mathewhe/aqua_rat huggingface dataset:
Question: A man buys Rs. 50 shares in a company which pays 10% dividend.If the man gets 12.5% on his investment,at what price did he buy the shares ?
(A) Rs. 37.50
(B) Rs. 40
(C) Rs. 48
(D) Rs. 52
(E) None
Rationale: Solution
Dividend on 1 share = Rs. (10/100x50)=Rs.5
Rs. 12.50 is an income on an investment of Rs.100.
Rs. 5 is an income on an investment of Rs.(100x2/25x5)= Rs.40
∴ Cost of 1 share = Rs. 40.
Answer B
Answer: (B) Rs. 40
Question: If both 5^2 and 3^3 are factors of n x (2^5) x (6^2) x (7^3), what is the smallest possible positive value of n?
.
(A) 25
(B) 27
(C) 45
(D) 75
(E) 125
Rationale: If both 5^2 & 3^3 are factors, then they must be present in the number.
Leaving rest of the prime factors and splitting 6^2 into 3^2 * 2^3.
The number is lacking 5^2 & a 3, so that 5^2 and 3^3 is a factor.
Hence the smallest number is 5^2 * 3 = 75
ANSWER:D
Answer: (D) 75
Question: How long will a boy take to run round a square field of side 35 metres. If he runs at the rate of 9km/hr ?
(A) 56 sec
(B) 1minute
(C) 45sec
(D) 58sec
(E) 50sec
Rationale: Speed = 9 km/hr = 9*5/18 = 5/2 m/sec
distance = 35*4 = 140 m
time taken = 140*2/5 = 56 sec.
Answer is A
Answer: (A) 56 sec
Question: A class contains five juniors and five seniors. If one member of the class is assigned at random to present a paper on a certain subject, and another member of the class is randomly assigned to assist him, what is the probability R that both will be juniors?
(A) 1/10
(B) 1/5
(C) 2/9
(D) 2/5
(E) 1/2
Rationale: I think you're right. The other way to do it (but the long way) is to figure out the probability that it is not two Juniors.
2 seniors = P(Senior) * P(Senior) = 2/9
1 Senior and 1 Junior = (1/2) *(5/9)*2 = 5/9
Probability that it is not two Juniors is 5/9+2/9 = 7/9 so the probability R that it is two juniors is 1- (7/9) = 2/9.C
Answer: (C) 2/9
Question: Two cyclist start on a circular track from a given point but in opposite direction with speeds of 7m/s and 8m/s. If the circumference of the circle is 600meters, after what time will they meet at the starting point?
(A) 20sec
(B) 15sec
(C) 30sec
(D) 50sec
(E) 40min
Rationale: They meet every 600/7+8 = 40sec
Answer is E
Answer: (E) 40min
Question: The average of 5 quantities is 9. The average of 3 of them is 4. What is the average of remaining 2 numbers?
(A) 16.5
(B) 10
(C) 8
(D) 9.5
(E) None of these
Rationale: ANSWER: A
(5x9-3x4)/2=16.5
Answer: (A) 16.5
Question: Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2178?
(A) 2228
(B) 2771
(C) 2200
(D) 2877
(E) 1112
Rationale: Explanation:
Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2178.
=> (90%) of (110%) of x = Rs. 2178.
=> (90/100)(110/100)x = 2178
=> x = (2178 * 100)/(9 * 11)
=> x = Rs. 2200
Answer:C
Answer: (C) 2200
Question: The number 0.8 is how much greater than 1/8 ?
(A) ½
(B) 27/40
(C) 1/50
(D) 1/500
(E) 2/500
Rationale: let x be the difference
then
.8-1/8=x
8/10-1/8=x
x=27/40
ans B
Answer: (B) 27/40
Question: How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters ?
(A) 5^10
(B) 5^11
(C) 5^18
(D) 5^12
(E) 5^16
Rationale: Each of the 10 letters can be posted in any of the 5 boxes.
So, the first letter has 5 options, so does the second letter and so on and so forth for all of the 10 letters.
i.e. 5*5*5*….*5 (upto 10 times)
= 5 ^ 10.
Answer: A
Answer: (A) 5^10
Question: The difference between C.I. and S.I. on an amount of $15,000 for 2 years is $54. What is the rate of interest per annum?
