mathewhe/aqua_rat huggingface dataset:
Question: Assume that 20 cows and 40 goats can be kept for 10 days for Rs.460. If the cost of keeping 5 goats is the same as the cost of keeping 1 cow, what will be the cost for keeping 50 cows and 30 goats for 12 days?
(A) Rs.1104
(B) Rs.1000
(C) Rs.934
(D) Rs.1210
(E) Rs.1410
Rationale: Explanation :
Assume that cost of keeping a cow for 1 day = c ,
cost of keeping a goat for 1 day = g
Cost of keeping 20 cows and 40 goats for 10 days = 460
Cost of keeping 20 cows and 40 goats for 1 day = 460/10 = 46
=> 20c + 40g = 46
=> 10c + 20g = 23 ---(1)
Given that 5g = c
Hence equation (1) can be written as 10c + 4c = 23 => 14c =23
=> c=23/14
cost of keeping 50 cows and 30 goats for 1 day
= 50c + 30g
= 50c + 6c (substituted 5g = c)
= 56 c = 56×23/14
= 92
Cost of keeping 50 cows and 30 goats for 12 days = 12×92 = 1104
Answer : Option A
Answer: (A) Rs.1104
Question: Two observations were made of a clock at different time:
1st observation:
The hour hand is exactly at a minute mark and the minute hand is six minutes ahead of it.
2nd observation:
The hour hand is exactly on a dissimilar minute mark and the minute hand is seven minutes ahead of it.
Can you find out how much time has passed between the above two observations?
(A) 1 hours and 12 minutes
(B) 3 hours and 12 minutes
(C) 2 hours and 12 minutes
(D) 4 hours and 12 minutes
(E) 5 hours and 12 minutes
Rationale: Solution:
The time at first observation:
1:12
The time at second observation:
3:24
Thus, two hours and twelve minutes have passed between the two observations.
Answer C
Answer: (C) 2 hours and 12 minutes
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
(A) 2
(B) 7
(C) 6
(D) 9
(E) 2
Rationale: 1/10 + 1/15 - 1/x = 1/18
x = 9
Answer: D
Answer: (D) 9
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/83 hours
(B) 33/13 hours
(C) 31/13 hours
(D) 30/13 hours
(E) 30/14 hours
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream = d/s = 60/26
= 30/13 hours.
Answer:D
Answer: (D) 30/13 hours
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What is the weight of the new person?
(A) 75 Kg
(B) 50 Kg
(C) 85 Kg
(D) 80 Kg
(E) 60 KG
Rationale: Explanation:
Total increase in weight = 8 × 2.5 = 20
If x is the weight of the new person, total increase in weight = x−65
=> 20 = x - 65
=> x = 20 + 65 = 85
Answer: Option C
Answer: (C) 85 Kg
Question: Given distinct positive integers 1, 11, 5, x, 2, and 9, which of the following could be the median?
(A) 3
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: The median of a set with even number of terms is the average of two middle terms when arranged in ascending (or descending) order.
Arrange numbers in ascending order: 1, 2, 5, 9, 11, and x.
Now, x can not possibly be less than 3 as given that all integers are positive and distinct (and we already have 1, 2, and 5).
Next, if x is 5<x<9 then the median will be the average of 5 and x. As all answers for the median are integers, then try odd values for x:
If x=6, then median=(5+6)/2=5.5 --> not among answer choices;
If x=7, then median=(5+7)/2=6 --> OK;
Answer: C.
Answer: (C) 6
Question: A and B can do a piece of work in 12 days and 24days. Both starts the work together for some time, but B leaves the job 6 days before the work is completed. Find the time in which work is finished.
(A) 10 days
(B) 12 days
(C) 14 days
(D) 5 days
(E) 6 days
Rationale: Explanation:
A & B completes the work in 12*24/12+24 = 12*24/36 = 8 days
2 days work = 2+1/8 = ¼ work
Remaining work = 1-1/4 = ¾
A completes ¾ work in ¾*16 = 12 days
Answer: Option B
Answer: (B) 12 days
Question: In what ratio should a variety of Rice costing Rs. 20 per kg be mixed with another variety of Rice costing Rs. 31.50 per kg to obtain a mixture costing Rs. 23.75 per kg?
