mathewhe/aqua_rat huggingface dataset:
Question: Train A and Train B began traveling towards each other from opposite ends of a 480-mile long track at 1:00 PM. If Train A traveled at 35 miles per hour and Train B traveled at 25 miles per hour, at what time did the trains meet?
(A) 5:40 PM
(B) 6:00 PM
(C) 7:20 PM
(D) 9:00 PM
(E) 9:20 PM
Rationale: This question tests your concepts of relative speed:
If two trains are moving in opposite direction, then distance will reduce at a rate of (Speed of 1 + Speed of 2)
If two trains are moving in same direction, then distance will reduce at a rate of (Speed of 1 - Speed of 2)
Here the trains are moving towards each other, hence in opposite direction.
Trains will cover the 500 mile track in a time of 500/(25 + 35) = 480/60 = 8 hours
Trains started at 1:00 PM, there they will meet at 9:00 PM
Option D
Answer: (D) 9:00 PM
Question: An amount of 1,00,000 is invested in two types of shares. The first yields an interest of 9% p.a. and the second, 11% p.a. If the total interest at the end of one year is 9 3⁄4% , then the amount invested in each share was:
(A) 52,500; 47,500
(B) 62,500; 37,500
(C) 72,500: 27,500
(D) 82,500; 17,500
(E) None of these
Rationale: Let the sum invested at 9% be x and that invested at 11% be (100000 – x).
Then,
(x×9×1/100)+[(100000−x)×11×1/100]
= (100000×39/4×1/100)
⇒ 9x+1100000−11x/100=39000/4=9750
⇒ 2x = (1100000 – 975000) = 125000 ⇒ x = 62500.
∴ Sum invested at 9% = 62500.
Sum invested at 11% = (100000 – 62500) = 37500.
Answer B
Answer: (B) 62,500; 37,500
Question: What is the product of all positive factors of 12?
(A) 39
(B) 324
(C) 1728
(D) 3042
(E) 5832
Rationale: Positive factors of 12 are 1, 2, 3, 4, 6, 12.
So product is: 12*6*4*3*2*1 = 1728
Answer: C
Answer: (C) 1728
Question: A wheel rotates 20 times every minute and moves 15 cm during each rotation. How many metres does the wheel move in one hour?
(A) 6 metre
(B) 18 metre
(C) 180 metre
(D) 1200 metre
(E) 130 metre
Rationale: Number of times wheel moves in 1 hour = 12 * 60 = 1200
:. Distance moves = (1200*15) cms = 18000 cms
In metres = 180 metre
ANSWER:C
Answer: (C) 180 metre
Question: 16 men can complete a piece of work in 30 days. In how many days can 20 men complete that piece of work?
(A) 55 days
(B) 77 days
(C) 20 days
(D) 24 days
(E) 44 days
Rationale: 16 * 30 = 20 * x => x
= 24 days
Answer: D
Answer: (D) 24 days
Question: The rate of increase of the price of sugar is observed to be two percent more than the inflation rate expressed in percentage. The price of sugar, on January 1, 1994, is Rs. 20 per kg. The inflation rate for the years 1994 and 1995 are expected to be 8% each. The expected price of sugar on January 1, 1996 would be
(A) 23.6
(B) 24.0
(C) 24.2
(D) 24.6
(E) None of these
Rationale: Explanation :
Increase in the price of sugar = (8+2)= 10%
Hence, price of the sugar on Jan 1, 1996
=> (20 * 110 * 110)/( 100 * 100 ) = Rs 24.20.
Answer : C
Answer: (C) 24.2
Question: Find the odd man out
444, 300, 200, 136, 87, 84, 80
(A) 80
(B) 87
(C) 136
(D) 200
(E) 444
Rationale: All are even natural numbers except 87.
ANSWER:B
Answer: (B) 87
Question: If x and y are integers and 3^(x-4) = 3^(y+2), what is x in terms of y?
(A) y - 6
(B) y- 5
(C) y - 2
(D) y + 2
(E) y + 6
Rationale: Answer: A
3^(x-4) = 3^(y+2)
Since the base is the same, I isolated the equations and solved for y.
x-4 = y+2
x=y+6
Ans : E
Answer: (E) y + 6
Question: 1,3,5,7,9,..50 find term of sequnce for this.
