MU-NLPC/Calc-aqua_rat huggingface dataset:
If a + b = x and a - b = y , then 3ab =
can someone explain!	Select the correct option:  A) (3x^2 - 3y^2)/4  B) (3y^2 - 3x^2)/4  C) 3x+3y/2  D) 3x - 3y/2  E) 3x^2 - 3y^2/2

Solution: plugging numbers is quite fast in this case:   Let   a=1   b=2   Then; x= 1+2= 
1+2 = 3
> 3 and Y= 1-2=> -1   Question asks 3ab=.........   As our number 3ab= 3*1*2= 
3*1*2 = 6
6   now plug the value of x and y in the answer choices. Option A gives 6 and that is the number we need.   Hence: (3x^2 - 3y^2)/4ns is (3x^2 - 3y^2)/4.
Answer: A
Set A contains all the even numbers between 32 and 80 inclusive. Set B contains all the even numbers between 62 and 110 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A? Choose the correct choice from the following answers: A) 450 B) 550 C) 650 D) 750 E) 850

Solution: Each term in set B is 30 more than the corresponding term in set A.   The difference of the sums = 25 * 30= 
25 * 30 = 750
750.   The answer is 750.
Answer: D
When Q is divided by 9, the remainder is 4. All of the following are possible values of Q, except for which of the following?	Choose the correct option.
A) 13	B) 31	C) 49	D) 57	E) 67

Solution: The number can be expressed in the form of 9x+4 where x can 0,1,2,3,4....   by evaluating the answer choices carefully we can clearly observe that 57 is the only number which can't be expressed Q in the form of 9x+4   In other words we can also say that the (answer - 4) will not be divisible by 9.57 is the number which doesn't follow this condition   Correct Answer - 57
Answer: D
The price of 80 apples is equal to that of 120 oranges. The price of 60 apples and 75 oranges together is Rs.1320. The total price of 25 apples and 40 oranges is
Choices
A) 680	B) 620	C) 720	D) 480	E) 700

Solution: Let the price of one apple = a and price of one orange = b   The price of 80 apples is equal to that of 120 oranges   80a = 120b   => 2a = 3b ==> b=2a/3 ------------(1)   price of 60 apples and 75 oranges together is Rs.1320   =>60a + 75b = 1320   => 4a + 5b = 88 ==> 4a + 5(2a/3) = 88 -------(from equation 1)   => 12a + 10a = 88 × 3   => 6a + 5a = 44 × 3   => 11a = 44 × 3   => a = 4 × 3 = 12   b = 2a/3   b = 2*12/3= 
2*12/3 = 8
8   Total price of 25 apples and 40 oranges= 25a + 40b = (25 × 12) + (40 × 8) = 300 + 320= 
300 + 320 = 620
620   Ans - 620
Answer: B
In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is
Rs. 30 in all, how many 5 p coins are there? Choose one:	A) 150	B) 130	C) 120	D) 110	E) 140

Solution: Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.   Then, sum of their values = Rs. (25X/100 + 10X2X/100 + 5X3X/100) = RS 60X/100   60X/100 = 30 X =30 X 10/60 = 50   Hence, the number of 5 p coins = (3 x 50) = 150.   150NSWER 150 150
Answer: A
Sally has $100 in pennies. She wants to stack her pennies into three large piles and five small piles. The large piles are all the same size, and the small piles are all the same size. Additionally, Sally wants all of the small piles put together to equal one of the large piles. How many pennies does Sally put in one of the small piles?
Choose the correct choice:
A) 2500 pennies B) 500 pennies C) 250 pennies D) 100 pennies E) 50 pennies

Solution: B. Each large pile gets 1/4 of the total pennies. Each small pile gets 1/5 of the remaining 1/4 of the total pennies. So each small pile gets 1/20 of the total pennies. $100 is 10,000 pennies. 1/20 of 10,000 is 500, so the correct answer is 500 pennies: 500 pennies.
Answer: B
If 32.5% of the 880 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class?
Choices:	A) 110	B) 330	C) 550	D) 594	E) 880