(A) 5%
(B) 6%
(C) 7%
(D) 8%
(E) 9%
Rationale: $54 is the interest on the first year of interest.
Let x be the interest rate.
The interest after the first year is 15000*x.
The interest on the first year's interest is 15000*x*x
15000*x^2 = 54
x = 0.06
The answer is B.
Answer: (B) 6%
Question: The difference in compound interest earned on a deposit (compounded annually) in year 1 and year 2 is $ 40. Had the interest rate been three times its present value, the difference z would have been how much?
(A) 40/3
(B) 40
(C) 120
(D) 360
(E) 420
Rationale: CASE 1:
Deposit = $x;
Rate of increase = r.
Interest yearned in 1 year = xr. Deposit in 1 year = x + xr.
Interest yearned in 2 year = (x + xr)r.
The difference z= (x + xr)r - xr = xr^2 = 40.
CASE 2:
Deposit = $x;
Rate of increase = 3r.
Interest yearned in 1 year = x(3r). Deposit in 1 year = x + 3xr.
Interest yearned in 2 year = (x + 3xr)3r.
The difference = (x + 3xr)3r - 3xr = 9xr^2. Since from CASE 1 we know that xr^2 = 40, then 9xr^2 = 9*40 = 360.
Answer: D.
Answer: (D) 360
Question: Lagaan is levied on the 60 percent of the cultivated land. The revenue department collected total Rs. 3,84,000 through the lagaan from the village of Mettur. Mettur, a very rich farmer, paid only Rs.480 as lagaan. The percentage of total land of Mettur over the total taxable land of the village is:
(A) 0.20833
(B) 0.34667
(C) 0.45788
(D) 0.78452
(E) 0.97343
Rationale: Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x
\therefore Cultivated land of village = 384000x
\therefore Required percentage = \inline \frac{800x}{384000}\times 100 = 0.20833
A
Answer: (A) 0.20833
Question: Each light bulb at a hotel is either incandescent or fluorescent. At a certain moment, forty percent of the incandescent bulbs are switched on, and eighty percent of the fluorescent bulbs are switched on. If 75 percent of all the bulbs are switched on at this moment, what percent of the bulbs that are switched on are incandescent?
(A) 6.7%
(B) 10.3%
(C) 14.5%
(D) 18.2%
(E) 23.6%
Rationale: Let I be the number of incandescent bulbs.
Let F be the number of fluorescent bulbs.
0.4I + 0.8F = 0.75(I+F)
0.05F = 0.35I
F = 7I
This means that for every 1 incandescent bulb, there are 7 fluorescent bulbs.
The percent of bulbs that are switched on which are incandescent is:
0.4I / (0.4I + 0.8F) = 0.4I / (0.4I + 0.8*7I) = 0.4I / 6I = 1/15 which is about 6.7%.
The answer is A.
Answer: (A) 6.7%
Question: A man is standing on a railway bridge which is 165 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed.
(A) 10 m/sec
(B) 13.75 m/sec
(C) 18 m/sec
(D) 19 m/sec
(E) 25 m/sec
Rationale: If length of train is l and speed of train is s, then
l/s = 8
(l+165)/s = 20
(l+165)/l = 20/8 =5/2
2l+330 =5*l
3*l= 330
l=110 mtrs
s= l/8 = 110/8 = 13.75 m/sec
ANSWER:B
Answer: (B) 13.75 m/sec
Question: A grocer is storing soap boxes in cartons that measure 25 inches by 48 inches by 60 inches. If the measurement of each soap box is 8 inches by 6 inches by 5 inches, then what is the maximum number of soap boxes that can be placed in each carton?
(A) 210
(B) 252
(C) 280
(D) 320
(E) 300
Rationale: however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers
Dimensions of the box =25*48*60
Dimensions of the soap = 5*6*8
we get = 5x6x10 = 300
so the question is why this particular arrangement, in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number
the answer is (E)
Answer: (E) 300
Question: A Book was sold at a loss of 10%. If it was sold for $140 more, there would have been a gain of 4%. What is the cost price?
(A) $1200
(B) $1300
(C) $1000
(D) $1700
(E) $1050
Rationale: C
$1000
90%
104%
--------
14% ---- 140
100% ---- ? => $1000
Answer: (C) $1000
Question: A straight line is formed using two points A(3,3) and B(6,6). Another point P(x,y) lies between A and B such that AP/BP = 2. What are the coordinates of P?
