MU-NLPC/Calc-aqua_rat huggingface dataset:
In Mike's opinion, his weight is greater than 65kg but leas than 72 kg. His brother does not agree with Mike and he thinks that Mike's weight is greater than 60kg but less than 70kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Mike?
Choose the correct choice from the following options
A) 50.5 kg
B) 56.5 kg
C) 60.9 kg
D) 66.5 kg
E) 75.5 kg

Solution: Let Mike's weight be X kg.   According to Mike, 65 < X < 72.   According to Mike's brother, 60 < X < 70.   According to Mike's mother, X < 68.   The values satisfying all the above conditions are 66 and 67.   Required average = (66 + 67) / 2= 
(66 + 67) / 2 = 133/2 = around 66.5
66.5 kg   66.5 kg
Answer: D
15 men take 21 days of 8 hrs. each to do a piece of work. How many days of 9 hrs. each would it take for 21 women if 3 women do as much work as 2 men?
Pick
A) 30	B) 20	C) 19	D) 29	E) 39

Solution: Let 1Man does 1unit/hr of work   15M in 21 days of 8hrs will do (15*21*8) units   3W = 2M   1W=(2/3)units/hr   21W with 9hrs a day will take   (15*21*8)/(21*9*(2/3))= 
  (15*21*8)/(21*9*(2/3)) = 20
> 20 Days   ANSWER:20
Answer: B
In a group of 70 children and 10 youngsters, each child got sweets that are 15% of the total number of children and each youngster got sweets that are 25% of the total number of children. How many sweets were there?  Choose the correct choice from the following choices
A) 1140 B) 1160 C) 1180 D) 1200 E) 1040

Solution: Number of sweets each child got = 15% of 80 = 15/100 * 80= 
15/100 * 80 = 12
12.   Number of sweets 80 children got= 70 * 12= 
70 * 12 = 840
840.   Number of sweets each youngster got= 25% of 80 = 25/100 * 80= 
25/100 * 80 = 20
20.   Number of sweets 10 youngsters got= 10 * 20= 
10 * 20 = 200
200.   Total number of sweets= 840 + 200= 
840 + 200 = 1_040
1040.   1040)
Answer: E
Average of five numbers is 8, and the sum of three of the numbers is 21, what is the average of the other 2 numbers? Choose the correct choice from the following
A) 9.1	B) 5.2	C) 9.5	D) 7.8	E) 5.6

Solution: Let the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e)/5=8a+b+c=21(21+d+e)/5=821+d+e=40d+e=19average=19/2= 
19/2 = 19/2 = around 9.5
9.5Ans 9.5
Answer: C
We had $1400 left after spending 30% of the money that we took for shopping. How much money did we start with?
Choose the correct choice from the following:
A) $2000 B) $2100 C) $2200 D) $2300 E) $2400

Solution: Let x be the amount of money we started with.   0.7x = 1400   x = 2000   The answer is $2000.
Answer: A
5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.90 only. Menâ€™s wages are?  Choose the correct option.
A) Rs.6	B) Rs.6.5	C) Rs.8	D) Rs.5	E) Rs.2

Solution: Answer: Option A   5M = xW = 8b   5M + xW + 8b ----- 90 Rs.   5M + 5M + 5M ----- 90 Rs.   15M ------ 90 Rs. => 1M = 6Rs.
Answer: A
Calculate the % profit or loss, if the cost price of 9 balls is equal to the selling price of 14 balls. Choices:
A) 35.7%  B) 25.7%  C) 15.7%  D) 55.7%  E) 45.7%

Solution: Let the cost price of 1 balls be Rs 1   Cost of 14 balls= Rs 14   Selling price of 14 balls = 9   Gain/loss = 14 - 9= 
14 - 9 = 5
5   %=5/14âˆ—100= 35.7   35.7%nswer: 35.7%
Answer: A
A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?  Choose one
A) 10/21 B) 11/21 C) 2/7 D) 5/7 E) 13/21

Solution: 5c2/7c2=10/21   10/21NSWER:10/21
Answer: A
The average marks of a class of 26 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?
Choose the correct choice
A) 52.2
B) 59.5
C) 52.8
D) 52.5
E) 53.1