Solution: Students enrolled in biology are 32.5% and therefore not enrolled are 67.5%. so of 880 is  880*.675= 
 880*.675 = 594
594   Answer is 594 594
Answer: D
The average of temperatures at noontime from Monday to Friday is 50; the lowest one is 45, what is the possible maximum range of the temperatures? Choose the correct choice from the following answers:	A) 20	B) 25	C) 40	D) 45	E) 75

Solution: Average=50, Sum of temperatures=50*5= 
50*5 = 250
250   As the min temperature is 45, max would be   250-4*45= 
  250-4*45 = 70
70 --> The range=70(max)-45(min)=25   Answer: 25.
Answer: B
A and B entered into a partnership investing Rs. 13,000 and Rs. 12,000 respectively.After 3 months, A withdrew Rs. 5000 while B invested Rs. 5000 more, After 3 more months, C joins the business with a capital of Rs. 21,000, The share of B exceeds that of C, out of a total profit of Rs. 26,400 after one year by? Choose the correct choice from the following answers:
A) 8340 B) 3600 C) 2787 D) 1287 E) 3627

Solution: A : B : C = (16000 * 3 + 11000 * 9) : (12000 * 3 + 17000 * 9) : (21000 * 6)   = 147 : 189 : 126   = 7 : 9 ; 6.   Difference of B and C's shares = Rs. ( 26400 * 9/22 - 26400 * 6/22 )   = Rs. 3600.   Answer: 3600
Answer: B
A certain sum is invested at simple interest at 15% 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. 900. Find the sum?
Pick
A) s. 7000  B) s. 9000  C) s. 15000  D) s. 17000  E) s. 27000

Solution: Let the sum be Rs. x.   (x * 15 * 2)/100 - (x * 12 * 2)/100 = 900   => 30x/100 - 24x/100 =900   => 6x/100 = 900   => x = 15000.   ANSWER:s. 15000
Answer: C
If an integer n is divisible by3, 5, 12. what is the next larger integer divisible by all these numbers	Answers:
A) n+3
B) n+5
C) n+12
D) n+60
E) n+15

Solution: If n is divisible by 3, 5 and 12 it must a multiple of the lcm of 3, 5 and 12 which is 60.   n=60k   n   + 60= 
  + 60 = 60
60 k + 60= 
+ 60 = 60
60(k + 1)   The answer is n+60.
Answer: D
If it is 6:12 in the evening on a certain day, what time in the morning was it exactly 1,440,711 minutes earlier? (Assume standard time in one location.)
Choose the correct choice from the following:
A) 6:12	B) 6:15	C) 6:18	D) 6:21	E) 6:24

Solution: 6:12 minus 1,440,711 must end with 1, the only answer choice which ends with 1 is D.   Answer: 6:21.
Answer: D
x^2-y^2= 16 and 2. xy=4 so find out x+y=? tell that both statement are required to find out the value of x+Y
Options:
A) 6 B) 7 C) 8 D) 9 E) 5

Solution: x^2-y^2= 16 = 25-9 =5^2-3^2   => (x+y)*(x-y)=(5+3)*(5-3)   => (x+y)=(5+3)= 
(5+3) = 8
8   ANSWER:8
Answer: C
A number increased by 20% gives 480. The number is Choose one
A) 250
B) 400
C) 450
D) 500
E) 520

Solution: Formula = TOTAL=100% ,INCRESE = "+" DECREASE= "-"   A number means = 100 %   That same number increased by 20 % = 120 %   120 % -------> 480 (120 × 4 = 480)   100 % -------> 400 (100 × 4 = 400)   400)
Answer: B
n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4 ?  Choose the correct choice from the following:  A) 6  B) 3  C) 2  D) 1  E) 8

Solution: Let n=4q+3.Then, 2n=8q+6=4(2q+1)+2.   Thus when 2n is divided by 4, the remainder is 2.   Answer is 2
Answer: C
A company has two models of computers, model P and model Q. Operating at a constant rate, a model P computer can complete a certain task in 12 minutes and a model Q computer can complete the same task in 6 minutes. If the company used the same number of each model of computer to complete the task in 1 minute, how many model P computers were used?	Choose the correct choice from the following.
A) 3 B) 4 C) 1 D) 5 E) 6