(A) 1345
(B) 1567
(C) 1243
(D) 2767
(E) 2500
Rationale: This is an arithmetic progression, and we can write down
a=1a=1 ,d=2d=2 , n=50n=50 .
We now use the formula, so that
Sn=12n(2a+(n−1)l)Sn=12n(2a+(n−1)l)
S50=12×50×(2×1+(50−1)×2)S50=12×50×(2×1+(50−1)×2)
=25×(2+49×2)=25×(2+49×2)
=25×(2+98)=25×(2+98)
=2500=2500 .
E
Answer: (E) 2500
Question: If (27/4)x - 18 = 3x+27
what is the value of x?
(A) 12
(B) -12
(C) 1/12
(D) -1/12
(E) 3
Rationale: (27/4)x - 18 = 3x+27
=> 27x - 72 = 12x + 108
=> 15x = 180
=> x = 12
Answer: A
Answer: (A) 12
Question: If n is the product of the integers from 1 to 10, inclusive, how many different prime factors greater than 1 does n have?
(A) Four
(B) Five
(C) Six
(D) Seven
(E) Eight
Rationale: n = 1*2*3*4*5*6*7*8*9*10
The prime factors of n are 2, 3, 5, and 7.
There are 4 prime factors.
The answer is A.
Answer: (A) Four
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 48 sec
(B) 77
(C) 55
(D) 27
(E) 21
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125 = 48 sec.
Answer: A
Answer: (A) 48 sec
Question: When positive integer X is divided by positive integer Y, the remainder is 11.52. If X/Y = 96.12, what is the value of Y?
(A) 96
(B) 75
(C) 48
(D) 25
(E) 12
Rationale: When positive integer x is divided by positive integer y, the remainder is 11.52 --> x=qy+11.52;
x/y=96.12 --> x=96y+0.12y (so q above equals to 96);
0.12y=11.52 --> y=96.
Answer: A.
Answer: (A) 96
Question: Three independent strategies A, B and C have been initiated for cost cutting in a company producing respectively 30%, 40% and 10% savings. Assuming that they operate independently, what is the net saving achieved?
(A) 56%
(B) 64%
(C) 62.2%
(D) 68%
(E) 61%
Rationale: If initial cost is Rs 100, then
Final cost will be 100*0.7*0.6*0.9 = Rs. 37.8
savings = 100-37.8=62.2
so 62.2%
ANSWER:C
Answer: (C) 62.2%
Question: Amy has two decks of 50 cards each: Deck 1 and Deck 2. She takes 8 black cards from Deck 2 and adds them to Deck 1 and shuffles it thoroughly. She now picks a card from the newly formed pack of cards. If the probability of either picking a red ace or a king from the newly formed pack is greater than 1/8, what is the probability that Amy picks a black king or a red Jack from the new pack?
(A) 1/6
(B) 1/8
(C) 1/9
(D) 1/10
(E) 1/12
Rationale: Your solution is correct answer should be 1/9.
C
Answer: (C) 1/9
Question: Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in:
(A) 6 hours
(B) 20/3hours
(C) 7 hours
(D) 15/2hours
(E) 17/2hours
Rationale: Taking the lcm(12,15,20) = 60 liters (capacity of the tank)
In 1 hr : A can fill 5 liters(60/12), B = 4 liters C = 3 liters
Its given that A is open all time and B & C alternately.
So in 1st hr : A+B = 9 liters
2nd hr : A+C = 8 liters
3rd hr : A+B = 9 liters
4th hr : A+C = 8 liters
5th hr : A+B = 9 liters
6th hr : A+C = 8 liters
7th hr : A+B = 9 liters
Total = 60 liters
ANSWER:C
Answer: (C) 7 hours
Question: The area of a square garden is Q square feet and the perimeter is P feet. If Q=2P+33, what is the perimeter of the garden in feet?
(A) 28
(B) 32
(C) 36
(D) 40
(E) 44
Rationale: Let x be the length of one side of the square garden.
x^2 = 8x + 33
x^2 - 8x - 33 = 0
(x-11)(x+3) = 0
x = 11, -3
P = 4(11) = 44
The answer is E.
Answer: (E) 44
Question: In a certain experiment, the data collected is the number of organisms per sample, and this data follows a normal distribution. If the sample of data has a mean of 50 and a standard deviation of 10, which of the following is exactly 1.75 standard deviations more than the mean?
