MU-NLPC/Calc-aqua_rat huggingface dataset:
A person traveled 3 equal distances 4km/hr, 5km/hr, 6km/hr then find its avg speed? Choose the correct option
A) 5.2km/hr  B) 3.18km/hr  C) 4.86km/hr  D) 2.16km/hr  E) 6.32km/hr

Solution: avg speed = 3xyz/(xy+yz+zx)   required answer is = 3*4*5*6/ (20+30+24) = 4.86km/hr   Answer is 4.86km/hr
Answer: C
The ratio of 3 seconds to 30 hours	Choose the correct choice from the following choices:
A) 1:80
B) 1:36000
C) 1:600
D) 1:400
E) 1:500

Solution: 1 hour =3600 sec   then 30 hours =30*3600= 
30*3600 = 108_000
108000   so ,3:108000=1:36000   ANSWER:1:36000
Answer: B
A and B go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?	Choose the correct choice:  A) 110 sec  B) 130 sec  C) 120 sec  D) 140 sec  E) 150 sec

Solution: 120 sec   120 sec   Time taken to meet for the first time at the starting point   = L120 secM { length of the track / speed of A , length of the track / speed of B}   = L120 secM { 600/ (36 * 5/18) , 600/ (54 * 5 /18) }   = L120 secM (60, 40) = 120 sec.
Answer: C
When 60 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number? Choose the correct choice from the following answers
A) 3 : 4  B) 4 : 3  C) 2 : 3  D) Data inadequate  E) None of these

Solution: Let the first and the second numbers be x and y respect then   y + 60% of x = 140% of y   or, y + 0.6x = 1.4y   or, 0.6x = 0.4y   ∴ x : y = 0.4 : 0.6 = 2 : 3   Answer 2 : 3
Answer: C
A salt manufacturing company produced a total of 3000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?	Choose the correct choice:	A) 5520	B) 2789	C) 3550	D) 2889	E) 2788

Solution: Total production of salt by the company in that year = 3000 + 3100+ 3200 + .... + 4100 = 42600.   Average monthly production of salt for that year = 42600/12= 
42600/12 = 3_550
3550.   Answer: 3550
Answer: C
Find out the wrong number in the given sequence of numbers.
1, 2, 6, 15, 31, 56, 91 Options:
A) 2
B) 6
C) 15
D) 31
E) 91

Solution: 1(result) + (1*1) = 2.   2(result) + (2*2) = 6.   6(result) + (3*3) = 15.   15(result) + (4*4) = 31.   31(result) + (5*5) = 56.   56(result) + (6*6) = 92.   Now we are getting 92 not 91.. So 91 is the wrong number of the given.   answer : 91
Answer: E
A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.  Select the correct option
A) 1928  B) 1900  C) 1927  D) 1919  E) 1917

Solution: 65 * 6 : 84 * 5 : 100 * 3   26:28:20   C share = 74000 * 95/100 = 7030 * 20/74= 
7030 * 20/74 = 1_900
> 1900   Answer: 1900
Answer: B
A boy was asked to multiply a number by 25. He instead multiplied the next number by 52 and got the answers 324 more than the correct answer. The number to be multiplied was Pick
A) 10	B) 12	C) 15	D) 25	E) 35

Solution: Let the number be a   52xa=25xa+324   52a=25a+324   52a-25a=324   27a=324   a=12.   ANSWER:12
Answer: B
In an examination it is required to get 30% of minimum marks to pass. A student got 170 marks and was declared failed by 10 marks difference. Then what is total marks:? Choose the correct choice.
A) 550 B) 500 C) 600 D) 700 E) None of these

Solution: Explanation:   30 % -------> 180 ( 30 * 6 = 180)   100% -------> 600 (100 * 6 = 600)   Answer: Option 600
Answer: C
The ratio of 2 numbers is 3:7 and their H.C.F. is 10. Their L.C.M. is ?  Choose the correct choice:	A) 220	B) 210	C) 252	D) 236	E) 260