(A) (7/2, 7/2)
(B) (4, 4)
(C) (21/5, 21/5)
(D) (9/2, 9/2)
(E) (5, 5)
Rationale: The equation of the straight line is y = x, so the x- and y-coordinates of P are the same.
The x, y coordinates are 2/3 of the distance from 3 to 6.
x = 3 + (6-3)*(2/3) = 3 + 2 = 5 = y
The answer is E.
Answer: (E) (5, 5)
Question: John sells encyclopedias door-to-door. He earns $160 on every paycheck, regardless of how many sets he sells. In addition, he earns commission as follows:
Commission Sales
10% $0.00 - $10,000.00
5% $10,000.01 --->
He does not earn double commission.That is, if his sales are $12,000, he earns 10% on the first $10,000 and 5% on the remaining $2,000.
His largest paycheck of the year was $1,320. What were his sales for that pay period?
(A) A)13,000
(B) B)13,200
(C) C)16,400
(D) D)15,800
(E) E)19,600
Rationale: His pay check was $1320.
Out of this, $160 was his fixed salary so the total commission he earned was $1320 - $160 = $1160
He earns 10% on the sales of first $10,000 which gives a commission of $1000.
He earns 5% on every subsequent dollar. Since he earns another $160, he must have had sales of another 160*(100/5) = 3200
So his total sales must have been $10,000 + $3200 = $13,200
B
Answer: (B) B)13,200
Question: The C.P of 16 books is equal to the S.P of 18 books. Find his gain% or loss%?
(A) 16 2/3% loss
(B) 11 1/9% loss
(C) 16 3/3% loss
(D) 36 2/3% loss
(E) 56 2/3% loss
Rationale: 16 CP = 18 SP
18 --- 2 CP loss
100 --- ? => 11 1/9% loss
Answer:B
Answer: (B) 11 1/9% loss
Question: On multiplying a number A by 153, the result obtained was 102325. However, it is found that both the 2's are wrong. Find the correct result.
(A) 104345
(B) 107375
(C) 108385
(D) 109395
(E) 105355
Rationale: The only thing you actually know about the correct number A is that it is divisible by 153 and has 5 as a factor.
You should immediately try to find the factors of 153 and look for them in the options.
153 = 9*17
Divisibility by 9 is easy to check. Only (D) satisfies.
Answer: (D) 109395
Question: From a group of 3 boys and 3 girls, 2 children are to be randomly selected. What is the probability that 1 boy and 1 girl will be selected?
(A) 1/10
(B) 4/9
(C) 1/2
(D) 9/15
(E) 2/3
Rationale: The total number of ways to choose 2 children from 6 is 6C2 = 15
The number of ways to choose 1 boy and 1 girl is 3*3 = 9
P(1 boy and 1 girl) = 9/15
The answer is D.
Answer: (D) 9/15
Question: In what time will a train 110 m long cross an electric pole, it its speed be 128 km/hr?
(A) 2.5 sec
(B) 2.9 sec
(C) 3.1 sec
(D) 8.7 sec
(E) 8.5 sec
Rationale: Speed = 128 * 5/18 = 36 m/sec
Time taken = 110/36 = 3.1 sec.
Answer: C
Answer: (C) 3.1 sec
Question: In the following list of numerals, how many 3s are followed by 3, but NOT preceded by 3?
2463315 7833346233339723
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: total 3 are there
ANSWER:C
Answer: (C) 3
Question: Two circular signs are to be painted. If the diameter of the larger sign is seven times that of the smaller sign, how many times more paint is needed to paint the larger sign? (We can assume that a given amount of paint covers the same area on both signs.)
(A) 7
(B) 14
(C) 42
(D) 49
(E) 98
Rationale: Let R be the radius of the smaller sign.
Then the diameter of the smaller sign is 2R, the diameter of the larger sign is 14R, and the radius of the larger sign is 7R.
The area A of the smaller sign is A = piR^2.
The area of the larger sign is pi(7R)^2=49piR^2=49A.
Since the area is 49 times larger, we need 49 times more paint for the larger sign.
The answer is D.