(A) a) 48
(B) b) 67.5
(C) c) 72
(D) d) 77.5
(E) e) 81
Rationale: Standard Deviation is a relatively rare category in the Quant section, although you're like to be tested on it 1 time on Test Day. You'll never be asked to calculate SD though, so you really just need to learn the basic 'concepts' behind it.
Here, we're told two things about a group of numbers:
1) The average of the group is 50
2) The standard deviation of the group is 10
If you go 1 SDupfrom the average, you hit.....50+10 = 60
If you go 1 SDdownfrom the average, you hit.....50-10 = 40
If you go 2 SDsupfrom the average, you hit.....50+2(10) = 70
If you go 2 SDsdownfrom the average, you hit.....50-2(10) = 30
Etc.
Here, we're asked for the number that is EXACTLY 1.75 SDs above the mean....
1.75 SDsupwould be.....50 + 1.75(10) = 67.5
B
Answer: (B) b) 67.5
Question: If the sum of the interior angles of a regular polygon measures up to 1620 degrees, then how many sides does the polygon have?
(A) 10
(B) 16
(C) 12
(D) 11
(E) 14
Rationale: one of the interior angle = 180 - 360/n
sum of the interior angles is = n (180 - 360/n)
given
n(180 - 360/n)=1620
180n - 360 = 1620
180n = 1980
n = 1980/180 = 11
ANSWER:D
Answer: (D) 11
Question: A certain club has 10 members, including Warry. One of the 10 members is chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Warry will be either the member chose to be secretary or the member chose to be treasurer?
(A) 1/720
(B) 1/80
(C) 1/10
(D) 1/9
(E) 1/5
Rationale: In order to become a secretary the person cannot be chosen as a president. This can be done in 9/10 ways. Then to become a secretary this person's probability is 1/9
Probability to become a secretary = (9/10 * 1/9) = 1/10
Similar concept for treasurer. Probability of not president = 9/10, Probability of not secretary = 8/9, probability of treasurer 1/8
probability to become a treasurer = (9/10 * 8/9 * 1/8) = 1/10
Since, the problem is saying Warry secretary OR Treasurer it is addition: 1/10 + 1/10 = 1/5=E
Answer: (E) 1/5
Question: What is the perimeter of a square with area 9p^2/4 ?
(A) 3p/4
(B) 3p^2/4
(C) 6p
(D) 3p^2
(E) 4p/3
Rationale: Area of square, (side)^2 = (3p/2)^2
Therefore side of the square = 3p/2
Perimeter of square = 4*side = 4* (3p/2) = 6p
Answer is C.
Answer: (C) 6p
Question: If 18,888 – n is divisible by 11, and 0 < n < 11, what is n?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: 18,888 / 11 = 1717 with a remainder of 1.
We need to subtract the remainder to get a multiple of 11.
The answer is A.
Answer: (A) 1
Question: If 18 is 15 percent of 30 percent of a certain number , what is the number?
(A)  9
(B)  36
(C)  40
(D)  81
(E)  400
Rationale: The math involved in this question can be 'set up' (and dealt with) in a variety of ways.
Here, if you're going to take a calculation-based approach, converting the percents to fractions would likely help you speed up (and avoid the last bit of math).
We're told that 18 is 15 percent of 30 percent of a certain number. We're asked for that number.
18 = (.15)(.3)(X)
18 = (3/20)(3/10)(X)
18 = (9/200)(X)
Since 9/200 is a relatively small fraction (it's far less than 10%), we know that 18 is LESS than 10% of X. Based on the given answer choices, there's only one number that is LARGE enough to fit that description....
Final Answer:
E
Answer: (E)  400
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
(A) 16 seconds
(B) 34 seconds
(C) 14 seconds
(D) 12 seconds
(E) 15 seconds
Rationale: Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5
= 12 seconds.
Answer: D
Answer: (D) 12 seconds
Question: What is the present worth of Rs. 143 due in 2 years at 5% simple interest per annum
(A) 110
(B) 120
(C) 130
(D) 140
(E) None of these
Rationale: Explanation:
Let the present worth be Rs.x
Then,S.I.= Rs.(143 - x)
= (x*5*2/100) = 143 - x
= 10x = 14300 - 100x
= 110x = 14300
x= 130
Answer: C
Answer: (C) 130
Question: A man gets a simple interest of Rs.1000 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate.
