mathewhe/aqua_rat huggingface dataset:
Question: Andrew went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 19
(B) 19.7
(C) 21
(D) 23
(E) 25
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
B)
Answer: (B) 19.7
Question: Lucy deposited $62500 in an investment fund that provided 16 percent annual return compounded quarterly. If she made no other transactions with the fund, in how much time, in years, did her investment earn a total interest of $5100?
(A) 0.5
(B) 2
(C) 3
(D) 6
(E) 6.1
Rationale: A = P + I = 62500 + 5100 = 67600
67600 = 62500(1 + 16/4*100)^(4t)
(676/625) = (104/100)^(4t)
(26/25)^2 = (26/25)^4t
t = 1/2 yrs
Answer: A
Answer: (A) 0.5
Question: complete the numerical series with the correct number
5+3+1=15517
9+2+2=181834
5+6+4=302044
5+4+2=201026
9+3+5= ?
(A) 468645
(B) 454586
(C) 274569
(D) 454386
(E) 444586
Rationale: 9+3+5= 274569
Answer : C
Answer: (C) 274569
Question: If 4^k = 5, then 4^(2k+2) =
(A) 400
(B) 540
(C) 100
(D) 830
(E) 420
Rationale: 4^k=5
4^2k=5^2
4^2k=25
4^(2k+2)
=4^2k*4^2
=25*16
=400
Answer: A
Answer: (A) 400
Question: A certain elevator has a safe weight limit of 2,500 pounds. What is the greatest possible number of people who can safely ride on the elevator at one time with the average (arithmetic mean) weight of half the riders being 180 pounds and the average weight of the others being 230 pounds?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 12
Rationale: Lets assume there are 2X people.
Half of them have average weight of 180 and other half has 230.
Maximum Weight is = 2500
So 180*X + 230*X = 2500
=> 410X = 2500
=> X is approximately equal to 6.
So total people is 2*6 = 12
Answer E.
Answer: (E) 12
Question: Sum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be?
(A) 6, 9
(B) 10, 5
(C) 7, 8
(D) 9, 6
(E) 8, 5
Rationale: Explanation:
x + y = 15
2x – 3y = 5
x = 10 y = 5
ANSWER IS B
Answer: (B) 10, 5
Question: Two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 6 seconds. The length of the faster train is
(A) 80 m
(B) 100 m
(C) 120 m
(D) 135 m
(E) None
Rationale: Solution
Relative Speed	= (36 + 45) km/hr
= (81 x 5/18) m/sec
= (45/2) m/sec
Length of the train	= (45 / 2 x 6) m
= 135 m.
Answer D
Answer: (D) 135 m
Question: A number whose fifth part increased by 6 is equal to its fourth part diminished by 6 is ?
(A) 160
(B) 180
(C) 200
(D) 240
(E) None
Rationale: Answer
Let the number be N.
Then, (N/5) + 6 = (N/4) - 6
â‡’ (N/4) - (N/5) = 12
â‡’ (5N - 4N)/20 = 12
âˆ´ N = 240
Option: D
Answer: (D) 240
Question: In the coordinate plane, one of the vertices of a square is the point (-6, -4). If the diagonals of that square intersect at point (3, 2), what is the area of that square?
(A) 100
(B) 169
(C) 324
(D) 196
(E) 225
Rationale: One point (-6-4), Intersection (3,2) so the distance from the first point -6-3=-9 is the midpoint of the square --> whole side 18, 18*18=324
C
Answer: (C) 324
Question: There were 36,000 hardback copies of a certain novel sold before the paperback version was issued. From the time the first paperback copy was sold until the last copy of the novel was sold 9 times as many paperback copies as hardback copies were sold. If a total of 440,000 copies of the novel were sold in all, how many paperback copies were sold?
(A) 45,000
(B) 360,000
(C) 364,500
(D) 363,600
(E) 396,900
Rationale: Say x was the # of hardback copies sold from the time the first paperback copy was sold.
Then the total # of paperback copies sold was 9x;
Hence the total # of copies sold was (hardback)+(paperback)=(36+x)+(9x)=440--> x=40.4.
So, the total # of paperback copies sold was 9x=9*40.4=363.6 or 363,600.
Answer: D.
Answer: (D) 363,600
Question: The speed of a boat in upstream is 35 kmph and the speed of the boat downstream is 50 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 5.5 kmph
(B) 8.5 kmph
(C) 7.15 kmph
(D) 7.5 kmph
(E) 17.5 kmph
Rationale: Speed of the boat in still water = (35+50)/2 = 42.5 kmph. Speed of the stream
= (50-35)/2
= 7.5 kmph.
