mathewhe/aqua_rat huggingface dataset:
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
(A) 1 kmph
(B) 7 kmph
(C) 8 kmph
(D) 9 kmph
(E) 6 kmph
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A
Answer: (A) 1 kmph
Question: If a1 = 1 and an+1= 2an + 5, n = 1, 2 .. , then a30 is equal to ?
(A) a. 5*2^99-6
(B) b. 5*2^99+6
(C) c. 6*2^29 - 5
(D) d. 6*2^99-5
(E) e. 6*2^99-6
Rationale: Here is my solution:
an+1=2an+5............(1)
lets ADD 5 to both sides....
so (an+1) + 5= 2 (an+5)....................taking 2 as common factor
now a1=1. so for n=1, an+5=6.......
putting n=1. we get both sides as,
a2 + 5= 2 * 6 ..............as ( an+5=6 .......(for n=1)..)
a2= 2 *6 - 5
a2= 2 * 2 *3 - 5
a2= 2^2 *3 - 5................. so with same progression
a30= 2^30 * 3 - 5
a30=2 * 2^29 * 3 - 5
a30= 6 * 2^29 - 5
C
Answer: (C) c. 6*2^29 - 5
Question: There are 9 kids and 5 chairs. In how many ways kids can occupy the chairs?
(A) 1760
(B) 1840
(C) 1560
(D) 1740
(E) 15120
Rationale: total kids = 9
total chairs = 5
1st chair can be occupy in 9ways
2nd chair can be occupy in 8ways
3rd chair can be occupy in 7ways
4th chair can be occupy in 6ways
5th chair can be occupy in 5ways
total number of ways =9*8*7*6*5 = 15120 ways
correct option is E
Answer: (E) 15120
Question: In an examination, a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination ?
(A) 12
(B) 27
(C) 26
(D) 11
(E) 22
Rationale: Let the number of papers be x. Then, 63x + 20 + 2 = 65x or 2x
= 22 or x
= 11.
Answer: D
Answer: (D) 11
Question: The sum of two numbers is 62, and one of them is 12 more than the other. What are the two numbers?
(A) 36-48
(B) 50-34
(C) 60-24
(D) 42-42
(E) 25-37
Rationale: In this problem, we are asked to find two numbers. Therefore, we must let x be one of them. Let x, then, be the first number.
We are told that the other number is 12 more, x + 12.
The problem states that their sum is 62:
word problem = 62
The line over x + 12 is a grouping symbol called a vinculum. It saves us writing parentheses.
We have:
2x = 62 âˆ’ 12
= 50.
x = 50/2
= 25.
This is the first number. Therefore the other number is
x + 12 = 25 + 12 = 37.
The sum of 25 + 37 is 62.
E
Answer: (E) 25-37
Question: Molly and Max are driving at a rate of 100 kilometers per hour. What is their driving speed in miles per hour? [1km = 0.6 miles]
(A) 600
(B) 60
(C) 6
(D) 0.6
(E) None of the above
Rationale: To calculate the equivalent of miles in a kilometer
0.6 kilometers= 1 mile
100 kilometers = (0.6)*100 = 60 miles
Speed in kilometers/hour = 60
Correct answer - B
Answer: (B) 60
Question: All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 148 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A
(A) 168
(B) 6289
(C) 1268
(D) 1184
(E) 1232
Rationale: Explanation:
B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.
Quantity of water in B = 8k - 5k = 3k.
Quantity of water in container C = 8k - 3k = 5k
Container: A B C
Quantity of water: 8k 3k 5k
It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water.
5k - 148 = 3k + 148 => 2k = 296 => k = 148
The initial quantity of water in A = 8k = 8 * 148 = 1184 liters.
Answer: Option D
Answer: (D) 1184
Question: The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was
(A) Rs.12008
(B) Rs.12000
(C) Rs.12002
(D) Rs.1229
(E) Rs.12021
Rationale: Explanation:
= Rs.12000
Answer: B
Answer: (B) Rs.12000
Question: On the x-y coordinate plane there is a parabola, y=x(6-x). Which of the following points is in the region that is enclosed by this parabola and the x-axis?
I. (1, 6) II. (3, 11) III. (5, 4)
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III
Rationale: Since co-efficient of x^2 is negative, the parabola will be downward facing. So the parabola and the x axis will enclose some points where the y-values of the parabola are positive.