Answer: (D) 49
Question: A,B and C engage in a business with a joint capital of Rs. 25000. If at the end of a year A gets Rs.5000, B Rs.2000 and C Rs.3000 out of profits, how much capital did B contribute?
(A) Rs.6000
(B) Rs.5500
(C) Rs.4500
(D) Rs.4000
(E) Rs.5000
Rationale: Total profit = Rs.10000 B's profit share =2000/10000 =1/5 of the total profit B's capital =1/5*25000=Rs.5000 Answer : E
Answer: (E) Rs.5000
Question: A side of beef lost 20 percent of its weight in processing. If the side of beef weighed 640 pounds after processing, how many pounds did it weigh before processing?
(A) 191
(B) 355
(C) 800
(D) 840
(E) 900
Rationale: Let weight of side of beef before processing = x
(80/100)*x = 640
=> x = (640 * 100)/80 = 800
Answer C
Answer: (C) 800
Question: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 33 percent, what is the discount rate on Pony jeans?
(A) 9%
(B) 10%
(C) 11%
(D) 12%
(E) 65%
Rationale: x discount on Pony jeans, (0.33-x) discount on Fox jeans.
Set the equation: 3*15(0.33-x)+2*18x=9 --> x=0.65=65%
Answer: E.
Answer: (E) 65%
Question: Murugan, Prasanna and Arun invested Rs.8000, Rs.4000 and Rs.8000 respectively in a business. Arun left after six months .If after eight months, there was a gain of Rs.4005, then what will be the share of Prasanna?
(A) Rs.890
(B) Rs.1335
(C) Rs.1602
(D) Rs. 1780
(E) None
Rationale: Solution
Murugan : Prasanna : Arun	=(8000×6):(4000×8):(8000×8)
= 48 : 32 : 64
= 3 : 2 : 4.
Kamal's share	= Rs.4005×2/9)
= Rs.890.
Answer A
Answer: (A) Rs.890
Question: The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 56. Find their present ages.
(A) 16, 28, 38
(B) 16, 28, 36
(C) 16, 28, 32
(D) 16, 28, 30
(E) 16, 28, 31
Rationale: Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
20x = 80 => x = 4
Their present ages are 16, 28 and 36 years respectively.
Answer: B
Answer: (B) 16, 28, 36
Question: If the price of a TV is first decreased by 20% and then increased by 50%, then the net change in the price will be :
(A) 20% increase
(B) 10% increase
(C) 10% decrease
(D) 6% increase
(E) None of these
Rationale: Explanation :
Solution: let the original price be Rs. 100.
New final price = 150% of(80% of 100) =Rs. 150/100 * 80/100 * 100 = Rs. 120.
.'. Increase = 20%
Answer : A
Answer: (A) 20% increase
Question: Weights of two friends Ram and Shyam are in the ratio of 4 : 5. Ram’s weight increases by 10% and the total weight of Ram and Shyam together becomes 82.8 kg, with an increase of 15%. By what per cent did the weight of Shyam increase?
(A) 12.5%
(B) 17.5%
(C) 19%
(D) 21%
(E) None of these
Rationale: Let the weights of Ram and Shyam be 4x and 5x. Now,according to question,
4x×110/100+Shyam?snewwt4x×110100+Shyam?s new wt = 82.8........ (i)
and 4x + 5x = 9x+115/100= 82.8........ (ii)
From (ii), x = 8
Putting in (i),
we get Shyam’s new wt = (82.8 – 35.2) = 47.6
% increase in Shyam’s wt = (47.6−40/40×100) = 19
Answer C
Answer: (C) 19%
Question: nine baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?
(A) 40320
(B) 40213
(C) 40311
(D) 24089
(E) 25608
Rationale: it is like a circular arrangement.
total ways for n people to arrange in a circle is = factorial (n-1)
in this case n= 9
hence ans = 8 factorial = 40320
hence A
Answer: (A) 40320
Question: Two numbers are respectively 20% and 25% more than a third number. The percentage that is first of the second is?
(A) 86%
(B) 98%
(C) 96%
(D) 36%
(E) 91%
Rationale: I II III
120 125 100
125----------120
100-----------? => 96%
Answer: C
Answer: (C) 96%
Question: Two numbers are in the ratio of 1 : 2. If 10 be added to both, their ratio changes to 3 : 5. The greater number is
(A) 20
(B) 24
(C) 28
(D) 32
(E) 40
Rationale: Let the ratio be X : Y,
Given X/Y = 1/2 ,
(X + 10)/(Y + 10) = 3/5
=> X = 20
And Y = 40
ANSWER:E
Answer: (E) 40
Question: If y exceeds x by 30%, then x is less than y by?