Answer:D
Answer: (D) 7.5 kmph
Question: A city with a population of 160,080 is to be divided into 8 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?
(A) 18,200
(B) 18,300
(C) 18,400
(D) 18,500
(E) 18,600
Rationale: The minimum possible population occurs when all the other districts have a population that is 10% greater than the least populated district.
Let p be the population of the least populated district.
Then 160,080 = p + 7(1.1)p
8.7p=160,080
p = 18,400
The answer is C.
Answer: (C) 18,400
Question: If x inches are cut from the length, l, of a rectangle and y inches are cut from the width, w, of the same rectangle, then which of the following correctly expresses the amount of the area of the original rectangle that was removed in terms of l, w, x, and y?
(A) xy
(B) lw – yx
(C) ly + wx – xy
(D) lx + wy – xy
(E) xy – lw – wy
Rationale: Initial Area = l*w
Area after cutting rectangle = (l-x)*(w-y)
Area removed = Initial Area - Final Area = l*w - (l-x)*(w-y) = l*w - [l*w-x*w-l*y+x*y) = x*w+l*y-x*y
Answer: Option C
Answer: (C) ly + wx – xy
Question: A Cuban cigar would cost 3 dollar less than 1.5 times a French cigar, had the French cigar cost 0.7 dollar less than it does now. An Arabian cigar costs 50 cents more than 1.5 times the Cuban cigar. The three cigars together cost 74.7 dollars. What is the price of the French cigar?
(A) 19.7$.
(B) 23$.
(C) 14.7$.
(D) 35$.
(E) 37.4$.
Rationale: The three cigars together cost 74.7 dollars. If each cost the same , they would have cost a little less than 25 dollars each.
From the given data we know French cigar < Cuban cigar < Arabic cigar
and each is more expensive 1.5 times. Therefore eliminate options A,D,E straightaway . Since French cigar is at least 1.5 times cheaper we know B cannot be the answer.
Therefore C is the answer.
Answer: (C) 14.7$.
Question: If a computer program generates three-digit odd numbers using the numbers 5, 7, 0, 4, and 1, and the digits can be repeated, what is the probability that the number formed from the program is a multiple of three?
(A) 1/1
(B) 1/2
(C) 1/3
(D) 1/6
(E) 1/7
Rationale: C
Answer: (C) 1/3
Question: From a group of 6boys&4girls a Committee of 4 persons is to be formed. In how many different ways can it be done, so that the committee has at least 2 boys?
(A) 120
(B) 135
(C) 185
(D) 210
(E) 240
Rationale: The committee of 4 persons is to be so formed that it has at least 2 men. The different ways that we can choose to form such a committee are:
(i) 2m. 2w in 6C2 x 4 C1=6X5 - 2X1 X 3X3 2X1 =n an (ii) 3m. 1w in 6C3 x 4C1 =6X5X4 3X2X1 X4 _n - a ''''
(iii) 4m in 6C4 -2x1 = 15 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least 2 men. = 90 + 18 + 15 = 185
C
Answer: (C) 185
Question: In a bucket there are 3 blue balls and 2 red balls. What is the probability of drawing at least one blue ball when drawing two consecutive balls randomly?
(A) 9/10
(B) 16/20
(C) 2/5
(D) 3/5
(E) ½
Rationale: P(at least one blue) = 1 - P(no blue, so 2 red) = 1- 2/5*1/4 = 9/10.
Answer: A.
Answer: (A) 9/10
Question: What will be the cost of house to paint which area equal to 484 sq ft, if the price per foot of building is Rs. 20
(A) 1800
(B) 1760
(C) 1400
(D) 2600
(E) 3600
Rationale: Let the side of the square plot be a ft.
a2 = 484 => a = 22
Length of the fence = Perimeter of the plot = 4a = 88 ft.
Cost of building the fence = 88 * 20
= Rs.1760.
Answer: B
Answer: (B) 1760
Question: In 1990 a total of j earthquakes occurred worldwide, some but not all of which occurred in Asia. If c of these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia?
(A) j/c
(B) c/j
(C) c/(j-c)
(D) j/(j-c)
(E) 1- (c/j)
Rationale: We're given a couple of facts to work with:
1) There were a total of j earthquakes
2) Of those earthquakes, c of them occurred in Asia
We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia.