(A) 16 : 30
(B) 30 : 14
(C) 16 : 31
(D) 31 : 15
(E) 15 : 31
Rationale: Let us say the ratio of the quantities of cheaper and dearer varieties = x : y
By the rule of allegation, x/y = (31.50 - 23.75) / (23.75 - 20) = 31/15
ANSWER:D
Answer: (D) 31 : 15
Question: The retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the 10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability X that 3 of Sam’s 4 funds grew by at least 10% over last year?
(A)  6C3 / 10C4
(B)  6C3 * 4C1 / 10C4
(C)  6C3 * 4C1 / 10P4
(D)  6P3 * 4P1 / 10C4
(E)  6P3 * 4P1 / 10P4
Rationale: Look at the answers. B is the only answer choice that uses only combination formulas and takes into account all the factors.
We know this is a combination, not a permutation. This rules out choices C, DE.
A clearly isn't the answer because X 6C3 only accounts for 3 of the funds he chose. 10C4, the denominator, is correct, so the numerator must be wrong.
B it is.
Answer: (B)  6C3 * 4C1 / 10C4
Question: Mike, Jim and Bob are all professional fisherman. Mike can catch 21 fish in one hour, Jim can catch twice as much and Bob can catch 50% more than Jim. If the three started to fish together and after 40 minutes Mike and Bob left, how many fish did the three fishermen catch in one hour?
(A) 64.
(B) 72.
(C) 86
(D) 98
(E) 112
Rationale: We are given
Rate of catching the fish for all three people
M - 21 fish/hour
J - 42 fish/hour
B - 63 fish/hour.
So in 1 hour, if they work together they can catch - 126 fish.
It is given they work together for first 40 min,
So by then they will have caught 2/3 * 128 = 84
Last 20 mins J will work alone and he can catch 1/3*42 = 14 in the remaining 20 mins, thus the total fishes they will catch in one hour = 84+14 = 98
ANSWER:D
Answer: (D) 98
Question: A reduction of 15% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
(A) 2.8
(B) 2.3
(C) 1.8
(D) 2.1
(E) 2.9
Rationale: 100*(15/100) = 15 --- 10
? --- 1 => Rs.1.5
100 --- 85
? --- 1.5 => Rs.1.8
Answer: C
Answer: (C) 1.8
Question: In a certain game, you perform three tasks. You flip a quarter, and success would be tails. You roll a single die, and success would be a odd number. You pick a card from a full playing-card deck, and success would be picking a heart card. If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?
(A) 7/16
(B) 1/16
(C) 25/8
(D) 11/13
(E) 8/13
Rationale: Event(1): Probability of getting tail in a flip of coin = 1/2
Event(2): Probability of getting odd number in a roll of dice = 3/6 = 1/2
Event(3): Probability of getting heart in a pack of card = 13/52 = 1/4
Probability of winning is having exactly one successful event is:
P(success 1)* P(Fail 2)* P(Fail 3) + P(Fail 1)* P(Success 2)* P(Fail 3) + P(Fail 1)* P(Fail 2)* P(Success 3)
= 1/2*1/2*3/4 +1/2*1/2*3/4 +1/2*1/2*1/4
=3/16 + 3/16 +1/16
=7/16
Answer :A
Answer: (A) 7/16
Question: The tax on a commodity is diminished by 20% but its consumption is increased by 20%. Find the decrease percent in the revenue derived from it?
(A) 12%
(B) 4%
(C) 16%
(D) 20%
(E) 22%
Rationale: Explanation:
100 * 100 = 10000
80 * 120 = 9600
10000------- 400
100 ------- ? = 4%
B
Answer: (B) 4%
Question: Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?
(A) 6/17
(B) 6/11
(C) 6/18
(D) 6/19
(E) 6/10
Rationale: Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20
Part filled by C in 3 minutes = 3/10
Required ratio = 3/10 * 20/11 = 6/11
Answer: B
Answer: (B) 6/11
Question: Two isosceles Triangles have equal vertical angles and their areas are in the ratio 9:25. Find the ratio of their corresponding heights .
(A)  4/5
(B)  5/4
(C)  3/2
(D)  5/7
(E)  3/5
Rationale: We are basically given that the triangles are similar.
In two similar triangles, the ratio of their areas is the square of the ratio of their sides and also, the square of the ratio of their corresponding heights.