Solution: Let's say 1 work is processing 12 gb of data.   Model P : 1 gb per min   Model Q : 2 gb per min   Working together, 1 P and 1 Q = 3 gb per min   So, 4 times as many computers would work at 12 gb per min.   So no. of P = 4   Answer is 4
Answer: B
The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides?	Choose one:
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: S = (1 + 2 + 3)/2= 
(1 + 2 + 3)/2 = 3
3=> No triangle exists   3nswer: 3
Answer: A
mr. depak has $459,774 in his bank account. What is the least amount of money (in whole number of dollars) that he must add to his account if he wants to split this money evenly among her six best friends?
Options:
Select:	A) $0	B) $2	C) $3	D) $4	E) $6

Solution: To find the least amount deepak should add to his saving account to split the money evenly among his 6 best friends,   he needs to make the total divisible by 6   Simply add the individual digits of the total = 4+5+9+7+7+4= 
4+5+9+7+7+4 = 36
36   If you add 0 , the number is divisible by 6 (36+ 0)   Correct Option : $0
Answer: A
A person standing on a railway platform noticed that a train took 21 seconds to completely pass through the platform which was 84m long and it took 9 seconds in passing him.Find the speed of the train? Select
A) 6m/sec
B) 5m/sec
C) 12m/sec
D) 7m/sec
E) None

Solution: Let the length of the train be x m.   then, then train covers x meters in 9 seconds and (x+84)m in 21 seconds.   Therefore, x/9=(x+84)/21 =63m   So, the length of the train=63m   Speed of the train=63/9= 
63/9 = 7
7m/sec   Answer: Option 7m/sec
Answer: D
If A is a positive integer, which of the following must be odd?  Select the correct option:  A) A+1  B) A^2+A  C) A^2+A+1  D) x^2−1  E) 3x^2−3

Solution: A. A+1 = can be odd or even. Since O + O =E or E + O = O   B. A^2 + A = A(A+1). Since from the above derivation we already know the term A+1 can be Odd or Even, directly substitute here. A(ODD) = Even (When A is Even) or A(EVEN) = EVEN [When A is ODD]   C. Here's the answer. Since we know the term A^2 + A can always take a EVEN number, EVEN + 1 = ODD   Hence A^2+A+1.
Answer: C
How many different four letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?
Choose the correct choice from the following answers
A) 59	B) 11!/(2!*2!*2!)	C) 56	D) 23	E) 11!/(3!*2!*2!*2!)

Solution: Available letters:   M E D I T R A N (8 letters)   E _ _ R   We have 1 combination for E and 1 combination for R, and also we have 8 combinations for the 2nd letter and 7 combinations for the last letter, so:   E 8 7 R = 1 * 8 * 7 * 1= 
1 * 8 * 7 * 1 = 56
56   ANSWER:56
Answer: C
George has 8 candies in a bag, 3 of which are sweet while the other 5 are sour. He pulls out 2 of the candies simultaneously, and at random. What is the probability that exactly one of the candies he picked is sour?	Choose one
A) 2/8
B) 3/15
C) 2/28
D) 3/5
E) 15/28

Solution: The probability is equal to the number of desired choices divided by the total number of possibilities.   Probability = Favorable/Total   Total = 8C2 = 8*7/2= 
8*7/2 = 28
28   Favorable:   Pick 1 sour out of 3 sour   AND   pick 1 sweet out of 5 sweet.   3C1*5C1=3*5= 
3*5 = 15
15   P=15/28   When you use combination method, it is picking all possible cases and the order doesn't matter. Whereas, upon choosing probability method to solve, order matters.   Thus,   Total Probability:   Probability of choosing sour candy first AND Probability of choosing sweet candy   OR   Probability of choosing sweet candy first AND Probability of choosing sour candy   Answer: 15/28
Answer: E
A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?  Choose the correct choice from the following answers:
A) 150
B) 788
C) 267
D) 266
E) 123

Solution: Length of the train be ‘X’   X + 150/15 = X + 250/20   4X + 600 = 3X + 750   X = 150m   150nswer:150
Answer: A
A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 21 hrs and a machine of type S does the same job in 42 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?  Choose the correct choice
A) 6	B) 7	C) 8	D) 9	E) 10