Let's TEST VALUES
j = 5 total earthquakes
c = 2 occurred in Asia
Thus, there were 3 earthquakes that DID NOT occur in Asia....
The answer to the question is 2:3
We just need to plug in the values for j and c and find the match...
Answer A: j/c = 5/2 NOT a match
Answer B: c/j = 2/5 NOT a match
Answer C: c/(j-c) = 2/(5-2) = 2/3 This IS a match
Answer D: j/(j-c) = 5/(5-2) = 5/3 NOT a match
Answer E: 1 - (c/j) = 1-2/5 = 3/5 NOT a match
C
Answer: (C) c/(j-c)
Question: Walking at the rate of 5kmph a man cover certain distance in 5hr. Running at a speed of 15 kmph the man will cover the same distance in.
(A) 12 min
(B) 36 min
(C) 40 min
(D) 48 min
(E) 60 min
Rationale: Distance = Speed * time
5*5 = 25km
New Speed = 15 kmph
Therefore time = 25/15 = 5/3 =36min
Answer : B
Answer: (B) 36 min
Question: There are 4 people of different heights standing in order of increasing height. The difference is 2 inches between the first person and the second person, and also between the second person and the third person. The difference between the third person and the fourth person is 6 inches and the average height is 78. How tall is the fourth person?
(A) 82
(B) 84
(C) 86
(D) 88
(E) 90
Rationale: Let x be the height of the first person.
Then the heights are x, x+2, x+4, and x+10.
4x+16 = 4(78) = 312
x = 74 and the fourth person has a height of 74+10 = 84 inches
The answer is B.
Answer: (B) 84
Question: If a < b < c , which of the following must be true?
(I) a < b^2
(II) a < c - b
(III) a^2 < b^2 < c^2
(A) None
(B) I only
(C) II only
(D) III only
(E) II and III
Rationale: (I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2.
(II) a < c-b . Not necessarily true: try a=1, b=2, and c=5/2.
(III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1.
None of the options must be true.
Answer: A.
Answer: (A) None
Question: On selling 9 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:
(A) s. 145
(B) s. 150
(C) s. 155
(D) s. 160
(E) s. 180
Rationale: (C.P. of 9 balls) - (S.P. of 9 balls) = (C.P. of 5 balls)
C.P. of 4 balls = S.P. of 9 balls = Rs.720.
C.P. of 1 ball = Rs.720/4	= Rs. 180.
Answer: Option E
Answer: (E) s. 180
Question: How long does a train 60 m long travelling at 60 kmph takes to cross a bridge of 80 m in length?
(A) 5.8 sec
(B) 8.4 sec
(C) 12.4 sec
(D) 6.8 sec
(E) 1.8 sec
Rationale: B
16.8 sec
D = 60 + 80 = 140 m
S = 60 * 5/18 = 50/3
T = 140 * 3/50 = 8.4 sec
Answer is B
Answer: (B) 8.4 sec
Question: Five pieces of wood have an average length of 132cm and a median length of 140cm. What is the maximum possible length, in cm, of the shortest piece of wood?
(A) a) 90
(B) b) 100
(C) c) 110
(D) d) 120
(E) e) 140
Rationale: D. 120
sum of all lengths of all 5 pieces of wood = 132 * 5 = 660
3rd piece (sorted in increasing length) length = 140 (median)
for sum of first 2 wood length to become max, last two should be least.
let 4th, 5th wood also have length 140 each.
total of last 3 = 140 * 3 = 420
sum of first 2 = 660 - 420 = 240
each of these 2 will have length 240/2 = 120
Answer D
Answer: (D) d) 120
Question: The measurement of a rectangular box with lid is 25cmx12cmx18cm. Find the volume of the largest sphere that can be inscribed in the box (in terms of πcm3). (Hint: The lowest measure of rectangular box represents the diameter of the largest sphere)
(A) 288
(B) 48
(C) 72
(D) 864
(E) 964
Rationale: d=12, r=6;
Volume of the largest sphere= 4/3πr3
= 4/3 *π*6*6*6= 288πcm3 ANSWER:A
Answer: (A) 288
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 4 hours and 49 hours respectively. The ratio of their speeds is:
(A) 2 : 3
(B) 4 : 3
(C) 6 : 7
(D) 7 : 2
(E) None of these
Rationale: Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = âˆšb : âˆša = âˆš49 : âˆš4 = 7 : 2.