Therefore, area/AREA=height^2/HEIGHT^2=9/25 --> height/HEIGHT=3/5.
Answer: E.
Answer: (E)  3/5
Question: What is theleast number should be added to 519, so the sum of the number is completely divisible by 25?
(A) 1
(B) 2
(C) 5
(D) 6
(E) 8
Rationale: (519/ 25) gives remainder 19
19 + 6 = 25, So we need to add 6
Answer : D
Answer: (D) 6
Question: A train 410 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40
(B) 56
(C) 44
(D) 42
(E) 34
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 410 + 140 = 550 m
Required time = 550 * 2/25 = 44 sec
Answer: Option C
Answer: (C) 44
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.15 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 65 sec
(B) 30 sec
(C) 48 sec
(D) 33 sec
(E) 12 sec
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.15 = 1.25 km = 1250 m.
Required time = 1250 * 3/125
= 30 sec.
Answer:B
Answer: (B) 30 sec
Question: which number need to add to 859622 to get a number exactly divisible by 456?
(A) 123234
(B) 345467
(C) 467879
(D) 356687
(E) 859622
Rationale: Dividend = Quotient * Divisor + Reminder
859622 / 456 gives quotient = 1885 and reminder = 62.
So, the next number divisible by 456 is 456 places infront of 456 * 1885
Which means 456 – 62 = 394 should be added to 859622.
E
Answer: (E) 859622
Question: Tom can lay bus route between twogiven bus stop in 16 days and Andy can do the same job in 12 days. With help of John, they did the job in 4 days only. Then, John alone can do the job in how many days?
(A) 9 1/5
(B) 9 3/5
(C) 9 5/7
(D) 10 1/5
(E) 10 3/5
Rationale: (A + B + C)'s 1 day's work =	1	,
4
A's 1 day's work =	1	,
16
B's 1 day's work =	1	.
12
Therefore C's 1 day's work =	1	-	(	1	+	1	)	=	(	1	-	7	)	=	5	.
4	16	12	4	48	48
So, C alone can do the work in	48	= 9 3	/5days.
5	5
B
Answer: (B) 9 3/5
Question: At Company K, 20 percent of the employees are secretaries and 60 percent are salespeople. If there are 45 other employees of Company K, how many employees does Company K have?
(A)  160
(B)  180
(C)  190
(D)  225
(E)  400
Rationale: Let the total number of employees in the company be x
% of secretaries = 20%
% of salespeople = 60%
% of of employees other than secretaries and salespeople = 100 - 80 = 20%
But this number is given as 45
so 20% of x = 45
x = 225
Therefore there a total of 225 employees in the company K
Correct answer - D
Answer: (D)  225
Question: The diagonal of a rectangle is cm and its area is 20 sq. cm. The perimeter of the rectangle must be:
(A) 18
(B) 77
(C) 625
(D) 276
(E) 191
Rationale: Explanation:
(or) {\color{Black} l^{2}+b^{2}=41}
Also,
{\color{Black} (l+b)^{2}=l^{2}+b^{2}+2lb}
= 41 + 40 = 81
(l + b) = 9.
Perimeter = 2(l + b) = 18 cm.
Answer: A) 18
Answer: (A) 18
Question: Series Problem like 4 12 x 44 46 132 134 begin of the Skype highlighting 44 46 132 134 end of the Skype highlighting. Find x?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: 134-132=2
46-44=2
x-12=2
x=14
ANSWER:B
Answer: (B) 14
Question: in a division sum the divisor is 12 times the quotient and 5 times the remainder.if the remainder is 48 what is the dividend
(A) 4748
(B) 4848
(C) 4846
(D) 4847
(E) 4840
Rationale: Dividend = divisor*quotient + remainder
divisor = 5*remainder = 5*48 = 240
now,
divisor = 12* quotient
240 = 12*quotient
quotient = 240/12 = 20
Dividend = divisor*quotient + remainder
Dividend = (240*20) + 48 = 4848
ANSWER:B
Answer: (B) 4848
Question: We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $560. How many green hats did we buy?
(A) A)36
(B) B)50
(C) C)40
(D) D)42
(E) E)44
Rationale: Let B be the number of blue hats and let G be the number of green hats.
B+G=85.
B=85-G.