Solution: Type R completes 1/21 of the job each hour.   Type S completes 1/42 of the job each hour.   Together R and S complete 1/21 +1/42 = 1/14 of the job each hour.   Let n be the number of each type of machine.   2*n*(1/14) = 1 job completed   n = 7   The answer is 7.
Answer: B
A cow was standing on a bridge, 5m away from the middle of the bridge. A train was coming towards the bridge from the end nearest to the cow. Seeing this cow ran towards the train and managed to escape when the train was 2m away from the bridge. If it had run in opposite direction(i.e away from the train) it would have been hit by the train 2m before the end of the bridge. What is the length of bridge in meters assuming speed of the train is 4 times that of the cow.	Options:  A) 32  B) 36  C) 40  D) 44  E) 50

Solution: Explanation :   Explation:   Let length of bridge is X   then middle of bridge is X/2.   and Cow is standing at X/2-5 from the end so   After seeing the train it would run opposite direction and cover distance of X/2-5 when the train is 2m away from other side.   So, the bridge from one side to cow is {(X/2-5)+(X/2-5)}=X-10   so remaining distance is 10m   the cow is hit before 2m i.e cow covers 8m and train will cover 32 m.   32nswer : 32
Answer: A
A fort had provision of food for 150 men for 30 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is: Choose the correct option:  A) 29 1/5  B) 24  C) 42  D) 54  E) 48

Solution: After 10 days : 150 men had food for 20 days.   Suppose 125 men had food for x days.   Now, Less men, More days (Indirect Proportion)   Therefore 125 : 150 :: 20 : x <=> 125 x x = 150 x 20   => x =150 x 20/125   => x = 24.   Correct answer is 24
Answer: B
The number of diagonals of a polygon of n sides is given by the formula q=n(n-3)/2. If a polygon has twice as many diagonals as sides, how many sides does it have?  Choose the correct choice from the following answers
A) 3 B) 5 C) 6 D) 7 E) 8

Solution: q=n(n-3)   q=2*n   2n=n(n-3)   =>2=n-3   =>n=5   Answer 5
Answer: B
Rs. 6000 is lent out in two parts. One part is lent at 4% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?  Choose the correct choice
A) 5:1	B) 5:5	C) 5:7	D) 5:4	E) 5:2

Solution: Let the amount lent at 4% be Rs. x   Amount lent at 10% is Rs. (6000 - x)   Total interest for one year on the two sums lent   = 4/100 x + 10/100 (6000 - x) = 600 - 3x/50   => 600 - 3/50 x = 450 => x = 2500   Amount lent at 10% = 3500   Required ratio = 2500 : 3500 = 5:7   Answer:5:7
Answer: C
What number comes next in the following number series? 12, 50, 202, 810, 3242, _____	Choose the correct choice from the following choices
A) 12400 B) 12800 C) 12970 D) 13015 E) 16000

Solution: 1212 × 4 + 2 = 5050 × 4 + 2 = 202202 × 4 + 2 = 810810 × 4 + 2 = 32423242 × 4 + 2 = 12970 12970
Answer: C
A family I know has several children. Each boy in this family has as many sisters as brothers but each girl has twice as many brothers as sisters. How many brothers and sisters are there?	Options:
A) 4 brothers and 2 sisters	B) 4 brothers and 3 sisters	C) 3 brothers and 3 sisters	D) 4 brothers and 5 sisters	E) 4 brothers and 6 sisters

Solution: let no. of girls=g n boys=b   b=g+1 ..........(i) as each boy have equal no. of sisters and brothers and he is not included in brothers.so,1 is for him in g+1.   now ,   b=2(g-1)........(ii) as each girl have g-1 sisters.   solving (i) and(ii) we get g=3 and b=4   ANSWER:4 brothers and 3 sisters
Answer: B
The ages of Old and Young total 48. Old is twice as old as Young was when Old was half as old as Young will be when Young is three times as Old was when Old was three times as old as Young. How old is Old?  Choose the correct answer.
A) 23 B) 27 C) 12 D) 43 E) 37

Solution: Explanation:   From the options itself,we can see that option c   old = 30   young = 18   30 + 18= 
30 + 18 = 48
48   By reducing this years only by one   Before 6years   old= 24 (half of young)   young = 12 (twice of old)   Answer: 12
Answer: C
In a sports club with 80 members, 48 play badminton and 46 play tennis and 7 do not play either. How many members play both badminton and tennis?  Choices:	A) 23	B) 21	C) 20	D) 26	E) 27