(A) 1/7%
(B) 1/9%
(C) 1/11%
(D) 1/13%
(E) 1/17%
Rationale: X=100	y=130
130------30
100-------? => 23 1/13%
Answer:D
Answer: (D) 1/13%
Question: How many multiples of 10 are there between 10 and 1000, exclusive?
(A) 98
(B) 99
(C) 100
(D) 101
(E) 97
Rationale: 98
multiples of 5 between 1 and 36 exclusive.
from 10 * 2 upto 10*99, (2,3,4,...,99). Hence, 98 multiples !
correct option is A
Answer: (A) 98
Question: In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 79 more candidates got selected than A. What was the number of candidates appeared from each State?
(A) 7000
(B) 7900
(C) 6000
(D) 5000
(E) 4000
Rationale: State A and State B had an equal number of candidates appeared.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 79 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 79
=> total appeared candidates in State B = 79 x 100 = 7900
=> total appeared candidates in State A = total appeared candidates in State B = 7900
Answer: (B) 7900
Question: Which of the following describes all values of x for which 1–x^2 <= 0?
(A)  x >= 1
(B)  x <= –1
(C)  0 <= x <= 1
(D)  x <= –1 or x >= 1
(E)  –1 <= x <= 1
Rationale: Which of the following describes all values of x for which 1–x^2 >= 0?
(A) x >= 1
Plugged in 2. 1–(2)^2 >= 0 -3>=0? yes. But are these all the values? No. Wrong
(B) x <= –1
Plugged in -2. 1–(-2)^2 >= 0 -3>=0? yes. But are these all the values? No. Wrong.
(C) 0 <= x <= 1
Start with 0. 1-0 = 1. Wrong. All the other values wrong as well.
(D) x <= –1 or x >= 1
This is the Correct Answer as it captures both A and B. Answer is D.
(E) –1 <= x <= 1
Plug in 0. Value is greater than 0. Wrong.
Correct answer is D.
Answer: (D)  x <= –1 or x >= 1
Question: Three years ago, John’s age was half of the age he will be in 8 years. How old is he now?
(A) 14years
(B) 15years
(C) 16years
(D) 17years
(E) 18years
Rationale: Let John=j,j-3=(j+8)/2,then j=14years
ANSWER:A
Answer: (A) 14years
Question: If 9a - b = 10b + 70 = -12b - 2a, what is the value of 9a - 11b?
(A) -4
(B) 70
(C) 0
(D) 2
(E) 4
Rationale: This implies 9a - b = 10b + 70, 9a -b = -12b -2a, 10b + 70 = -12b -2a
Manipulating the second equation gives us 9a - b = 10b + 70 ==> 9a - 11b = 70
Answer is B
Answer: (B) 70
Question: Ten years ago, the age of Anand was one-third the age of Bala at that time. The present age of Bala is 14 years more than the present age of Anand. Find the present age of Anand?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: Let the present ages of Anand and Bala be 'a' and 'b' respectively.
a - 10 = 1/3 (b - 10) --- (1)
b = a + 14
Substituting b = a + 12 in first equation,
a - 10 = 1/3 (a + 4) => 3a - 30 = a + 4
=> 2a = 26 => a = 13.
ANSWER:A
Answer: (A) 13
Question: In covering a distance of 30 km, Arun takes 22 hours more than Anil. If Arun doubles his speed, then he would take 1 hour less than Anil. What is Arun's speed?
(A) 8kmph
(B) 5kmph
(C) 4kmph
(D) 7kmph
(E) 9kmph
Rationale: Explanation:
If Arun doubles his speed, he needs 3 hour less. Double speed means half time. Hence, half of the time required by Arun to cover 30 km =3 hour
i.e., Time required by Arun to cover 30 km =6 hour
Arun's speed =30/6=5 kmph
ANSWER IS B
Answer: (B) 5kmph
Question: Income and expenditure of a person are in the ratio 15 : 8. If the income of the person is Rs. 15000, then find his savings?