Answer D
Answer: (D) 7 : 2
Question: What is the remainder when 9^19 is divided by 5 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: 9^0 = 1
9^1 = 9
9^2 = 81
9^3 = 729
9^4 = ...1
9^5 = .....9
And so on in a distinct last-digit pattern of 9,1,9,1... after ignoring the first last-digit of 1
19/2 = 9 (with a remainder of 1) So the last number is a 9.
Alternatively, 19 is an odd number and hence the last digit is a 9
When 9^19 is divided by 5 the remainder is 4, ANS = E
Answer: (E) 4
Question: The length of the bridge, which a train 140 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 239
(B) 277
(C) 235
(D) 88
(E) 232
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (140 + X)/30
= 25/2 ==> 2(140 + X) = 750 ==> X = 235 m.
Answer: C
Answer: (C) 235
Question: Average of 9 results is 111. If the average of first four results is 106 and average of last four results is 112 Then find the fifth result?
(A) 121
(B) 131
(C) 115
(D) 127
(E) 125
Rationale: Option 'D'
Answer: (D) 127
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 16. The larger of the two numbers is:
(A) 276
(B) 299
(C) 322
(D) 345
(E) 368
Rationale: Clearly, the numbers are (23 x 13) and (23 x 16).
Larger number = (23 x 16) = 368.
Answer: Option E
Answer: (E) 368
Question: If a and b are both odd numbers, which of the following is an odd number?
(A) a + b
(B) b+a
(C) ab
(D) ab + 1
(E) NOne
Rationale: Sol.
Product of two odd numbers is always odd.
Answer C
Answer: (C) ab
Question: 7 + 3 x 14 + 6 x 7^2 + 6 x 7^3 + 6 x 7^4 + 6 x 7^5 + 6 x 7^6 + 6 x 7^7 =
(A)  7^21
(B)  7^14
(C)  7^10
(D)  7^8
(E)  None of the above
Rationale: Let's see that 7 + 3 x 14 is 49 or 7^2, then: 7^2 + 6 x 7^2 becomes 7 x 7^2 that is 7^3. So we follow with the next element: 7^3 + 6 x 7^3 is equal to 7 x 7^3 that is 7^4. Then is assumed right before 6 x 7^7: 7^7 + 6 x 7^7 becomes 7 x 7^7 that is 7^8. Thus, the correct answer is the option D, 7^8.
Answer: (D)  7^8
Question: Find the area between two concentric circles defined by
x2 + y2 -2x + 4y + 1 = 0
x2 + y2 -2x + 4y - 11 = 0
(A) 40 Pi
(B) 19 Pi
(C) 12 Pi
(D) 46 Pi
(E) 22 Pi
Rationale: Rewrite equations of circles in standard form. Hence equation x2 + y2 -2x + 4y + 1 = 0 may be written as
(x - 1)2 + (y + 2) 2 = 4 = 22
and equation x2 + y2 -2x + 4y - 11 = 0 as
(x - 1)2 + (y + 2) 2 = 16 = 42
Knowing the radii, the area of the ring is Pi (4)2 - Pi (2)2 = 12 Pi
correct answer C
Answer: (C) 12 Pi
Question: If 5 men and 2 boys working together, can do three times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?
(A) 3:2
(B) 2:1
(C) 3:3
(D) 1:2
(E) 6:1
Rationale: 5M + 2B = 3(1M + 1B)
5M + 2B = 3M + 3B
2M = 1B
The required ratio of work done by a man and a boy = 1:2
D
Answer: (D) 1:2
Question: When integer P is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?
I. 3P
II. 2P
III. 4P + 10
IV. 5P
V .6P
(A) I
(B) II
(C) III
(D) IV
(E) V
Rationale: D
Answer: (D) IV
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
(A) 33 1/8 %
(B) 33 7/3 %
(C) 33 1/3 %
(D) 33 5/8 %
(E) 34 1/3 %
Rationale: The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 4
Profit = SP - CP = 4 - 3 = 1
Profit Percent = 1/3 * 100 = 33 1/3 %
Answer: C
Answer: (C) 33 1/3 %
Question: 3*13+3*14+3*17+11 = ?
(A) 125
(B) 126
(C) 130
(D) 143
(E) 151
Rationale: 3*13+3*14+3*17+11 = 39 + 42 + 51 + 11 = 143
The answer is D.
Answer: (D) 143
Question: Pipe A that can fill a tank in two hour and pipe B that can fill the tank in an hour are opened simultaneously when the tank is empty. Pipe B is shut 30 minutes before the tank overflows. When will the tank overflow?