6B+7G=560.
6(85-G)+7G=560.
510-6G+7G=560.
G=560-510=50.
The answer is B.
Answer: (B) B)50
Question: Gary’s Gas Station serves an average of 15 cars per hour on Saturdays, 10 cars per hour on Sundays, and 9 cars per hour on all other days of the week. If the station is open from 6 a.m. to 10 p.m. every day, how many cars does Gary’s station serve over the course of a typical week?
(A) 1,120
(B) 1,200
(C) 1,240
(D) 1,280
(E) 1,320
Rationale: 6 a.m. to 10 p.m. = 16 hours
Number of cars serviced on weekdays = (16 * 9 * 5)
Number of cars serviced on Saturday = (16 * 15)
Number of cars serviced on Sunday = (16 * 10)
Number of cars served in a week = 16(45 + 15 + 10) = 16 * 70 = 1120
Answer: A
Answer: (A) 1,120
Question: Before 7 years, dog A’s age was 4 times of dog B’s age and after 4 years, dog A’s age will be 3 times of dog B’s age. What is the difference of dog A’s age and dog B’s now?
(A) 36
(B) 42
(C) 54
(D) 60
(E) 70
Rationale: A - 7 = 4(B - 7) --> A - 4B = -21.............1
A + 4 = 3(B + 4) --> A - 3B = 8.............2
(2) - (1) --> B = 29 --> A =3(22)=99
A - B = 99 - 29 = 70
Answer: E
Answer: (E) 70
Question: Suresh borrows Rs. 10,000 for 2 years at 4 % p.a. simple interest. He lends it to Ramesh at 6 % p.a. for 2 years. Find his gain in this transaction per year.
(A) Rs. 150
(B) Rs. 200
(C) Rs. 400
(D) Rs. 450
(E) None of these
Rationale: Explanation:
Given:
We have to calculate the gain in 2 years.
1) In case of Suresh
S.I.(10000 × 4 × 2)/100= Rs. 800
2) In case of Ramesh
S.I.(10000 × 6 × 2)/100= Rs. 1200
Suresh has a pay a simple interest of Rs. 80 to the person from whom he borrowed Rs. 1000 and Ramesh has to pay Rs. 120 to Suresh.
Hence, gain in 2 years = 1200 – 800 = Rs. 400
But we are asked to find gain of Suresh per year. Therefore,
Gain in 1 year = 400 / 2 = Rs. 200
ANSWER IS B
Answer: (B) Rs. 200
Question: The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the width of this rectangle.
(A) W = 27
(B) W = 15
(C) W = 38
(D) W =43
(E) W = 13
Rationale: L * W = 300 : area , L is the length and W is the width.
2 L + 2 W = 70 : perimeter
L = 35 - w : solve for L
(35 - W) * W = 300 : substitute in the area equation
W = 15 and L = 20 : solve for W and find L using L = 35 - w.
correct answer B
Answer: (B) W = 15
Question: If the product of 2 integers is negative, at most how many of the integers can be negative?
(A) 1
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: The product of 2 integers is negative
Thus an odd number of integers need to be negative to have a negative product
We are asked at most how many are required.
So, the highest odd integer before 6,i.e. 1
Correct Option : A
Answer: (A) 1
Question: The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers ?
(A) 12/35
(B) 24/32
(C) 31/24
(D) 12/26
(E) 12/25
Rationale: Let the numbers be a and b. Then, a + b = 12 and ab = 35.
a + b/ab = 12/35
1/b+ 1/a= 12/35
Sum of reciprocals of given numbers =12/35
ANSWER: A
Answer: (A) 12/35
Question: A and B complete a work in 20 days. A alone can do it in 40 days. If both together can do the work in how many days?
(A) 1.0875 days
(B) 0.1875 days
(C) 0.0675 days
(D) 0.075 days
(E) 0.0175 days
Rationale: 1/20 + 1/40 = 0.075 days
ANSWER:D
Answer: (D) 0.075 days
Question: In a mayoral election, Candidate X received 1/5 more votes than candidate Y, and Candidate Y received 1/2 fewer votes than Z. If Z received 20,000 votes how many votes did candidate X received?