Solution: 48+46= 
48+46 = 94
94   but where as total number is   80-7= 
  80-7 = 73
73   therefore answer is   94-73= 
  94-73 = 21
21   Hence Answer is 21
Answer: B
he population of a city is 110,000. If it increases at the rate of 6% per annum, then what will be its population 2 years hence? Choose the correct choice:	A) 123596	B) 1237723	C) 123776	D) 123728	E) 123718

Solution: Population after n years = P [1 + (R/100)]2   Population after 2 years = 110000 * [1 + 6/100]2 = (110000 x 53/50 x 53/50) = 123596   123596NSWER: 123596
Answer: A
Combine terms: 6a + 26b -4b – 16a.
Options
A) 4a + 22b B) -28a + 30b C) -10a + 22b D) 28a + 30b E) 5a + 30b

Solution: Solution:   6a + 26b -4b – 16a.   = 6a – 16a + 26b – 4b.   = -10a + 22b.   Answer: (-10a + 22b)
Answer: C
Saturn travels around the Sun at an approximate speed of 5.82 miles per second. This speed is how many kilometers per hour? (1 km = 0.6 miles) Select the correct option:  A) 30,560  B) 31,650  C) 32,740  D) 33,830  E) 34,920

Solution: The speed is 5.82 miles/s. Then 5.82/0.6= 
5.82/0.6 = 9.7
9.7 km/s   9.7*3600= 34,920 kph   The answer is 34,920.
Answer: E
A sum of money is sufficient to pay A's wages for 21 days and B's wages for 28 days. The same money is sufficient to pay the wages of both for? Choose the correct choice from the following answers:
A) 10 days  B) 12 days  C) 15 days  D) 20 days  E) 18 days

Solution: Let the total money be $x   A's 1 day work = $ x/21   12 days's 1 day work = $ x/28   A+12 days 1 day work = $ x/12   The money is sufficient to pay the wages of both for 12 days   Answer is 12 days
Answer: B
The bear alarm at Grizzly’s Peak ski resort sounds an average of once every thirty days, but the alarm is so sensitively calibrated that it sounds an average of ten false alarms for every undetected bear. Despite this, the alarm only sounds for three out of four bears that actually appear at the resort. If the alarm sounds, what is the probability that a bear has actually been sighted?  Pick one
A) 1/4
B) 3/13
C) 27/52
D) 3/4
E) 10/13

Solution: How many times the alarm goes off --> 10 false + 3 true   How many of these alarms are true --> 3 true alarms   Therefore, p = true alarms/total alarms = 3/13   Or, we can calculate the p (of alarm sounding but no bear detected, i.e. false alarm),   10 times when the alarm goes off - no bear is seen   13 times in all the alarm goes off   So, 10/13 is the p that alarm is a false alarm   Subtracting 10/13 from 1 is the p that it's a true alarm --> (1-10/13) = 3/13....Answer 3/13
Answer: B
Find the number, when 15 is subtracted from 7 times the number, the result is 10 more than twice of the number  Choose the correct choice from the following answers
A) 5  B) 15  C) 7.5  D) 4  E) 3

Solution: Explanation:   Let the number be x.   7x -15 = 2x + 10 => 5x = 25 => x = 5   Option 5
Answer: A
What is the remainder when 980*1050*880*1010 is divided by 22?  Select
A) 15
B) 10
C) 12
D) 8
E) 3

Solution: OA is 'C'.   OE:   take the remainder from each of 980/22, 1050/22 and so on..   980/22 gives remainder = 12   1050/22 gives remainder = 16   880/22 gives remainder = 0   1010/22 gives remainder = 20   the net remainder is the product of above individual remainders. i.e = 12*16*0*20   break them into pairs 12*16/22 gives remainder 16   and 0*20/22 gives remainder 20   so 16*20/22 gives remainder 12.   Answer: 12
Answer: C
If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. What is the actual distance travelled by him?
Choose the correct answer:	A) 50	B) 60	C) 40	D) 30	E) 25