(A) 6999
(B) 7000
(C) 7001
(D) 7002
(E) 7003
Rationale: Let the income and the expenditure of the person be Rs. 15x and Rs. 8x respectively.
Income, 15x = 15000 => x = 1000
Savings = Income - expenditure = 15x - 8x = 7x = 7(1000)
So, savings = Rs. 7000.
Answer:B
Answer: (B) 7000
Question: There are 5,290 feet in 1 mile and 12 inches in one foot. How many inches are in a mile?
(A) 5,280 - 12
(B) 5,280/12
(C) 12(5,280)
(D) 12^2(5,280)
(E) 12*5,290
Rationale: 1 feet = 12 inches
1 mile = 5290 feet
1 mile = 5290*12 inches
Ans: E
Answer: (E) 12*5,290
Question: When two dice are rolled, what is the probability that the sum of the two numbers is 5?
(A)  1/9
(B)  2/9
(C)  1/3
(D)  2/3
(E)  None of the above
Rationale: We have 4 outcomes that satisfy the question:
1-4
2-3
3-2
4-1
the probability is (1/6*1/6)*4= 4/36= 1/9
I think the answer is A
Answer: (A)  1/9
Question: The average age of 50 students in a class is 10years. If teacher's age is also included then average increases 1year then find the teacher's age?
(A) 59
(B) 55
(C) 61
(D) 45
(E) 36
Rationale: Total age of 50 students = 50*10 = 500
Total age of 51 persons = 51*11 = 561
Age of teacher = 561-500 = 61years
Answer is C
Answer: (C) 61
Question: A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 380 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?
(A)  90
(B)  110
(C)  120
(D)  130
(E)  240
Rationale: Orchestra Seats - a
Balcony Seats - b
a+b = 380
and 12a + 8b = 3320
Solving equations simultaneously (Multiply Equation 1 with 8 and subtract from second equation)
4a = 3320 - 8*380 = 3320 - 3040 = 280
i.e. a = 70
and b = 380-70 = 310
More seats in balcony than orchestra = b-a = 310 - 70 = 240
Answer: option E
Answer: (E)  240
Question: Two horses start trotting towards each other, one from A to B and another from B to A. They cross each other after one hour and the first horse reaches B, 5/6 hour before the second horse reaches A. If the distance between A and B is 50 km. what is the speed of the slower horse?
(A) 30 km/h
(B) 15 km/h
(C) 25 km/h
(D) 20 km/h
(E) 27 km/h
Rationale: Explanation:
If the speed of the faster horse be \inline f_{s} and that of slower horse be Ss.then
Now, you can go through options.
The speed of slower horse is 20km/h
Since, 20+30=50 and 50/20=50/30=5/6
ANSWER IS D
Answer: (D) 20 km/h
Question: If a tank A can be filled within 10 hrs and 1/4th of tank B is filled in 19 hrs. Then what is the duration of the tank B to fill completely?
(A) 74
(B) 75
(C) 76
(D) 77
(E) 78
Rationale: 1/4th of tank B takes 19hrs then
to fill completely it takes 19*4 = 76hrs
ANSWER:C
Answer: (C) 76
Question: Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 6th shift?
(A) 1/27
(B) 1/54
(C) 1/81
(D) 1/162
(E) 1/486
Rationale: Fraction of area unpainted after FIRST shift of Amit = 1-(1/2) = 1/2
Fraction of area unpainted after FIRST shift of Ian = (1/2)-(1/3)(1/2) = (2/3)(1/2)
Fraction of area unpainted after SECOND shift of Amit = (1/2)(2/3)(1/2)
Fraction of area unpainted after SECOND shift of Ian = (2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after THIRD shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after THIRD shift of Ian = (2/3)(1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after FORTH shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after FORTH shift of Ian = (2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after FIFTH shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after FIFTH shift of Ian = (2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after SIXTH shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)=486
Answer: option E
Answer: (E) 1/486
Question: Find the area of the quadrilateral of one of its diagonals is 28 cm and its off sets 8 cm and 2 cm?
(A) 140 cm2
(B) 150 cm2
(C) 168 cm2
(D) 182 cm2
(E) 200 cm2
Rationale: 1/2 * 28(8 + 2)
= 140 cm2
Answer: A
Answer: (A) 140 cm2