(A) 36 mins
(B) 35 mins
(C) 40 mins
(D) 32 mins
(E) 30 mins
Rationale: The last 30 minutes only pipe A was open. Since it needs 2 hour to fill the tank, then in 30 minutes it fills 1/4th of the tank, thus 3/4 of the tank is filled with both pipes open.
The combined rate of two pipes is 1 + 2 = 3 tanks/hour, therefore to fill 3/4th of the tank they need (time) = (work)/(rate) = (3/4)/3 = 1/4 hours = 15 minutes.
Total time = 15 + 15 = 30 minutes.
Answer: E
Answer: (E) 30 mins
Question: Find next number in sequence
81 87 69 82 84 ?
(A) 90
(B) 92
(C) 88
(D) 85
(E) 89
Rationale: E
89 (ASCII CODE OF Y)
Q W E R T Y
81 87 69 82 84 ?
Answer: (E) 89
Question: What flavor of Network Address Translation can be used to have one IP address allow many users to connect to the global Internet?
(A) NAT
(B) Static
(C) PAT
(D) Dynamic
(E) DD
Rationale: Explanation:
Port Address Translation (PAT) allows a one-to-many approach to network address translation.
Answer: Option D
Answer: (D) Dynamic
Question: Manoj borrowed Rs.4050 from Anwar at 6% p.a. simple interest for three years. He then added some more money to the borrowed sum and lent it to Ramu for the same time at 9% p.a. simple interest. If Manoj gains Rs.824.85 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Ramu?
(A) 22877
(B) 5755
(C) 2778
(D) 6787
(E) 1771
Rationale: Let the sum lent by Manoj to Ramu be Rs.P.
Amount gained by Manoj = P. 3.9 /100 = 4050.3.6/100 = Rs.824.85
27P = 72900 = 82485
P = (82485 + 72900)/27 = 3055 + 2700 = Rs.5755
Answer: B
Answer: (B) 5755
Question: Murali travelled from city A to city B at a speed of 30 kmph and from city B to city C at 70 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3
(A) kmph
(B) kmph
(C) kmph
(D) kmph
(E) kmph
Rationale: Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/30 + (3x)/70
= (14x + 9x)/210 = 23x/210
= (2x + 3x)/(23x/210) = 45.6 kmph.
Answer: B
Answer: (B) kmph
Question: If x is 12 percent greater than 80, then x =
(A) 89.6
(B) 91.0
(C) 88.0
(D) 70.9
(E) 71.2
Rationale: 12% of 80 = (80*0.12) = 9.6
12% greater than 80 = 80 + 9.6 = 89.6
Answer is clearly A.
Answer: (A) 89.6
Question: What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 3, 4, and 5?
(A) 3.5
(B) 3
(C) 5
(D) 4
(E) 2.5
Rationale: Some of pyhtagron triplets we need to keep it in mind.
Like {( 2,3,5) , ( 5,12,13) ,( 7, 24,25), ( 11, 60,61).
So now we know the triangle is an right angle triangle. The circle circumscribes the triangle.
The circum raduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 5 / 2 = 2.5
Ans. E
Answer: (E) 2.5
Question: 10 men do a work in 10days. How many men are needed to finish the work in 4days?
(A) 25
(B) 20
(C) 30
(D) 10
(E) 15
Rationale: men required to finish the work in 4days = 10*10/4 = 25
Answer is A
Answer: (A) 25
Question: A river 2m deep and 45 m wide is flowing at the rate of 3 kmph the amount of water that runs into the sea per minute is?
(A) 1390
(B) 2887
(C) 2778
(D) 2779
(E) 2121
Rationale: 2(25 * 15 + 15 * 8 + 25 * 8)
2(375 + 120 + 200) => 1390
Answer:A
Answer: (A) 1390
Question: A rectangular floor is covered by a rug except for a strip Y meters wide along each of the four edge. If the floor is P meters by Q meters, what is the area of the rug in square meters?
(A) 4(P-2Y)(Q-2Y)
(B) 3(P-2Y)(Q-2Y)
(C) (P-2Y)(Q-2Y)
(D) (P-2Y)(Q-2Y)/3
(E) (P-2Y)(Q-2Y)/4
Rationale: A strip of Y meters is covering the inner rectangular rug for all 4 sides.