Solution: Sum of the marks for the class of 26 students = 26 * 40= 
26 * 40 = 1_040
1040   Sum of the marks for the class of 50 students= 50 * 60= 
50 * 60 = 3_000
3000   Sum of the marks for the class of 76 students=   1040 + 3000= 
1040 + 3000 = 4_040
4040   Average marks of all the students= 4040/76   = 53.15   Answer:53.1
Answer: E
If 2m + n = 7 and m + 2n = 5, then (2m + n)/2 =  Choices:
A) 1
B) 7/2
C) 17/5
D) 18/5
E) 4

Solution: 2*(m+2m = 5) equals 2m+4n=10   2m+4n=10   - 2m + n= 7   = 3n=3   Therefore n = 1   Plug and solve...   2m + 1 = 7   2m=6   m=3   (6+1)/2= 7/2   7/2
Answer: B
If an object travels 80 feet in 4 seconds, what is the object’s approximate speed in miles per hour? (Note: 1 mile = 5280 feet)	Choose the correct choice
A) 7.25
B) 9.47
C) 11.58
D) 13.64
E) 15.92

Solution: 80 feet/4 seconds = 20 feet/second   (20 feet/second)*(3600 seconds/hour)*(1 mile/5280 feet) = 13.64 miles/hour (approximately)   The answer is 13.64.
Answer: D
A box contains 35 mangoes out of which 8 are spoilt. If eight mangoes are chosen at random, find the probability that A number is selected at random from first hundred natural numbers. What is the chance that it is a multiple of either 11 or 15? Choose the correct choice:	A) 5/20	B) 3/20	C) 7/20	D) 11/20	E) 9/20

Solution: The probability that the number is a multiple of 11 is 9/100. (Since 11*9= 
11*9 = 99
99).   Similarly the probability that the number is a multiple of 15 is 6/100. {Since   15*6= 
  15*6 = 90
90).   Neither 11 nor 15 has common multiple from 1 to 100. Hence these events are mutually exclusive events. Therefore chance that the selected number is a multiple of 11 or 15 is (9+6)/100= 3/20.   ANSWER:3/20
Answer: B
A girl has 10 jeans and 12 shirts. In how many different ways can she select a jeans and a shirts? Choose the correct choice from the following choices: A) A)100 B) B)102 C) C)108 D) D)110 E) E)120

Solution: The girl can select one jeans in 10 ways.   The girl can select one shirt in 12 ways.   The number of ways in which he can select one jeans and one shirt is 10 * 12= 
10 * 12 = 120
120 ways.   120
Answer: E
A man takes 6 hours 15 minutes in walking a distance and riding back to the starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride both ways, is  Choose the correct choice from the following answers
A) 4 hours  B) 4 hours 30 minutes  C) 4 hours 45 minutes  D) 5 hours  E) None of these

Solution: Explanation:   Time taken in walking both ways = 7 hours 45 minutes --------(i)   Time taken in walking one way and riding back= 6 hours 15 minutes-------(ii)   By equation (ii)*2 -(i), we have   Time taken to man ride both ways, = 12 hours 30 minutes - 7 hours 45 minutes   = 4 hours 45   Answer: 4 hours 45 minutes
Answer: C
If x^2+(1/x^2)=9, x^4+(1/x^4)=?  Pick one:
A) 10
B) 11
C) 12
D) 14
E) 79

Solution: -> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=9^2-2=79.   Thus, the answer is 79.
Answer: E
There are 100 men in town. Out of which 85% were married, 70% have a phone, 75% own a car, 80% own a house. What is the maximum number of people who are married, own a phone, own a car and own a house?  Pick one:
A) 50
B) 60
C) 70
D) 80
E) 90

Solution: total persons=100   no.peoplehaving phone=70   no.people having car=75   no.people having house=80   no.people got marriage=85   people got married,having car,house,phone=70   ANSWER:70
Answer: C
A person purchased a TV set for Rs. 15000 and a DVD player for Rs. 6000. He sold both the items together for Rs. 31500. What percentage of profit did he make?  Choose the correct answer:  A) 48%  B) 50%  C) 40%  D) 45%  E) 20%

Solution: The total CP = Rs. 15000 + Rs. 6000   = Rs. 21000 and SP   = Rs. 31500   Profit(%)   = (31500 - 21000)/21000 * 100= 
(31500 - 21000)/21000 * 100 = 50
50%   Answer: 50%
Answer: B
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 seconds. The speed of the train is: Choose the correct choice:
A) 56
B) 50
C) 72
D) 27
E) 25

Solution: Speed of the train relative to man = (125/10) m/sec   = (25/2) m/sec. [(25/2) * (18/5)] km/hr   = 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: 50
Answer: B
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?
Choose the correct choice
A) 5:40 PM B) 6:00 PM C) 7:20 PM D) 9:00 PM E) 9:20 PM

