 240
(C) 887
(D) 166
(E) 210
Rationale: 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)/34 = 15 => x = 210 m.
Answer: E
Answer: (E) 210
Question: A pump can fill a tank with a water in 2 hours. Because of a leak, it took 2x1/3 hours to fill the tank. The leak can drain all the water of the tank in
(A) 5 hrs
(B) 7 hrs
(C) 12 hrs
(D) 14 hrs
(E) None
Rationale: Sol.
Work done by the leak in 1 hour = (1/2 - 3/7) = 1/14.
∴ Leak will empty the tank in 14 hrs.
Answer D
Answer: (D) 14 hrs
Question: Two cyclist start from the same places in opposite directions. One is going towards north at 5kmph and the other is going towards south 5kmph. What time will they take to be 50km apart?
(A) 1hr
(B) 2hrs
(C) 3hrs
(D) 5hrs
(E) 6hrs
Rationale: To be (5+5) km apart, they take 1 hour
To be 50 km apart, they take 1/10 *50 = 5 hrs
Answer is D
Answer: (D) 5hrs
Question: Among three numbers, the first is twice the second and thrice the third. If the average of three numbers is 49.50, then what is the difference between the first and the third number?
(A) 28
(B) 54
(C) 39.5
(D) 41.5
(E) None of these
Rationale: 6x, 3x, 2x.
Now average = 6x+3x+2x/9 = 39.5
On solving we get the difference in between first and the third number = 54.
Answer:B.
Answer: (B) 54
Question: In a 2000 m race, A beats B by 150 meters or 50 seconds. Find the speed of B?
(A) 10m/s
(B) 2m/s
(C) 5m/s
(D) 7m/s
(E) 3m/s
Rationale: Since A beats B by 150 m or 50 seconds,
it implies that B covers 150 m in 50 seconds.
Hence speed of B = 150/50 = 3 m/s.
Answer: E
Answer: (E) 3m/s
Question: In a village of 2,700 people, 900 people are over 70 years old and 1200 people are female. It is known that 40 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a male or younger than 70 years old?
(A) 3/5
(B) 7/10
(C) 11/15
(D) 23/30
(E) 31/45
Rationale: The number of people younger than 70 years old is 2700-900 = 1800
The number of females older than 70 years old is 0.6*1200 = 720
The number of males older than 70 years old is 900-720 = 180
The number of people who are either male or younger than 70 is 1800+180 = 1980.
P(a person is younger than 70 or male) = 1980/2700 = 11/15
The answer is C.
Answer: (C) 11/15
Question: A starts a business with Rs. 3500. After 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. Find out B's contribution in the capital.
(A) 5000
(B) 7000
(C) 8000
(D) 9000
(E) 6000
Rationale: Ratio in which profit is divided =2:3
Assume that B's contribution to the capital =b
3500×12:b×7=2:3
⇒3500×12×3=2×b×7
⇒b=(3500×12×3)/2×7
=500×6×3=9000
Answer is D.
Answer: (D) 9000
Question: An engine moves at the speed of 90 kmph without any coaches attached to it.Speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached.When 9 coaches are attached speed decreases to 78 kmph.What will be the speed of train when 25 coaches are attached.
(A) 90
(B) 85
(C) 80
(D) 60
(E) 70
Rationale: 1.
No. of coaches =9
sqr root=3
speed decreases by 12
12=k*3
k=4
No. of coaches=25
swr root=5
decrease=5*4=20
New speed=90-20=70
E
Answer: (E) 70
Question: #p is defined as 2p-20 for any number p. What is p, if #(#(#p))=6?
(A) –108
(B) –44
(C) 10
(D) 16
(E) 18.25
Rationale: #p = 2p-20 --->#(#p) = 2(2p-20)-20 = 4p-60 and thus #(4p-60) = 2(4p-60)-20 = 8p-140 = 6 ---> 8p= 146 ---> p = 18.25, E is the correct answer.
Answer: (E) 18.25
Question: A milk man has 20 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk.If the cost of pure milk is Rs.18 per liter,then the profit of the milkman, when he sells all the mixture at cost price is:
(A) 22
(B) 25
(C) 27
(D) 29
(E) 11
Rationale: Explanation:
when the water is freely available and all the water is sold at the price of the milk, then the water gives the profit on the cost of 20 liters of milk.
Therefore, profit percentage = \inline \frac{5}{20}\times 100=25% % [ profit %= \inline \frac{profit}{cost\: price}\times 100 ]
Answer: B) 25%
Answer: (B) 25
Question: If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a four-percent vinegar solution, what was the concentration of the original solution?
(A) 19.3%
(B) 17%
(C) 20.67%
(D) 15.5%
(E) 12.5%
Rationale: Let X be the quantity of non-vinegar in the strong vinegar solution
Thus vinegar quantity will be 12 - X
When 50 ounces of water were added the percentage of vinegar becomes 4%, thus (12 - X)/62 = 4/100
From this equation X = 9.52
Answer (12-9.52)/12 = 20.67%
ANSWER:C
Answer: (C) 20.67%
Question: In a group of 80 children and 10 youngsters, each child got sweets that are 15% of the total number of children and each youngster got sweets that are 25% of the total number of children. How many sweets were there?
(A) 1140
(B) 1160
(C) 1180
(D) 1200
(E) 1210
Rationale: Number of sweets each child got = 15% of 80 = 15/100 * 80 = 12.
Number of sweets 80 children got = 80 * 12 = 960.
Number of sweets each youngster got = 25% of 80 = 25/100 * 80 = 20.
Number of sweets 10 youngsters got = 10 * 20 = 200.
Total number of sweets = 960 + 200 = 1160.
B)
Answer: (B) 1160
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
(A) 298 m
(B) 287 m
(C) 298 m
(D) 150 m
(E) 267 m
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer: D
Answer: (D) 150 m
Question: Seed mixture X is 40% ryegrass and 60% bluegrass by weight; seed mixture Y is 25% ryegrass and 75% fescue. If a mixture of X and Y contains 28% ryegrass, what percent of the weight of the mixture is from mixture X?
(A) 10%
(B) 20%
(C) 40%
(D) 50%
(E) 60%
Rationale: 28% is 3%-points above 25% and 12%-points below 40%.
Thus the ratio of mixture Y to mixture X is 4:1.
The percent of mixture X is 1/5 = 20%.
The answer is B.
Answer: (B) 20%
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
(A) 40
(B) 44
(C) 48
(D) 50
(E) 56
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
Answer:B
Answer: (B) 44