Solution: Speed = x/10---1   x+20 km if travelled at 14 km/hr   speed = x+20/14---2   from 1 & 2   x = 50   50NSWER 50
Answer: A
The average marks of a class of 30 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 from the following options:  A) 52.3  B) 52.2  C) 52.1  D) 52.5  E) 52.4

Solution: Sum of the marks for the class of 30 students = 30 * 40= 
30 * 40 = 1_200
1200   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 80 students=   1200 + 3000= 
1200 + 3000 = 4_200
4200   Average marks of all the students= 4200/80= 
4200/80 = 105/2 = around 52.5
52.5   Answer:52.5
Answer: D
In a box of 10 pens, a total of 2 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?	Options: A) 7/12 B) 11/20 C) 17/30 D) 28/45 E) 51/90

Solution: # defective pens = 2   # good pens = 8   Probability of the 1st pen being good = 8/10   Probability of the 2nd pen being good = 7/9   Total probability = 8/10 * 7/9 = 28/45   The answer is 28/45.
Answer: D
If the probability of rain on any given day in City X is 20%, what is probability that it rains on exactly 3 days in a 4 day period? Choose the correct choice
A) 16/625 B) 8/125 C) 6/125 D) 4/25 E) 3/25

Solution: One possible way is rain-rain-rain-no rain.   The probability of this is 1/5*1/5*1/5*4/5 = 4/625   The number of possible ways is 4C3 = 4, so we multiply this by 4.   P(rain on exactly 3 days) = 4*4/625 =16/625   The answer is 16/625.
Answer: A
If 41/88 = 0.46590, what is the 77th digit to the right of the decimal point of the fraction? Choose the most appropriate option:  A) 6  B) 2  C) 5  D) 0  E) 9

Solution: we are not concerned what 41/88 means..   we have to look at the decimal..   0.6590means 0.465909090....   so leaving girst,second and third digit to the right of decimal, all ODD numbered are 0 and all EVEn numbered are 9..   here 77 is odd, so ans is 0   Answer is 0
Answer: D
Milk contains 10% water. What content of pure milk should be added to 20 liters of milk to reduce this to 5%?  Choose the correct choice from the following
A) 20liters  B) 25liters  C) 30liters  D) 15liters  E) 18liters

Solution: Quantity of water in 20 liters = 10% of 20 liters = 2 liters   Let x liters of pure milk be added.   Then, 2/(20+x) = 5/100   5x = 100   x=20 liters   20litersnswer is 20liters
Answer: A
In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by ?
Choose the most appropriate option:
A) 25 m  B) 75 m  C) 85 m  D) 05 m  E) 15 m

Solution: Explanation:   A:B = 200 : 169   A:C = 200 : 182   =   => 182:169   When C covers 182 m , B Covers 169 m   When C covers 350 m , B Covers   => 325 m   So C beats B by (350 - 325)= 
(350 - 325) = 25
25 m.   25 mnswer: 25 m
Answer: A
A train passes a station platform in 39 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?	Select:
A) 328
B) 279
C) 240
D) 285
E) 231

Solution: Speed = [54 * 5/18] m/sec = 15 m/sec.   Length of the train = (15 * 20)= 
(15 * 20) = 300
300 m.   Let the length of the platform be x meters.   Then, x + 300 / 39= 15   x + 300 = 585   x = 285 m. Answer:285
Answer: D
The length of a rectangular plot is 10mtr more than its width. The cost of fencing the plot along its perimeter at the rate of Rs. 6.5mtr is Rs.1950. The perimeter of the plot is?	Select the correct option
A) 126  B) 156  C) 190  D) 300  E) 260

Solution: Sol. Let width = x, Length = (10+x)   Perimeter = 2(x+(10+x))   = 2(2x=10)   & 2(2x+10)*6.5 = 1950   X = 70   Required perimeter = 2(70+80) = 300   300
Answer: D
A train of length L is traveling at a constant velocity and passes a pole in t seconds. If the same train travelling at the same velocity passes a platform in 2t seconds, then what is the length of the platform?	Select the correct option:  A) 0.5 L  B) L  C) 1.5 L  D) 2 L  E) 3

Solution: The train passes a pole in t seconds, so velocity v = L/t   (L+P)/v = 2t   (L+P) / (L/t) = 2t   P = L   The answer is L.
Answer: B