When x = 1, y = 5 lies on the parabola, so (1, 6) will not be enclosed by the parabola and x axis.
When x = 3, y = 9 lies on the parabola, so (3, 11) will not be enclosed by the parabola and x axis.
When x = 5, y = 5 lies on the parabola, so (5, 4) will be enclosed by the parabola and x axis.
The answer is C.
Answer: (C) III only
Question: In some quantity of ghee, 50% is pure ghee and 50% is vanaspati. If 20kg of pure ghee is added, then the strength of vanaspati ghee becomes 30%. The original quantity was?
(A) 25
(B) 15
(C) 30
(D) 45
(E) 20
Rationale: Let the original quantity be x
then, vanaspati ghee in xkg = 50x/100 kg= x/2kg
(x/2)/(x+20) = 30/100
x/(2x+40) = 3/10
x = 30
Answer is C
Answer: (C) 30
Question: Raj goes to market to buy oranges. If he can bargain and reduce the price per orange by Rs.2, he can buy 30 oranges instead of 20 oranges with the money he has. How much money does he have ?
(A) 28
(B) 2
(C) 6
(D) 8
(E) 1
Rationale: Explanation: Let the money with Raj is M. So M/20−M/30=M/20−M/30=2. Check options. Option D satisfies.
Answer:B
Answer: (B) 2
Question: A side of beef lost 25 percent of its weight in processing. If the side of beef weighed 540 pounds after processing, how many pounds did it weigh before processing?
(A) 191
(B) 355
(C) 720
(D) 840
(E) 1,560
Rationale: Let weight of side of beef before processing = x
(75/100)*x = 540
=> x = (540 * 100)/75 = 720
Answer C
Answer: (C) 720
Question: A restaurant meal cost $36.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then total amount paid must have been between:
(A) $40 and $42
(B) $39 and $42
(C) $38 and 40
(D) $37 and $39
(E) $36 and $37
Rationale: let tip=t
meal cost=36.50
range of tip = from 10% of 36.5 to 15% of 36.5 = 3.55 to 5.325
hence range of amount paid= 36.5+T= 40.05 to 41.825
ANSWER:A
Answer: (A) $40 and $42
Question: There is 60 lit of milk and water in which milk forms 84%.Howmuch water must be added to this solution to make it solution in which milk forms 50%
(A) 40.8
(B) 19.75
(C) 20.75
(D) 21.75
(E) 22.75
Rationale: 60*84/100=50.40 lit milk that is 9.60 lit water
let x lit water will be added then
(60+x)*50/100=50.40
so x=40.8
ANSWER:A
Answer: (A) 40.8
Question: On a certain transatlantic crossing, 40 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 50 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?
(A) 40%
(B) 50%
(C) 60%
(D) 80%
(E) 90%
Rationale: Let T be the total number of passengers.
Let x be the number of people with round trip tickets.
0.4T had round trip tickets and took their cars.
0.5x had round trip tickets and took their cars.
0.5x = 0.4T
x = 0.8T
The answer is D.
Answer: (D) 80%
Question: 12 men complete a work in 9 days. After they have worked for 6 days, 6 more men join them. How many days will they take to complete the remaining work?
(A) 2 days
(B) 7 days
(C) 8 days
(D) 9 days
(E) 45 days
Rationale: 1 man's 1 day work = 1/108
12 men's 6 day's work = 1/9 * 6 = 2/3
Remaining work = 1 - 2/3 = 1/3
18 men's 1 day work = 1/108 * 18 = 1/6
1/6 work is done by them in 1 day.
1/3 work is done by them in 6 * 1/3 = 2 days.
Answer:A
Answer: (A) 2 days
Question: Find the invalid no.from the following series 3, 7, 15, 31 , 63, 127, 257
(A) 3
(B) 7
(C) 257
(D) 63
(E) 31
Rationale: Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 257 is wrong.
C
Answer: (C) 257
Question: Find a positive number, which when increased by 8 is equal to 128 times reciprocal of the number.