Solution: Let the numbers be 3x and 7x   Their H.C.F. = 10   so the numbers are 3*10 , 7*10 = 30,70   L.C.M. = 210   Answer is 210
Answer: B
At a summer camp with 900 participants, 1/2 of the campers are aged 8 to 12. Next year, the number of campers aged 8 to 12 will increase by 1/3. After this change, what percentage of the total 900 campers will the 8- to 12-year-olds represent?  Options:
A) 64% B) 66 2/3% C) 62% D) 60% E) 56%

Solution: Total - 900 participants   campers are aged 8 to 12 = (1/2)*900= 
(1/2)*900 = 450
450   Next year, campers are aged 8 to 12= (4/3)*450= 
(4/3)*450 = 600
600   Percentage= (600/900)*100 = 66 2/3%   Answer: Option 66 2/3%
Answer: B
A man spends 1810 for buying bed sheets at 200 each and pillows at 70 each. What will be the ratio of bed sheets to pillows when maximum number of bed sheets are bought?	Choose the correct option
A) 3 : 8
B) 8 : 3
C) 9 : 1
D) 1 : 9
E) None of these

Solution: The man can’t purchase more than 8 bedsheets   ∴ cost of 8 bedsheets = 8 × 200 = 1600   Remaining amount = 1810 – 1600 = 210   And in 210, the man can purchase   210⁄70 = 3 pillows   Reqd ratio = 8 : 3   Answer 8 : 3
Answer: B
Look at this series: 8, 22, 8, 28, 8, ... What number should come next?	Choose the correct choice from the following:	A) 9	B) 29	C) 32	D) 34	E) 36

Solution: Explanation: This is a simple addition series with a random number, 8, interpolated as every other number. In the series, 6 is added to each number except 8, to arrive at the next number.   Answer: Option 34
Answer: D
A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose?  Choose one
A) 120	B) 240	C) 360	D) 480	E) 520

Solution: Let x be the number he chose, then   2⋅x−138=102   2x=240   x=120   correct answer 120
Answer: A
A shop sells two variants of chocolates - one that costs $3 and the other that costs $5. If the shop sold $121 chocolates on a given day, how many different combinations of (number of $3 sold, number of $5 sold) exist? Options:
A) 4  B) 6  C) 8  D) 10  E) 12

Solution: $121 = 23*$5 + 2*$3   We can find other combinations by reducing the $5 chocolates by 3 (which is -$15)and increasing the $3 chocolates by 5 (which is +$15).   The number of $5 chocolates can be 23, 20, 17, 14,...,2 for a total of 8 combinations.   The answer is 8.
Answer: C
2 trains starting at the same time from 2 stations 200km
apart and going in opposite direction cross each other ata
distance of 110km from one of the stations.what is the ratio of
their speeds.  Choose the correct choice from the following choices.
A) 10:9  B) 11:9  C) 9:9  D) 9:10  E) 5:6

Solution: In same time ,they cover 110km & 90 km respectively   so ratio of their speed =110:90 = 11:9   Answer is 11:9.
Answer: B
Find the average of all the numbers between 26 and 54 which are divisible by seven  Select the correct option
A) 18
B) 38.5
C) 44
D) 50.8
E) None of these

Solution: Explanation :   Average = (28 + 35 + 42 + 49)/4 = 154/4 = 38.5.   Answer : 38.5
Answer: B
The side of a square has the length of 6. What is the area of the region shaded?
Choose the correct choice from the following answers:	A) 48-8π	B) 48-6 π	C) 24+6π	D) 16+8π	E) 64-8π

Solution: The area of a square whose side is 6 – (the area of a square whose side is 4 + the area of the semi-circle whose side is 4) = the area of the region shaded   The correct answer is 48-6 π.
Answer: B
A painter intends to mixed two jars of paint to create a new color. He chooses one paint jar randomly from a display containing 2 red and 4 blue samples, and a second jar is chosen at random from a different display containing 3 red and 2 blue samples. If he plans on mixing the two chosen jars together, what is the probability that when mixed together, the result will be purple paint? (The color purple is created with 1 part red and 1 part blue.)
Choose the correct choice from the following:
A) 1/5
B) 1/2
C) 2/3
D) 4/5
E) 6/5