(A) Rs.500
(B) Rs.250
(C) Rs.5012.50
(D) Rs.512.5
(E) None of these.
Rationale: Let the principal be Rs.P
S.I at 5% p.a in 8 years on Rs.P = Rs.1000
(P)(8)(5)/100 = 1000
P = 2500
C.I on Rs.2P i.e., Rs.5000 at 5% p.a in two years
=5000{ [1 + 5/100]2 - 1} = 5000{ 212 - 202 /202}
= Rs.512.5
ANSWER:D
Answer: (D) Rs.512.5
Question: In a contest, a bowl contains 6 keys, one of which will open a treasure chest and Five of which will not. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If Kishore is allowed to draw two keys, simultaneously and at random, from the bowl as the first contestant, what is the probability that he wins the prize?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: The total possibilities existing while withdrawing two keys are: 6C2 = 15
For Kishore to win, 5 combinations exist assuming Key 1 to unlock the treasure E.g(1,2), (1,3)....(1,5)
P = 5/15= 1/3
Option B
Answer: (B) 1/3
Question: A train 180 m long running at 75 kmph crosses a platform in 40 sec. What is the length of the platform?
(A) 687
(B) 638
(C) 683
(D) 726
(E) 267
Rationale: D = 75 * 5/18 = 40
= 833 â€“ 150
= 683
Answer: C
Answer: (C) 683
Question: A ship sails out to a mark at the rate of 22 kmph. and sails back at the rate of 12 kmph. The average rate of sailing is ?
(A) 5 km/hr
(B) 12 km/hr
(C) 16 km/hr
(D) 25 km/hr
(E) None
Rationale: Answer
Average = ( 2uv / u +v ) km/hr
= ( 2 x 22 x 12 ) / (22 +12 ) km/hr.
= 16 km/hr.
Correct Option: C
Answer: (C) 16 km/hr
Question: A train 575 m long crosses a tunnel of length 325 in 90 sec. What is the speed of the train in kmph.
(A) 28
(B) 32
(C) 36
(D) 24
(E) 42
Rationale: Explanation :
Total distance traveled = Length of train + Length of tunnel = 575 + 325 = 900
Time taken to cross the tunnel = 90 sec.
Speed in kmph = distance/time *18/5 = 900/90 * 18/5 = 180/5 = 36 kmph
Answer: C
Answer: (C) 36
Question: A train with 120 wagons crosses John who is going in the same direction, in 36 seconds. It travels for half an hour from the time it starts overtaking the John ( he is riding on the horse) before it starts overtaking the Mike(who is also riding on his horse) coming from the opposite direction in 24 seconds. In how much time (in secs) after the train has crossed the Mike do the John meets to Mike?
(A) 3476 s
(B) 3500 s
(C) 3650 s
(D) 3670 s
(E) 3576 s
Rationale: Let the length of the train be L metres and speeds of the train Arun and Sriram be R, A and S respectively, then
---------- (i)
and ---------(ii)
From eq.(i) and (ii)
3(R - A ) = 2 (R + K)
R = 3A + 2K
In 30 minutes (i.e 1800 seconds), the train covers 1800R (distance) but the Arun also covers 1800 A (distance) in the same time. Therefore distance between Arun and Sriram, when the train has just crossed Sriram
= 1800 ( R - A) - 24 ( A + K)
Time required =
= (3600 - 24) = 3576 s
E
Answer: (E) 3576 s
Question: Of the votes cast on a certain proposal, 70 more were in favor of the proposal than were against it. If the number of votes against the proposal was 40 percent of the total vote, what was the total number of votes cast? (Each vote cast was either in favor of the proposal or against it.)
(A) 350
(B) 375
(C) 400
(D) 425
(E) 450
Rationale: Let x be the total number of votes cast.
0.6x = 0.4x + 70
0.2x = 70
x = 350
The answer is A.
Answer: (A) 350
Question: If two sides of a triangle are 6 and 8, which of the following could be the area of triangle?
1. 35
2. 48
3. 56
(A) a) 1 only
(B) b) 1 and 2 only
(C) c) 1 and 3 only
(D) d) 2 and 3 only
(E) e) 1, 2 and 3 only
Rationale: when two sides of a triangle are known , the maximum area occurs when the angle between those two sides is 90.
lets say base = 12 , height =8 (angle = 90)
maximum area = (1/2)*12*8 = 48 ( this is the same maximum area even when base is 8 and height is 12).
if we fix the base and keep lowering the angle, it will result in a lower height . hence the resulting area will always be < 48.