(A) 5
(B) 6
(C) 8
(D) 7
(E) 9
Rationale: Explanation:
Let the number be x. Then,
x + 8 = 128 x (1/x) => x<sup>2</sup> + 8x - 128 = 0
=> (x + 16)(x - 8) = 0
=> x = 8
Answer: Option C
Answer: (C) 8
Question: If x and y are positive integers, then x/y is
(A) Always even
(B) Always odd
(C) Even whenever x+y is Even
(D) Odd whenever x and y is odd
(E) It cannot be determined
Rationale: x and y are positive integers, then x/y is
Let's take odd as 25 and odd as 5.
IMO option B is correct answer..
If you consider your fourth scenario, that turns out to be even.
Hence option D should be correct.
Answer: (D) Odd whenever x and y is odd
Question: 1395 x 1395 = ?
(A) A)1951609
(B) B)1946025
(C) C)1951602
(D) D)1951603
(E) E)1951604
Rationale: 1395 x 1395	= (1395)2
= (1400 - 5)2
= (1400)2 + (5)2 - (2 x 1400 x 5)
= 1960000 + 25 - 14000
= 1960025 - 14000
= 1946025.
Answer:B
Answer: (B) B)1946025
Question: At Veridux Corporation, there are 210 employees. Of these, 90 are female, and the rest are males. There are a total of 40 managers, and the rest of the employees are associates. If there are a total of 135 male associates, how many female managers are there?
(A) 15
(B) 20
(C) 25
(D) 30
(E) 55
Rationale: Well, first letâ€™s take care of the â€œtotalsâ€. The numbers in the â€œtotalsâ€ row must add up. If 90 are females, the other 210 â€“ 90 = 120 must be males. Similarly, the numbers in the â€œtotalsâ€ column must add up. If 40 are managers, then the other 210 â€“ 40 = 170 must be associates.
Now, in the â€œassociateâ€ row, 135 + E = 170, which means E = 35 â€” the other 35 associates must be female.
Now, to find B, which is what the question is asking, we need only look at the sum in the â€œfemaleâ€ column: B + 35 = 90, which means B = 55. There are fifteen female managers in this company. Thus, the answer = (E).
Answer: (E) 55
Question: A circular logo is enlarged to fit the lid of a jar. The new diameter is 50 per cent larger than the original. By what percentage has the area of the logo increased?
(A) 50
(B) 80
(C) 100
(D) 125
(E) 250
Rationale: Let old diameter be 4 , so radius is 2
Old area = 4π
New diameter is 6 , so radius is 3
New area = 9π
Increase in area is 5π
% increase in area = 5/4*100
So, % increase is 125%
Answer will be (D)
Answer: (D) 125
Question: A man performs 1/2 of the total journey by rail, 1/3 by bus and the remaining 3km on foot. His total journey is
(A) 18km
(B) 10km
(C) 12km
(D) 24km
(E) 25km
Rationale: Explanation:
Let the journey be x km
Then, 1x/2 + 1x/3 +3 =x
5x +18 =6x
X = 18km
Answer: Option A
Answer: (A) 18km
Question: The sum of the ages of 5 children born at the intervals of 3 year each is 60 year. what is the age of the youngest child ?
(A) 4 year
(B) 6 year
(C) 10 year
(D) None of these
(E) 9 year
Rationale: Solution
let the ages of the children be x,(x + 3),(x + 6),(x + 9) and (x + 12) year.
then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 60 â‡” 5 x = 30 â‡” x= 6.
âˆ´ Age of the youngest child = x = 6 years. Answer B
Answer: (B) 6 year
Question: Mani paid a sum of money for purchasing 40 pens, which he recovered in full when he sold 25 of them. What was his percentage of profit or loss per pen?
(A) 50%
(B) 60%
(C) 70%
(D) 65%
(E) 55%
Rationale: B
33.33%
If the sum he paid whilst purchasing 40 pens = A,
Then the Cost Price of each pen = A/40.
Since the amount he got whilst selling 25 pens is also = A
Then the Selling Price of each pen = A/25.
Since Selling Price > Cost Price, he made a profit.
Profit per pen = Selling Price - Cost Price = A/25 - A/40 = 3A/200.
Profit percentage per pen = Profit per pen / Cost per pen x 100 = (3A/200) / (A/40) x 100 = 60%. Answer : B
Answer: (B) 60%
Question: Narasimha, Madhu and pavan started a business by investing Rs.1,20,000, Rs.1,35,000 and Rs 1, 50,000 respectively. Find the share of Pavan, out of an annual profit of Rs.56,700.