Solution: Painter has two buckets he has to randomly pick from 2 different lists ... Let these Lists be A and B ... He has to choose the first bucket from List A , and the second bucket from List B   FOR THE FIRST BUCKET ...   Red color - 2   Blue color - 2   FOR THE SECOND BUCKET   Red color - 3   Blue color -2   In order to get Purple he has to mix red with blue .. Both the LISTS contain either blue or red , therefore we have two scenarios :   Scenario I - He picks Red color from List A and Blue color from List B   Scenario II - He picks Blue color from List A and Red color from List B   Scenario I - Odds for red color from List A are 1/2 .. and for Blue color from List B are 2 /5 .. Multiplying them (because we have to find the odds that both colors are selected from their respective lists together (this is a AND not an OR problem) we get 1/5   Scenario II - Odds for blue color from List A are 1/2 , and for Red color from List B are 3/5 ... Multiplying them we get 3/10 ...   Both the scenarios are equally possible therefore we must ADD the two (not multiply ) because both of them do not have to hold true together (have to independently) for our desired result to be achieved ...   We get 1/5 + 3/10 = 4/5 (4/5)
Answer: D
There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is?  Pick one:
A) 128	B) 276	C) 100	D) 277	E) 110

Solution: Let the number of students in rooms A and B be x and y respectively.   Then, x - 10 = y + 10 ⇒ x - y = 20 .... (i)   and x + 20 = 2(y - 20) ⇒ x - 2y = -60 .... (ii)   Solving (i) and (ii) we get: x = 100 , y = 80.   ∴ The required answer A = 100.   Answer: 100
Answer: C
What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?  Select the correct option: A) 85 % B) 26 % C) 10 % D) 20 % E) 15 %

Solution: Explanation:   SP2 = 2/3 SP1   CP = 100   SP2 = 80   2/3 SP1 = 80   SP1 = 120   100 --- 20 => 20%   Answer:20 %
Answer: D
Of the families in City X in 1998, 30 percent owned a personal computer. The number of families in City X owning a computer in 2002 was 20 percent greater than it was in 1998, and the total number of families in City X was 8 percent greater in 2002 than it was in 1998. what percent of the families in City X owned a personal computer in 2002?
Pick
A) 50.12%
B) 52.66%
C) 56.33%
D) 33.33%
E) 74.12%

Solution: Say a 100 families existed in 1998 then the number of families owning a computer in 1998 - 30   Number of families owning computer in 2002 = 30 * 120/100= 
30 * 120/100 = 36
36   Number of families in 2002= 108   The percentage = 36/108 * 100 = 33.33%.   Option: 33.33%
Answer: D
A three-person committee must be chosen from a group of 7 professors and 15 graduate students. If at least one of the people on the committee must be a professor, how many different groups of people could be chosen for the committee?  Choose the most appropriate option
A) A)70 B) B)1085 C) C)630 D) D)1,260 E) E)1,980

Solution: Total number of ways to select at least one professor = Number of ways to select 3 people from 15 students and 7 professors - Number of ways to select 3 people from 15 student (i.e. without including any professor)   = 22C3 - 15C3 = 1540 - 455= 
1540 - 455 = 1_085
1085   ANSWER:1085
Answer: B
Running at the same constant rate,6 identical machines can produce a total of 270 bottles per minute.At this rate,how many bottles could 8 such machines produce in 4 minutes ? Choose the correct choice from the following
A) 648  B) 1800  C) 2700  D) 1440  E) None of these

Solution: Solution   Let the required number of bottles be x.   More machines,More bottles (Direct Proportion)   More minutes,More bottles (Direct Proportion)   âˆ´ 6 Ã— 1 Ã— x = 8 Ã— 4 Ã— 270 â‡” x = 8x4x270/6= 1440 . Answer 1440
Answer: D
A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?
Choose the most appropriate option.
A) 833 1/7 B) 833 1/3 C) 833 2/9 D) 833 1/1 E) 833 1/4