C,D and E are ruled out.
1 are possible areas as their areas are less than 48.
Hence the answer is A.
Answer: (A) a) 1 only
Question: Two trains 170 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.7
(B) 10.9
(C) 10.2
(D) 10.88
(E) 11.88
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 170 + 160 = 330 m.
Required time = 330 * 9/250
= 11.88 sec.
Answer:E
Answer: (E) 11.88
Question: Find the curved surface area, if the radius of a cone is 28 m and slant height is 30 m?
(A) 2550
(B) 2640
(C) 3960
(D) 4280
(E) 5490
Rationale: Cone curved surface area = Ï€rl
22/7 Ã— 28 Ã— 30 = 88 Ã— 30 = 2640 m(power2)
Answer is B.
Answer: (B) 2640
Question: It takes ten minutes to load a certain video on a cellphone, and fifteen seconds to load that same video on a laptop. If the two devices were connected so that they operated in concert at their respective rates, how many seconds would it take them to load the video, rounded to the nearest hundredth?
(A) 13.42
(B) 13.86
(C) 14.25
(D) 14.63
(E) 14.88
Rationale: The laptop can load the video at a rate of 1/15 of the video per second.
The phone can load the video at a rate of 1/(60*10) = 1/600 of the video per second.
The combined rate is 1/15 + 1/600 = 41/600 of the video per second.
The time required to load the video is 600/41 = 14.63 seconds.
The answer is D.
Answer: (D) 14.63
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) 22 km/h
(B) 88 km/h
(C) 11 km/h
(D) 20 km/h
(E) 87 km/h
Rationale: Explanation:
If the speed of the faster horse be \inline f_{s} and that of slower horse be \inline s_{s} then
\inline f_{s}+s_{s}=\frac{50}{1}=50
and \inline \frac{50}{s_{s}}-\frac{50}{f_{s}}=\frac{5}{6}
Now, you can go through options.
The speed of slower horse is 20km/h
Since, 20+30=50
and \inline \frac{50}{20}-\frac{50}{30}=\frac{5}{6}
Answer: D) 20 km/h
Answer: (D) 20 km/h
Question: A can finish a piece of work in 5 days. B can do it in 16 days. They work together for two days and then A goes away. In how many days will B finish the work?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 2/4 + (2 + x)/16 = 1 => x = 6 days
Answer: C
Answer: (C) 6
Question: A plane was originally flying at an altitude of x feet when it ascended 2,000 feet and then descended 5,000 feet. If the plane's altitude after these two changes was 1/6 its original altitude, then the solution of which of the following equations gives the plane's original altitude, in feet ?
(A) x + 2000 = 1/3*(x - 3000)
(B) 1/3*(x - 3000) = x
(C) x + 3000 = 1/3*x
(D) x - 3000 = 1/6*x
(E) x - 3000 = 1/3*x
Rationale: Plane's original altitude = x
Plane's new altitude after ascending 2000 ft = x+2000
Plane's new altitude after descending 5000 ft from previous altitude = x+2000-5000 = x-3000
So, after two changes plane is at 1/6 its original altitude => x-3000 = x/6
Answer (D)
Answer: (D) x - 3000 = 1/6*x
Question: If a, b, c are consecutive positive integers and a<b<c, which of the following must be true?
I. b-c is positive integer
II. abc is an even integer
III. (a+b+c)/3 is an integer
(A) I
(B) II
(C) I and II
(D) II and III
(E) I, II and III
Rationale: 1. b-c is negative because c is greater than b
2. abc
a can be either even or odd
if a=even; abc=even;
if a=odd,b=even; abc=even
Rule:
multiple of any number of integers if atleast once multiplied by an even number will result in even.
even*even=even
even*odd=even
Correct
3. (a+b+c) /3 is an integer
Again;
a=a
b=a+1
c=a+2
a+b+c=(a+a+1+a+2)=3a+3
3a is always divisible by 3
3 is divisible by 3.
Thus3a+3is also divisible by 3.
Rule:
if integer x is divisible by n
and
integer y is divisible by n
then; x+y must be divisible by n
Correct.