(A) 21,0009
(B) 21,008
(C) 21,000
(D) 21,002
(E) 21,0382
Rationale: Explanation:
Ratio of their investments = 120000 : 135000 : 150000 = 8 : 9 : 10
Share of Pavan = 10271027 × 56700 = 21,000
Answer: C
Answer: (C) 21,000
Question: TOM has 13 ten-dollar bills, 11 five-dollar bills, and 17 one-dollar bills. If TOM needs to pay exactly $128, what is the least number of bills he will need to use?
(A) 557
(B) 456
(C) 16
(D) 577
(E) 586585
Rationale: 128 is the total sum of money.
as we have 13 10 dollar bills so the closest we can get to 128 using the 10 dollar bills is by using 12 * 10 dollar bils
128-120 = 8
so now we need to get 8 from either 5 dollar bills or 1 dollar bills
8 - 5 (use only 1 5 dollar bill) = 3
so we can get 3 from using 3 $1 bills.
Hence 16 ( 12+1+3 )
ANSWER IS C
Answer: (C) 16
Question: Which of the following is a composite number ?
(A) 2
(B) 7
(C) 15
(D) 13
(E) 19
Rationale: Clearly 15 is a composite number. All others are prime. Ans : C
Answer: (C) 15
Question: What is the least value of x, So that 2x5472 is divisible by 9
(A) 7
(B) 8
(C) 9
(D) 3
(E) 2
Rationale: Explanation:
The sum of the digits of the number is divisible by 9.
Then the number is divisible by 9.
2 + x + 5 + 4 + 7 + 2 = 20 + x
Least value of x may be '7',
So that the total 20 + 7 = 27
is divisible by 9.
Answer: Option A
Answer: (A) 7
Question: A searchlight on top of the watchtower makes 4 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds?
(A) 5/6
(B) 4/5
(C) 3/4
(D) 2/3
(E) 1/2
Rationale: The searchlight completes one revolution every 15 seconds.
The probability that the man's area will be lit up is 5/15=1/3.
The probability that he will stay in the dark is 1-1/3=2/3
The answer is D.
Answer: (D) 2/3
Question: What could be the range of a set consisting of odd multiples of 3?
(A) 21
(B) 24
(C) 35
(D) 62
(E) 70
Rationale: Range = the difference between the greatest and the smallest numbers in the sequence. Our sequence is odd and is a multiple of 7. Every number in that sequence can be represented like this: 3*(2n+1) where n is any positive integer.
Range = 3*(2m + 1) - 3*(2n + 1) = 3*2*(m-n) = 6 * (m-n).
m, n - any positive integers
The answer must be divisible by 6, which is only 24.
The correct answer is B
Answer: (B) 24
Question: Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ?
(A) 2hrs, 48mins
(B) 6hrs, 32mins
(C) 7hrs, 12mins
(D) 13hrs, 4mins
(E) 14hrs, 24mins
Rationale: The rate of pump 1 = 4x job/minute.
The rate of pump 2 = 2x job/minute.
The rate of pump 3 = x job/minute.
Given that x+2x+4x=1/56 --> x=1/392 --> (time) = (reciprocal of rate) = 392 minutes = 6 hours and 32 minutes.
Answer: B.
Answer: (B) 6hrs, 32mins
Question: The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy?
(A) 6
(B) 9
(C) 8
(D) 4
(E) 2
Rationale: 3x + 5x + 7x = 45
x =3
3x = 9
Answer: B
Answer: (B) 9
Question: If the price has fallen by 20% what percent of its consumption be: increased so that the expenditure may be the same as before?
(A) A)11%
(B) B)10%
(C) 1/9 %
(D) 1/11 %
(E) 1/4%
Rationale: 100 – 20 = 80
80------20
100------? => 1/4%
ANSWER:E
Answer: (E) 1/4%
Question: Fill in the sequence:
10 10 22 9 24 8 26 ?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: D
7
There are two series - 20, 22, 24, 26 and 10, 9, 8, 7.
Answer: (D) 7
Question: The average of 10 numbers is calculated as 23. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
(A) A)16
(B) B)18
(C) C)19
(D) D)22
(E) E)24
Rationale: Explanation:
10 * 23 + 36 – 26 = 240=>240/10 = 24
E)
Answer: (E) E)24
Question: If it is 7:03 in the evening on a certain day, what time in the morning was it exactly 1,440,706 minutes earlier? (Assume standard time in one location.)