(A) 12000
(B) 22000
(C) 24000
(D) 26000
(E) 32000
Rationale: Z=20 --> Y received 1/2 fewer votes than Z --> Y=Z-1/2*Z=10;
X received 1/5 more votes than Y --> X=Y+1/5*Y=12.
Answer: A.
Answer: (A) 12000
Question: If a and b are odd integers, a Δ b represents the product of all odd integers between a and b, inclusive. If y is the smallest prime factor of (3 Δ 47) + 2, which of the following must be true?
(A) y is greater than 50
(B) 30 ≤ y ≤ 50
(C) 10 ≤ y < 30
(D) 3 ≤ y < 10
(E) y = 2
Rationale: (3 Δ 47) + 2 = 3*5*7*...*47+2 = odd + 2 = odd.
Now, 3*5*7*...*47 and 3*5*7*...*47 +2 are consecutive odd numbers. Consecutive odd numbers are co-prime, which means that they do not share any common factor but 1. For example, 25 and 27 are consecutive odd numbers and they do not share any common factor but 1.
Naturally every odd prime between 3 and 47, inclusive is a factor of 3*5*7*...*47, thus none of them is a factor of 3*5*7*...*47 +2. Since 3*5*7*...*47+2 = odd, then 2 is also not a factor of it, which means that the smallest prime factor of 3*5*7*...*47 +2 is greater than 50.
Answer: A.
Answer: (A) y is greater than 50
Question: If -3x > 9, which of the following must be true?
(A) x < -3
(B) x < -2
(C) x > 3
(D) x > -2
(E) x > 0
Rationale: -3x > 9
=> -x > 3
=> x < - 3
Answer A
Answer: (A) x < -3
Question: Boy sells a book for Rs. 810 he gets a loss of 10 %, To gain 10%, what should be the SP?
(A) 430
(B) 990
(C) 550
(D) 590
(E) 600
Rationale: Cost price = 810/90 x 100 = 900
To gain 10% = 900 x 10/100 = 90
SP = CP + gain = 900 + 90 = 990
Answer : B
Answer: (B) 990
Question: Each of the 59 members in a Arts class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 22 students sign up for the poetry club, 27 students for the history club, and 28 students for the writing club. If 6 students sign up for exactly two clubs, how many students sign up for all three clubs?
(A) 2
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Each of the 59 members in a Arts class is required to sign up for a minimum of one and a maximum of three academic clubs. Total = G1 + G2 + G3 - (# In exactly 2) - 2*(# in 3 sets)
59 = 22+27+28 - (6) - 2x
so, # In 3 sets = 6=C
Answer: (C) 6
Question: A manufacture of printer toner adjusts its price of color toner from $33 to $35 a cartridge and the price of standard black ink toner from $29 to $30 a cartridge if a document printing center spends an average of $1555 a month for toner of which 3/5 is for color cartridges how much more per month will the printing center spent?
(A) 78
(B) 79
(C) 60
(D) 80
(E) 90
Rationale: Total money spend per month = 1555
Money spend on color toner cartridges = 3/5*1555
= 933
Money spend on black ink toner cartridges = 2/5*1555
= 622
Number of color toned cartridges bought = 933/33
Number of black ink toned cartridges bought = 622/29
New price of color toned cartridges bought = 933/33*35
New price of black ink toned cartridges bought = 622/29*30
Total price = 1632.993
Additional money spend = Rs77.993
ANSWER:A
Answer: (A) 78
Question: Dany bought a total of 20 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Let X be the number of cards that cost $0.25 each and Y the number of cards that cost $0.15 each. The total number of cards is 20. Hence
X + Y = 20
If X is the number of cards at $0.25, then the X cards cost
0.25 X
If Y is the number of cards at $0.15, then the Y cards cost
0.15 Y
The total cost of the X cards and the the Y cards is known to be $4.2 and also given by
0.25 X + 0.15 Y = 4.2
We now need to solve the system of equations
X + Y = 20
0.25 X + 0.15 Y = 4.2
The first equation gives Y = 20 - X. Substitute y by 20 - x in the second equation and solve
0.25 X + 0.15 (20 - X) = 4.2
X(0.25 - 0.15) + 3 = 4.2
0.1 X = 1.2
X = 12 and Y = 20 - 12 = 8
correct answer C
Answer: (C) 8
Question: A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 300. Find the sum?