Length of inner rug = P-(2Y)
breadth of inner rug= Q-(2Y)
Area of Rug= (P-2Y)(Q-2Y)
Ânswer: C
Answer: (C) (P-2Y)(Q-2Y)
Question: By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
(A) 42 6/7%
(B) 42 9/7%
(C) 42 9/1%
(D) 32 6/7%
(E) 42 6/2%
Rationale: SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer: D
Answer: (D) 32 6/7%
Question: The basic one-way air fare for a child aged between 3 and 10 years costs half the regular fare for an adult plus a reservation charge that is the same on the child's ticket as on the adult's ticket. One reserved ticket for an adult costs $216 and the cost of a reserved ticket for an adult and a child (aged between 3 and 10) costs $327. What is the basic fare for the journey for an adult?
(A) $111
(B) $52.5
(C) $210
(D) $58.5
(E) $6
Rationale: Explanatory Answer
Step 1: Assign variables and frame equations
Let the basic fare for the child be $X.
Basic one-way air fare of a child costs half the regular fare for an adult
Therefore, the basic fare for an adult = 2(basic one-way airfare for a child) = $2X.
Reservation charge is the same on the child's ticket as on the adult's ticket.
Let the reservation charge per ticket be $Y
Hence, an adult ticket will cost (Basic fare + Reservation charges) = 2X + Y = $216 ..... (1)
And ticket for an adult and a child will cost (2X + Y) + (X + Y) = 3X + 2Y = $327 .... (2)
Step 2: Solve the equations and determine basic fare for an adult
Multiply equation (1) by 2: 4X + 2Y = 432 .... (3)
Subtract equation (2) from equation (3): (4X + 2Y = 432) - (3X + 2Y = 327)
∴ X = $105.
The basic fare of an adult ticket = 2X = 2*105 = $210
Answer C
Answer: (C) $210
Question: Three years ago, the average age of a family of 5 members was 17. A baby having been born, the average age of the family is the same today. What is the age of the child?
(A) 3
(B) 2
(C) 4
(D) 1
(E) 5
Rationale: Present age of 5 members = 5 x 17 + 3 x 5 = 100 years
Also, present ages of 5 members + Age of the baby = 6 x 17 = 102 years
Age of the baby = 102 – 100 = 2 years.
ANSWER:B
Answer: (B) 2
Question: Speed of a boat in still water is 5 km/hr and speed of the stream is 2 kmph. A man rows to a place at a distance of 252 km and comes back to the starting point the total time taken by him is.
(A) 160 hr
(B) 200 hr
(C) 120 hr
(D) 140 hr
(E) 180 hr
Rationale: Explanation:
Speed up stream = 5 - 2 = 3 km/hr
Speed down stream = 5 + 2 = 7 km/hr
Total time taken = 252/3 + 252/7 = 84 + 36 = 120 hr
Answer: Option B
Answer: (B) 200 hr
Question: How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
(A) 482
(B) 297
(C) 278
(D) 298
(E) 279
Rationale: 20000(11/10)4 - 20000(6/5)2
= 482
Answer:A
Answer: (A) 482
Question: P alone can complete a job in 6 days. The work done by Q alone in one day is equal to one-fifth of the work done by P alone in one day. In how many days can the work be completed if P and Q work together?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: P's rate is 1/6
Q's rate is 1/30
The combined rate is 1/6 + 1/30 = 1/5
If they work together, the job will take 5 days.
The answer is E.
Answer: (E) 5
Question: A company’s four cars running 10 hrs a day consume 1200 lts of fuel in 10 days. In the next 6 days, the company will need to run 9 cars for 12 hrs each so it rents 5 more cars which consume 15% less fuel than the company’s four cars. How many lts of fuel will be consumed in the next 6 days?
(A) 1200 lt
(B) 1555 lt
(C) 1664 lt
(D) 1782 lt
(E) 4800 lt
Rationale: Given that
4 cars running 10 hrs a day consume 1200 lts. of fuel in 10 days.
1 car consumption per hour per day = 1200 /4 *10 *10 = 3 litre
Now question say new car consume 15% less fuel than the company’s four cars = 85/100 of 3 = 2.55 ( 20 percent less than 3)
Hence we calculate total consumption for next 6 days, the company will need to run 5 new cars for 12 hrs = 2.55 *12 *6*5 =918
similarly = old 4 car consumption for next 6 days for 12 hrs = 3*6*12*4 = 864
hence total is = 918 +864 = 1782 lt
Ans is D .
Answer: (D) 1782 lt