(A) 7:09
(B) 7:11
(C) 7:17
(D) 7:22
(E) 7:34
Rationale: 7:03 minus 1,440,706 must end with 7, the only answer choice which ends with 7 is C.
Answer: C.
Answer: (C) 7:17
Question: If the selling price of 8 articles is same as the cost price of 12 articles. Find the gain or loss percentage?
(A) 30% gain
(B) 30% loss
(C) 50% gain
(D) 50% loss
(E) 60% loss
Rationale: Explanation:
Let the C.P of each article be Re 1. Then,
S.P of 8 articles = C.P of 12 articles = Rs. 12/-
Now, C.P of 8 articles = Rs. 8/-, S.p of 8 articles = Rs 12/-
Gain = Rs ( 12 - 10 ) = Rs 4/-.
Gain% = ( 4/8 * 100 ) % = 50% Gain
Answer: Option C
Answer: (C) 50% gain
Question: A train started from station 'A' and proceeded towards station 'B' at a speed of 48 Km/hr. Forty-five minutes later another train started from station 'B' and proceeded towards station 'A' at 50 Km/hr. If the distance between the two stations is 232 Km, at what distance from station 'A' will the trains meet?
(A) 160KM
(B) 108KM
(C) 132KM
(D) 144KM
(E) 134KM
Rationale: Train A started 45 min ago,by the time train B started,
It means Distance covered by the Train A in 45 min is 48*45/60=36km covered,
now remaining distance=196km
since they are moving towards each other relative speed=48+50=98kmph
and time=196/98=2hrs
In 2hrs trainAcovered 96km distance and 36 km already covered
=>96=36=132km
Hence,132 km from station A, trains meet eachother.
ANSWER:C
Answer: (C) 132KM
Question: Find the coordinates
of the midpoint of the line segment joining the points
A(–3,2) and B(7,8)
(A) (2,5)
(B) (1,5)
(C) (2,4)
(D) (3,5)
(E) (4,5)
Rationale: mid point of A(x1,y1) and B(x2,y2) can be calculated by
(x1+y1/2,x2+y2/2) hence ((-3+7)/2,(2+8)/2)=(2,5)
ANSWER:A
Answer: (A) (2,5)
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 225 km/hr
(B) 50 km/hr
(C) 99 km/hr
(D) 88 km/hr
(E) 66 km/hr
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x = 50 km/hr.
Answer: B
Answer: (B) 50 km/hr
Question: A grocery store priced a gallon of milk at 25% above the wholesale price of $4. If a customer comes in with a coupon for 5% off milk, how much does that customer pay?
(A) $4.95
(B) $4.75
(C) $5.05
(D) $4.50
(E) $5.25
Rationale: Wholesale cost of milk = $4
Milk was priced at 25% above $4 = $5
% discount given by coupon = 5%
Customer paid = .95 * 5 = $4.75
Answer B
Answer: (B) $4.75
Question: What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?
(A) 289
(B) 500
(C) 188
(D) 666
(E) 155
Rationale: 70 = (P*4*7/2)/100
P = 500
Answer:B
Answer: (B) 500
Question: If x and y are even integers, which of the following is an odd integer?
(A) xy +3
(B) x(y − 2)
(C) x(x + 5)
(D) 3x + 4y
(E) (x + 2)(y + 1)
Rationale: If a and b are even integers, then:
A. xy + 3: even + odd = odd
B. x(y− 2): even(even) = even
C. x(x+ 5): even(odd) = even
D. 3x + 4y: even + even = even
E. (x + 2)(y + 1): (even)(odd) = even
Answer is A
Answer: (A) xy +3
Question: If a number N is chosen at random from the set of two-digit integers whose digits are both prime numbers, what is the probability W that N is divisible by 3?
(A) 1/3
(B) ¼
(C) 9/25
(D) 5/16
(E) 0
Rationale: Prime digits are: 2, 3, 5, 7
Total number of 2 digit #s with both digits prime are: 4*4 = 16
out of these numbers divisible by 3 = 33, 27, 57, 72 and 75. I had to find the numbers manually using the 4 numbers above.
=> prob = 5/16.