(A) 7000
(B) 2500
(C) 2778
(D) 2800
(E) 2791
Rationale: Let the sum be Rs. x.
(x * 18 * 2)/100 - (x * 12 * 2)/100 = 300 => 36x/100 - 24x/100 =300
=> 12x/100 = 300 => x = 2500.Answer:B
Answer: (B) 2500
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) 22
(B) 28
(C) 20
(D) 10
(E) 17
Rationale: M = 15
S = 5
DS = 15 + 5 = 20
Answer:C
Answer: (C) 20
Question: What is the smallest positive integer x, such that 1,152x is a perfect cube?
(A) 4
(B) 6
(C) 8
(D) 12
(E) 18
Rationale: We need to make 1152x a perfect cube, hence we need to have the powers a multiple of 3
1152 = 2^7*3^2
The minimum value of x for which 1152x is a perfect cube = 2^2*3 = 12
Correct Option: D
Answer: (D) 12
Question: How many minutes does it take Dorathy to type 16 words if she types at the rate of 4 words per minute?
(A) 7
(B) 3
(C) 6
(D) 2
(E) 4
Rationale: time*rate=job --> time*4=16 --> time=16/4=2.
Answer: E.
Answer: (E) 4
Question: Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
(A) 22
(B) 74
(C) 77
(D) 27
(E) 29
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 300 / (15 + 25)5/18 = 300* 18 / 40 * 5 = 27 seconds.
Answer: D
Answer: (D) 27
Question: 40 litres of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 800 km using 1200 cc engine?
(A) 80 litres
(B) 90 litres
(C) 120 litres
(D) 170 litres
(E) None of these
Rationale: Explanatory Answer
To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 800/600*40 = 53.33 litres.
However, the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity.
i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too.
Therefore, with a 1200 cc engine, quantity of diesel required = 1200/800*53.33 = 80 litres.
Answer A
Answer: (A) 80 litres
Question: A person covered one-fourth of the total distance at 12 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
(A) 19 (1/8)kmph
(B) 19 (1/5)kmph
(C) 21 (7/3)kmph
(D) 27 (1/3)kmph
(E) 21 (1/8)kmph
Rationale: Let the total distance be x km
total time taken = (x/4)/12 + (3x/4)/24 = x/48+ x/32 = 5x/96
Average speed = x/(5x/96) = 96/5 kmph
= 19 1/5 kmph.
Answer:B
Answer: (B) 19 (1/5)kmph
Question: A rower can row upstream at 7 km/hr and downstream at 11 km/hr. What is the rower's rate in still water?
(A) 7.5 km/hr
(B) 8.0 km/hr
(C) 8.5 km/hr
(D) 9.0 km/hr
(E) 9.5 km/hr
Rationale: The rate in still water is 1/2 * (11 + 7) = 9 km/hr
The answer is D.
Answer: (D) 9.0 km/hr
Question: A man is 34 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is?
(A) 16
(B) 19
(C) 15
(D) 32
(E) 40
Rationale: Let the son's present age be x years.
Then, man's present age = (x + 24) years.
(x + 34) + 2 = 2(x + 2)
x + 36 = 2x + 4
=> x =32 .
Answer: D
Answer: (D) 32
Question: A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?
(A) 22
(B) 88
(C) 15
(D) 66
(E) 81
Rationale: B's 1 day work = (1/12 - 1/20) = 1/30
Now, (A + B)'s 1 day work = (1/20 + 1/60) = 1/15
So, A and B together will complete the work in 15 days.
Answer: C
Answer: (C) 15
Question: A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:
(A) 700
(B) 650
(C) 850
(D) 800
(E) 900
Rationale: Explanation :
Suppose originally he had x apples.
Then, (100 - 40)% of x = 420.
=> 60% of x = 420
=> 60 * x /100 = 420
=> x = (420 * 100) / 60
=> x = 700
Hence A is the answer
Answer : A
Answer: (A) 700
Question: A computer is programmed to multiply consecutive even integers 2*4*6*8*…*n until the product is divisible by 1419, What is the value of n?
(A) 86
(B) 38
(C) 62
(D) 122
(E) 672
Rationale: Factorise 1419.. 3*11*43..
So n has to be a multiple of largest prime number,61..
So n=2*43=86..
Ans :A
Answer: (A) 86