Solution: If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.   If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.   How many grams he has to give instead of one kilogram(1000 gm).   120 gm ------ 100 gm   1000 gm ------ ?   (1000 * 100)/120 = 2500/3   = 833 1/3 grams.   Answer: 833 1/3
Answer: B
The price of a VCR is marked at Rs. 12,000. If successive discounts of 15%, 10% and 5% be allowed, then at what price does a customer buy it?  Choose the correct choice from the following:  A) 8789  B) 8721  C) 2189  D) 2789  E) 2791

Solution: Actual price = 95% of 90% of 85% of Rs. 12000   = 95/100 * 90/100 * 85/100 * 12000   = Rs.8721.   Answer:8721
Answer: B
The average of 5 consecutive integers starting with m as the first integer is n. What is the average of 13 consecutive integers that start with (m + 2)?	Choose one:	A) m + 6	B) n + 6	C) n + 3	D) m + 5	E) n + 4

Solution: The average of consecutive numbers is the middle number.   Then n = m+2.   The average of 13 consecutive numbers starting from n is n+6.   The answer is n + 6.
Answer: B
The ratio of two quantities is 5 : 4. If each of the quantities is increased by 10, what is the ratio of the new quantities?
Options:	A) It cannot be determined from the information given	B) 5:4	C) 2:3	D) 1:5	E) 4:1

Solution: Since the ratio is 5:4 we can put the quantities as 5K and 4K.   Moreover increasing quantities implies that the quantities become 5K+10 and 4K+10. So the ratio is (5K+10):(4K+10). The ratio value depend on the value of K. So It cannot be determined from the information given.   The answer is It cannot be determined from the information given
Answer: A
If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 8, respectively, what is the probability that b/a will not be an integer?
Choose the correct choice from the following choices
A) 2/12 B) 3/12 C) 4/12 D) 1/2 E) 2/3

Solution: a is from the following set {1,2,3,4}   b is from the following set {8,10,12}   The total number of ways of choosing 2 integers, one from each set is  4*3= 
 4*3 = 12
12 ways.   The possibilities where b/a is not an integer is for the following outcomes:   {b,a}= {8,3},{10,3},{10,4} = 3 ways   Thus the probability is 3/12 = 1/4   The answer is 3/12.
Answer: B
If x is a positive number and a=√x∗x−x, which of the following must be true?
I. a is even
II. a is positive
III. a is an integer  Choices
A) I only  B) II only  C) III only  D) I and II  E) None of the above

Solution: If x=14 then a=√x∗x−x=1/2∗1/4−1/4=−1/8. Now, −1/8 is not an integer at all (hence not even) and also not positive, so none of the options MUST be true.   Answer: None of the above.
Answer: E
Ronald and Elan are working on an assignment. Ronald takes 6 hrs to type 32 pages on a computer, while Elan takes 5 hrs to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
Options
A) 8 hrs 19 min
B) 8 hrs 18 min
C) 8 hrs 15 min
D) 8 hrs 65 min
E) 8 hrs 18 min

Solution: Number of pages typed by Ronald in 1 hour   = 32/6 = 16/3   Number of pages typed by Elan in 1 hour   = 40/5= 
40/5 = 8
8   Number of pages typed by both in 1 hour= (16/3 + 8) = 40/3   Time taken by both to type 110 pages   = (110 * 3/40) = 8 1/4 = 8 hrs 15 min   Answer:8 hrs 15 min
Answer: C
If the sum of 7 consecutive integers is x, which of the must be true?
I. x is even
II. x is odd
III. x is a multiple of 7  Choose the correct choice from the following options:
A) I only B) II only C) III only D) I and III E) II and III

Solution: sum of 3 consecutive integers   = (n) + (n+1) + (n+2) ++ (n+3) + (n+4) + (n+5)+(n+6)   =7n+21   = odd + odd = even   = 7(n+3) = divisible by 7   Hence, x is even and divisible by 7.   Answer: I and III
Answer: D
Bruno and Sacha are running in the same direction around a stadium. Sacha runs at a constant speed of 6 meters per second, and Bruno runs at a constant speed of 5 meters per second. At a certain point Sacha overtakes Bruno. If two minute afterward, Sacha stops and waits for Bruno to reach him, then how many seconds does he have to wait?
Choose the correct choice from the following.
A) 12  B) 24  C) 36  D) 60  E) 72