Ans D. Took me 3:20 mins.
Answer: (D) 5/16
Question: In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 10 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
(A) 80%
(B) 105%
(C) 120%
(D) 124.2%
(E) 138%
Rationale: x = profits
r= revenue
x/r = 0,1
x= 10
r=100
2009:
r=80
x/80 = 0,10 = 10/100
x= 80*10/100
x= 8
8/10 = 0.8 = 800%, Answer A
Answer: (A) 80%
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) 4882.40
(B) 8082.40
(C) 4002.40
(D) 4082.40
(E) 9082.40
Rationale: 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: Option D
Answer: (D) 4082.40
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 7 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
(A) 9.5
(B) 9.4
(C) 9.3
(D) 9.2
(E) 9.1
Rationale: Net part filled in 1 hour = (1/4 - 1/7) = 3/28
The cistern will be filled in 28/3 hrs i.e., 9.3 hrs.Answer: C
Answer: (C) 9.3
Question: A dishonest person wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing 33 $ per litre so as to make a profit of 70% on cost when he sells the resulting milk and water mixture for 36$. In what ratio should he mix the water and milk?
(A) 1:120
(B) 67:120
(C) 67:8
(D) 8:120
(E) 1:2
Rationale: First of all, let's consider 1 liter of the stuff he is going to sell --- naive customers think it's pure milk, but we know it's some milk-water mixture. He is going to sell this liter of milk-water for $36.
This $36 should be a 20% increase over cost. Here, we need to think about percentage increases as multipliers.
Using multipliers
(cost)*1.70 = $36
cost = 36/1.7= 360/12 = $30
If he wants a 70% increase over cost on the sale of one liter of his milk-water, the cost has to be $21.17
Well, a liter of milk costs $33, so if he is going to use just $30 of milk in his mixture, that's 21.17/33 = 120/187 of a liter. If milk is 120/87 of the liter, then water is 67/187 of the liter, and the ratio of water to milk is 67:120. Answer choice(B)
Answer: (B) 67:120
Question: The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula C = 100,000p/(100 - p). According to this estimate, how much more would it cost to remove 90 percent of the pollutant from the pond than it would cost to remove 60 percent of the pollutant?
(A)  $300,000
(B)  $100,000
(C)  $50,000
(D)  $10,000
(E)  $5,000
Rationale: To remove 90% of pollutant
C= 100,000(90)/(100-90) = 900,000
To remove 60% of pollutant
C' = 100,000(60)/(100-60) = 600,000
Difference = C - C' = 300,000
Answer - A
Answer: (A)  $300,000
Question: A classroom has equal number of boys and girls. FIVE girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially?
(A) 16
(B) 24
(C) 32
(D) 48
(E) 20
Rationale: after 5 girls left remaining 5 girls
now boys 10 are twice as many as remaining girls.
initially boys=10 and girls=10.
ANSWER:E
Answer: (E) 20
Question: Without stoppages a train travels a certain distance with an average speed of 120 kmph and with stoppages it covers the same distance with an average speed of 90 kmph. What is the time in minutes per hour for which train stops?
(A) 5 min/hr
(B) 6 min/hr
(C) 12 min/hr
(D) 16 min/hr
(E) 15 min/hr
Rationale: Pick a smart number for the distance. lets say LCM 360
Without = 360/120 = 3 hours
With = 360/90= 4 hours
So in a trip of 4 hours, 1 hour is spent in stoppages
Hence, 60/4 = 15 min/hr on stoppages
Answer : E
Answer: (E) 15 min/hr
Question: A number is increased by 60 % and then decreased by 60 %. Find the net increase or decrease per cent.
(A) 19%
(B) 18%
(C) 27%
(D) 33%
(E) 36%
Rationale: Let the number be 100.
Increase in the number = 60 % = 60 % of 100
= (60/100 Ã— 100)
= 60
Therefore, increased number = 100 + 60 = 160
This number is decreased by 60 %
Therefore, decrease in number = 60 % of 160
= (60/100 Ã— 160)
= 9600/100
= 96
Therefore, new number = 160 - 96 = 64
Thus, net decreases = 100 - 64 = 36
Hence, net percentage decrease = (36/100 Ã— 100) %
= (3600/100) %
= 36 %
Answer:E
Answer: (E) 36%