Solution: 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= 
480/60 = 8
8 hours   Trains started at 1:00 PM, there they will meet at 9:00 PM   Option 9:00 PM
Answer: D
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:	Pick one:	A) 52,500; 47,500	B) 62,500; 37,500	C) 72,500: 27,500	D) 82,500; 17,500	E) None of these

Solution: 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= 
39000/4 = 9_750
9750   ⇒ 2x= (1100000 – 975000) = 125000 ⇒ x = 62500.   ∴ Sum invested at 9% = 62500.   Sum invested at 11% = (100000 – 62500) = 37500.   Answer 62,500; 37,500
Answer: B
What is the product of all positive factors of 12?  Choose the most appropriate option:
A) 39 B) 324 C) 1728 D) 3042 E) 5832

Solution: Positive factors of 12 are 1, 2, 3, 4, 6, 12.   So product is: 12*6*4*3*2*1= 
12*6*4*3*2*1 = 1_728
1728   Answer: 1728
Answer: C
A wheel rotates 20 times every minute and moves 15 cm during each rotation. How many metres does the wheel move in one hour?  Choose the correct option
A) 6 metre  B) 18 metre  C) 180 metre  D) 1200 metre  E) 130 metre

Solution: Number of times wheel moves in 1 hour = 12 * 60 = 1200   :. Distance moves = (1200*15)= 
(1200*15) = 18_000
18000 cms   In metres= 180 metre   ANSWER:180 metre
Answer: C
16 men can complete a piece of work in 30 days. In how many days can 20 men complete that piece of work?	Select the correct option.
A) 55 days  B) 77 days  C) 20 days  D) 24 days  E) 44 days

Solution: 16 * 30 = 20 * x => x   = 24 days   Answer: 24 days
Answer: D
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 Pick
A) 23.6
B) 24.0
C) 24.2
D) 24.6
E) None of these

Solution: Explanation :   Increase in the price of sugar = (8+2)= 
(8+2) = 10
10%   Hence, price of the sugar on Jan 1, 1996=> (20 * 110 * 110)/( 100 * 100 ) = Rs 24.20.   Answer : 24.2
Answer: C
Find the odd man out
444, 300, 200, 136, 87, 84, 80  Choices.
A) 80 B) 87 C) 136 D) 200 E) 444

Solution: All are even natural numbers except 87.   ANSWER:87
Answer: B
If x and y are integers and 3^(x-4) = 3^(y+2), what is x in terms of y? Choose the correct choice from the following
A) y - 6	B) y- 5	C) y - 2	D) y + 2	E) y + 6

Solution: 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 : y + 6
Answer: E
1,3,5,7,9,..50 find term of sequnce for this.
Answers:
A) 1345  B) 1567  C) 1243  D) 2767  E) 2500

Solution: 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 .   2500
Answer: E
If n is the product of the integers from 1 to 10, inclusive, how many different prime factors greater than 1 does n have?	Select:  A) Four  B) Five  C) Six  D) Seven  E) Eight

Solution: 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 Four.
Answer: A
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?	Choose the correct choice:
A) 48 sec B) 77 C) 55 D) 27 E) 21

Solution: Relative speed = 60 + 90= 
60 + 90 = 150
150 km/hr.= 150 * 5/18 = 125/3 m/sec.   Distance covered = 1.10 + 0.9= 
1.10 + 0.9 = 2
2 km= 2000 m.   Required time = 2000 * 3/125= 
2000 * 3/125 = 48
48 sec.   48 secnswer: 48 sec
Answer: A
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?  Choose the correct choice from the following
A) 96 B) 75 C) 48 D) 25 E) 12

Solution: 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.   96nswer: 96.
Answer: A
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?
Select: A) 56% B) 64% C) 62.2% D) 68% E) 61%

Solution: 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= 
100-37.8 = 62.2
62.2   so 62.2%   ANSWER:62.2%
Answer: C
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? Choose the correct choice:
A) 1/6  B) 1/8  C) 1/9  D) 1/10  E) 1/12

Solution: Your solution is correct answer should be 1/9.   1/9
Answer: C
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: Choose the correct choice
A) 6 hours  B) 20/3hours  C) 7 hours  D) 15/2hours  E) 17/2hours