Solution: the difference of the speed is 1m per second so in two minute Sacha will be 120 m ahead of Bruno..   Bruno will cover this in  120/5= 
 120/5 = 24
24 secs..   24
Answer: B
A team of six entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
Pick: A) 288 B) 497 C) 168 D) 127 E) 664

Solution: Explanation:   6 * 84= 
6 * 84 = 504
504 - 7= 
504 - 7 = 497
497   Answer:497
Answer: B
A group of people,dogs, and birds has seventy legs, thirty heads, and twenty
tails. How many cats are among this group? (Assume all birds have two legs and a tail.)	Choose the correct choice from the following choices.
A) 0 B) 5 C) 13 D) 15 E) 20

Solution: Write P, C, and B for the number of people, dogs, and birds respectively, so that   we have   2P + 4C + 2B = 70, P + C + B = 30,C + B = 20:   Comparing the last two equations we obtain P = 10, and the first equation simplifies to   4C + 2B = 50, or 2C + B = 25. Therefore,   C = (2C + 5) -(C + 5) = 25- 5 = 5   correct answer 5
Answer: B
A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.15 less, he could have gained 25%. What is the cost price? Choose one
A) 197 B) 375 C) 279 D) 278 E) 75

Solution: CP1 = 100 SP1 = 120   CP2 = 80 SP2 = 80 * (125/100)= 
80 * (125/100) = 100
100   20 ----- 100   15 ----- ?=> 75   Answer:75
Answer: E
A pool which was 5/6 full to begin with, was filled at a constant rate for 5/3 hours until it was until it was 6/7 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with?  Choose the correct option:	A) 68 hrs 45 mins.	B) 70 hrs.	C) 68 hrs 30 mins.	D) 11 hrs 40 mins.	E) 15 hrs 30 mins

Solution: The pool was 2/3 full initially.   In 5/3 hrs, it was filled to 6/7 of its capacity.   Therefore, in 5/3 hrs, 6/7 - 5/6 was the amount of volume filled.   So, 5/3 hrs = 6/7 - 5/6 = 1/42   Therefore, for filling the vessel from empty to full, you would require  5/3 * 42/1= 
 5/3 * 42/1 = 70
70 Hrs .   Hence 70 hrs.
Answer: B
A tank is filled in 5 hours by three pipes P, Q and R. The pipe R is twice as fast as Q and Q is twice as fast as P. How much time will pipe P alone take to fill the tank?  Options
A) 35 hrs B) 20 hrs C) 25 hrs D) 50 hrs E) 28 hrs

Solution: Pipe P alone - x hrs to fill   then Q and R -> x/2 and x/4 hrs   then 1/x+2/x+4/x = 1/5   7/x=1/5   x = 33 hrs   35 hrsNSWER 35 hrs
Answer: A
A man buys an article for rs.27.50 and sells it for rs.28.50. find his gain %.
Choose the correct choice from the following choices:
A) 2%
B) 3%
C) 4%
D) 5%
E) 6%

Solution: sol. cp=rs27.50, sp=rs 28.50   gain=rs(28.50 â€“27.50)=rs1.10   so gain%={(1.10/27.50)*100= 
(1.10/27.50)*100 = 4
4%   ANSWER 4%
Answer: C
A sporting goods store sold 64 Frisbees in one week, some for $3 and the rest for $4 each. If receipts from Frisbee sales for the week totaled $196 what is the fewest number of $4 Frisbees that could have been sold?  Choose the most appropriate option
A) 24  B) 12  C) 8  D) 2  E) 4

Solution: In this question however, because we are told that exactly 64 Frisbees have been sold and revenue was exactly $204, there is only one possible solution for the number of $3 and $4 Frisbees sold.   To solve, we have 2 equations and 2 unknowns   Let x = number of $3 Frisbees sold   Let y = number of $4 Frisbees sold   x + y = 64   3x + 4y = 196   x = 64 - y   3(64-y) + 4y = 196   192 - 3y + 4y = 196   y = 4   Answer: 4
Answer: E
A rectangular lawn of dimensions 70 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?  Pick one:	A) 2288	B) 2779	C) 2779	D) 3900	E) 3600