Ans :D
Answer: (D) II and III
Question: In how many ways can A, B, C, D and E be seated in a row such that A and C are not seated next to each other?
(A) 24
(B) 48
(C) 56
(D) 72
(E) 96
Rationale: When the constraint on an arrangement says,Two people should not be seated together,we do just the opposite. We make them sit together! Kind of tie them with a thread and assume they are one unit!
Let's see why....
These 5 people can be arranged in 5! ways. These are the total number of ways you get.
Now, when we tie 2 people together, we have only 4 entities to arrange. We can do this in 4! ways. But in each of these entities, the two people can sit in two different ways (Ac and BC). So number of ways in which these two people sit together is 4!*2!.
Now, the ways in which these two people will not be together will be 5!- 4!*2! = 4!(5 - 2) = 72
Answer :D
Answer: (D) 72
Question: Bat is bought for Rs.400 and sold at a gain of 20% find its selling price?
(A) Rs.320
(B) Rs.350
(C) Rs.370
(D) Rs.480
(E) None of these
Rationale: Explanation :
100 % = 400 (100 * 4 = 400)120 % = 480 (120 * 4 = 480)Selling price = Rs.480/-
Answer : D
Answer: (D) Rs.480
Question: Ray writes a two digit number. He sees that the number exceeds 4 times the sum of its digits by 3. If the number is increased by 18, the result is the same as the number formed by reversing the digits. Find the number.
(A) 2
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Solution: Let the two digit number be xy.
4(x + y) +3 = 10x + y .......(1)
10x + y + 18 = 10 y + x ....(2)
Solving 1st equation we get 2x - y = 1 .....(3)
Solving 2nd equation we get y - x = 2 .....(4)
Solving 3 and 4, we get x = 3 and y = 5
Answer:B
Answer: (B) 5
Question: A train takes 18 seconds to pass completely through a station 162 m long and 15 seconds through another station 120 m long.The length of the train is
(A) 70 m
(B) 80 m
(C) 90 m
(D) 100m
(E) 110m
Rationale: Let L be the length of the train.
The train covers a distance of (162 + L) in 18 seconds. The rate is then (162 + L)/18.
The train also covers a distance of (120 + L) in 15 seconds. The rate is then (120 + L)/15.
Presumably, the train is traveling at a constant rate. Therefore, set the two rates equal to each other and solve for L.
(162 + L)/18 = (120 + L)/15
i.e. 90
ANSWER:C
Answer: (C) 90 m
Question: A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of B in the profit.
(A) 1200
(B) 1400
(C) 2660
(D) 1600
(E) 1800
Rationale: A is a working member and for that, he receive 5% of the profit
= 5% of 7400 = 5*7400/100 = 370
Remaining amount = 7400-370 = 7030
Ratio of their investments = 6500*6 : 8400*5 : 10000*3
= 65*6 : 84*5 : 100*3 = 13*6 : 84 : 20*3 = 13*2 : 28 : 20
= 13 : 14 : 10
Share of B in the profit = 7030 * (14/37) = 190*14 = 2660
Answer is C
Answer: (C) 2660
Question: A distributor sells a product through an online store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $17 per item. What is the price that the buyer observers online if the distributor wants to maintain a 20% profit on the cost of the item?
(A) $22.50
(B) $23.50
(C) $24.50
(D) $25.50
(E) $26.50
Rationale: Let x be the price that buyers see online.
The distributor wants to receive 1.2(original price) which should be 80% of x.
1.2(17) = 0.8x
x = 1.2(17) / 0.8 = 1.5(17) = $25.50
The answer is D.
Answer: (D) $25.50
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years?
(A) 5%
(B) 7%
(C) 2%
(D) 1%
(E) 9%
Rationale: 160 = (180*4*R)/100
R = 5%
Answer: A
Answer: (A) 5%
Question: Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
(A) 2500 m^2
(B) 2510 m^2
(C) 2520 m^2
(D) 2600 m^2
(E) 2640 m^2
Rationale: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Answer: (C) 2520 m^2
Question: How many cubes of edge 2 dm can be cut out of a meter cube?
(A) 366
(B) 289
(C) 276
(D) 125
(E) 298
Rationale: 1 * 1* 1 = 2/10 * 2/10 * 2/10 * x
x = 125
Answer:D
Answer: (D) 125