Solution: 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+7 hours = 8 liters   3rd hr : A+B = 9 liters   4th hr : A+7 hours = 8 liters   5th hr : A+B = 9 liters   6th hr : A+7 hours = 8 liters   7th hr : A+B = 9 liters   Total = 60 liters   ANSWER:7 hours
Answer: C
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?	Pick:
A) 28 B) 32 C) 36 D) 40 E) 44

Solution: 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 44.
Answer: E
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?
Choose the most appropriate option:
A) a) 48  B) b) 67.5  C) c) 72  D) d) 77.5  E) e) 81

Solution: 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) 67.5
Answer: B
If the sum of the interior angles of a regular polygon measures up to 1620 degrees, then how many sides does the polygon have? Choose the correct choice from the following:  A) 10  B) 16  C) 12  D) 11  E) 14

Solution: 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= 
1980/180 = 11
11   ANSWER:11
Answer: D
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?
Choose the correct answer
A) 1/720  B) 1/80  C) 1/10  D) 1/9  E) 1/5

Solution: 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=1/5
Answer: E
What is the perimeter of a square with area 9p^2/4 ?
Select.
A) 3p/4
B) 3p^2/4
C) 6p
D) 3p^2
E) 4p/3

Solution: 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 6p.4* (3 /2)= 
4* (3 /2) = 6
6p   Answer is 6p.
Answer: C
If 18,888 – n is divisible by 11, and 0 < n < 11, what is n?  Choose the correct choice.
A) 1	B) 3	C) 5	D) 7	E) 9

Solution: 18,888 / 11 = 1717 with a remainder of 1.   We need to subtract the remainder to get a multiple of 11.   The answer is 1.
Answer: A
If 18 is 15 percent of 30 percent of a certain number , what is the number? Choose one: A) 9 B) 36 C) 40 D) 81 E) 400

Solution: 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:   400
Answer: E
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?
Options:
A) 16 seconds  B) 34 seconds  C) 14 seconds  D) 12 seconds  E) 15 seconds

Solution: Speed of the boat downstream = 15 + 3= 
15 + 3 = 18
18 kmph= 18 * 5/18= 
18 * 5/18 = 5
5 m/s   Hence time taken to cover 60 m= 60/5= 
60/5 = 12
12 seconds.   Answer: 12 seconds
Answer: D
What is the present worth of Rs. 143 due in 2 years at 5% simple interest per annum
Choose the correct choice from the following answers:  A) 110  B) 120  C) 130  D) 140  E) None of these

Solution: 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: 130
Answer: C
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. Choose the most appropriate option
A) Rs.500 B) Rs.250 C) Rs.5012.50 D) Rs.512.5 E) None of these.

Solution: 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:Rs.512.5
Answer: D
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?	Choose the correct choice:  A) 1/2  B) 1/3  C) 1/4  D) 1/5  E) 1/6

Solution: 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 1/3
Answer: B
A train 180 m long running at 75 kmph crosses a platform in 40 sec. What is the length of the platform?
Choose the correct answer:
A) 687	B) 638	C) 683	D) 726	E) 267

Solution: D = 75 * 5/18 = 40   = 833 â€“ 150   = 683   Answer: 683
Answer: C
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 ?
Answers.
A) 5 km/hr  B) 12 km/hr  C) 16 km/hr  D) 25 km/hr  E) None

Solution: Answer   Average = ( 2uv / u +v ) km/hr   = ( 2 x 22 x 12 ) / (22 +12 ) km/hr.   = 16 km/hr.   16 km/hrorrect Option: 16 km/hr
Answer: C
A train 575 m long crosses a tunnel of length 325 in 90 sec. What is the speed of the train in kmph.  Choose the most appropriate option
A) 28
B) 32
C) 36
D) 24
E) 42

Solution: Explanation :   Total distance traveled = Length of train + Length of tunnel = 575 + 325= 
575 + 325 = 900
900   Time taken to cross the tunnel= 90 sec.   Speed in kmph = distance/time *18/5 = 900/90 * 18/5 = 180/5= 
180/5 = 36
36 kmph   Answer: 36
Answer: C
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?	Choose the correct choice from the following choices.
A) 3476 s B) 3500 s C) 3650 s D) 3670 s E) 3576 s

Solution: 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)= 
(3600 - 24) = 3_576
3576 s   3576 s
Answer: E
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.)
Choose the correct choice
A) 350  B) 375  C) 400  D) 425  E) 450

Solution: Let x be the total number of votes cast.   0.6x = 0.4x + 70   0.2x = 70   x = 350   The answer is 350.
Answer: A