Solution: Area = (l + b â€“ d) d   (70 + 60 â€“ 10)10 => 1200 m2   1200 * 3 = Rs.3600   Answer:3600
Answer: E
John bought a total of 20 Mangoes and Oranges. Each Mango costs 80 cents and each orange costs 60 cents. If the average price of the 20 mangoes and oranges that John originally purchased was 65 cents, then how many oranges needs to return to raise the average price of his purchase to 72 cents?	Choose the correct choice from the following answers
A) 4  B) 5  C) 6  D) 9  E) 12

Solution: Let number of mangoes be x, number of oranges be 12-x   0.80x +(20-x)0.60/20 = 0.65   solving for x, we get x = 5 --> Mangoes 5, Oranges 15   Now, number of oranges to be returned be y   0.80*5 + (15-y)*0.60/20-y = 0.72   solving for y, y = 12   Ans: 12
Answer: E
If W = {1, 7, 18, 20, 29, 33}, how much less is the mean of the numbers in W than the median of the numbers in W? Answers.
A) 1.0 B) 1.5 C) 2.0 D) 2.5 E) 3.0

Solution: This is a good question to understand the difference between mean and median.   Mean: Average of all the numbers. (Sum of all the elements divided by the number of elements)   Median: Arrange the elements of the set in increasing order. If the number of terms is odd, the middle term is the median. If the number of terms is even, the average of middle two terms is the median   Coming to this question,   Mean = (1 + 7 + 18 + 20 + 29 + 33)/6= 
(1 + 7 + 18 + 20 + 29 + 33)/6 = 18
18   Median= (18 + 20)/2= 
(18 + 20)/2 = 19
19   Difference= 1   Option 1.0
Answer: A
If A and B are two prime numbers bigger than 2, which of the following can be true?
(1) A + B is an even number.
(2) A x B is also a prime number.
(3) A- B is also a even number.  Choose the correct option:
A) 1 only.  B) 1 and 3 only.  C) 3 only.  D) 2 and 3 only.  E) 1, 2 and 3.

Solution: Answer is D : 2 and 3 only   (1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true   (2) A x B is also a prime number. : Beats the property of primes, so false   (3) A^B is also a prime number. : True   Ans :1 and 3 only.
Answer: B
Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 16% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?	Choices
A) 5%
B) 17%
C) 16%
D) 13%
E) 30%

Solution: 60-(x+16+z) + 50-(x+16+y) + 35-(z+16+y) + x + y + z +16 = 100   where x = people who bought MilkChicken   y = people who bought chickenApples   z= people who bought Milk and Apples   x+y+z= the number of people who bought just exactly two products.   Hence solving the above equation we get,   113 -(x+y+z) = 100   Thus, x+y+z= 13   Answer: 13%
Answer: D
The simple interest at a% for a years will be $a on a sum of
Choose the correct choice from the following: A) $ (1000)/a B) $(100)a^2 C) $ a D) $ (100)/a E) $ 100a

Solution: Principal =$(100*a)/(a*a)=$(100/a).   Answer is $ (100)/a
Answer: D
Nicky and Cristina are running a race. Since Cristina is faster than Nicky, she gives him a 36 meter head start. If Cristina runs at a pace of 4 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?	Choose the most appropriate option: A) 15 seconds B) 18 seconds C) 25 seconds D) 36 seconds E) 45 seconds

Solution: used pluging in method   say t is the time for cristina to catch up with Nicky, the equation will be as under:   for Nicky=N=3*t+36   for Cristina=C=5*t   @t=36, N=144 C=144 right answer   ans:36 seconds
Answer: D
Two trains of length 100 m and 200 m are 200 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet? Answers.
A) 21/9 sec  B) 32/3 sec  C) 20/7 sec  D) 32/3 sec  E) 40/7 sec

Solution: They are moving in opposite directions, relative speed is equal to the sum of their speeds.   Relative speed = (54 + 72)*5/18 = 7*5= 
7*5 = 35
35 mps.   The time required= d/s = 200/35 = 40/7 sec.   Answer:40/7 sec
Answer: E