MU-NLPC/Calc-aqua_rat huggingface dataset:
A man walking at the rate of 6 km/hr crosses a bridge in 15 minutes. The length of the bridge is ______.	Pick:
A) 1000 m
B) 1250 m
C) 1500 m
D) 1800 m
E) 2300 m

Solution: Hint: To find the answer in meter, we will first convert distance from km/hour to meter/sec by multiplying it with 5/18 .Also, change 15 minutes to seconds by multiplying it with 60.   Distance = Speed x Time   1. Convert speed into m/sec:   6 x	5 / 18 m/s = 1.66 m/s   2. Convert time from minutes into seconds = 15 x 60 s = 900 sec   3. 1500 malculate : Distance = 1.66 x 900 = 1500 m   ANSWER IS 1500 m
Answer: C
A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is? Options
A) 1 kmph	B) 7 kmph	C) 2 kmph	D) 4 kmph	E) 6 kmph

Solution: Explanation:   DS = 6   US = 4   S = ?   S = (6 - 4)/2= 
(6 - 4)/2 = 1
1 kmph   1 kmphnswer: Option 1 kmph
Answer: A
If 70 percent of the members of a certain organization are women and 7/8 of the members of the organization are married men, which of the following statements concerning the membership must be true? I. The number of women in the organization is greater than the number of married men in the organization. II. The number of women in the organization is greater than the number of unmarried men in the organization. III. The number of married men in the organization is greater than the number of unmarried men in the organization.	Choices.
A) I  B) I,II  C) III  D) II  E) I,II & III

Solution: 7/10 (70%) of the members are women and 7/8 of the members are married men. Let the total numbers of members is 80 (the LCM of 10 and 8). Then there are:    7/10*80= 
 7/10*80 = 56
56 women;    80 - 56= 
 80 - 56 = 24
24 men;     7/8*24= 
  7/8*24 = 21
21 married men;    24 - 21= 
 24 - 21 = 3
3 unmarried men.   So, option I,II is true.   Answer: I,II
Answer: B
A certain deck of cards contains 2 black cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both be not black? Choices.
A) 15/28
B) 1/4
C) 9/16
D) 1/32
E) 1/16

Solution: The question asks they will both be not black. Considering that these are draws without replacement there are following possibilities :   draw 1, draw 2   ===== =====   1) Not black, black;   2) black, Not black;   3) black, black;   4) Not black, not black;   The answer has to be either P(4) OR all exclusion of the 3 previous conditions i.e. 1- [P(1) + P(2) + P(3)] => neither of the draws are black   P(4) = 6/8*5/7=15/28   1- [P(1) + P(2) + P(3)] = 1 - [ (6/8 * 2/7) + (2/8*6/7) + (2/8*1/7)] = 1 - [26/8*7] = 1 - [13/28] = 15/28   15/28
Answer: A
A monkey climbs 30 feet at the beginning of each hour and rests for a while when he slips back 20 feet before he again starts climbing in the beginning of the next hour. If he begins his ascent at 6.00 a.m., at what time will he first touch a flag at 120 feet from the ground? Answers.
A) 4 p.m.  B) 5 p.m.  C) 6 p.m.  D) 7 p.m.  E) None of these

Solution: Explanation:   Net ascent of the monkey in 1 hour = (30 - 20)= 
(30 - 20) = 10
10 feet.   So, the monkey ascends 90 feet in 9 hours i.e. till 3 p.m.   Clearly, in the next 1 hour i.e. till 4 p.m. the monkey ascends remaining 30 feet to touch the flag.   4 p.m.nswer:4 p.m.
Answer: A
A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he
covers with aspeed 4km/hr. Total time of travel is 18 hours. What is the maximum distance he
can cover?	Select the correct option
A) 20km B) 40km C) 60km D) 80km E) 90km

Solution: t=d/s, so   18=x/2*1/5+x/2*1/4(because half distance with 5 km/ph, and remaining half with 4km/hr)   18=x(18/80)   x=80km   ANSWER:80km
Answer: D
In the exam the average was found to be p mark. After deducting typographical error the average marks of 94 student reduced from 84 to 64 . Due to this the average came down by 18.8 marks. What was the number of students who took the exam?
Pick one:
A) 100
B) 120
C) 110
D) 130
E) 160

Solution: Explanation :   Number of student = (84-64) * 94/18.8= 
(84-64) * 94/18.8 = 100
100   100nswer : 100
Answer: A
A vessel of capacity 2 litre has 25% of alcohol and another vessel of capacity 6 litre had 30% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?
Choices:	A) 23%.	B) 71%.	C) 49%.	D) 29%.	E) 51%.

Solution: 25% of 2 litres = 0.5 litres   30% of 6 litres = 1.8 litres   Therefore, total quantity of alcohol is 2.3 litres.   This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 23%   23%.NSWER:23%.
Answer: A
A car starts from X and moves towards Y. At the same time another car starts from Y and moves towards X. Both travel at a constant speed and meet after 4 hours. During that time, the faster car traveled 1/3 of the distance XY. How long would it take the slower car to travel the distance XY?  Answers.
A) 6 hours B) 8 hours C) 10 hours D) 12 hours E) 15 hours

Solution: If one car travelled 1/3, then the other car must have travelled only 2/3, as they are meeting after 4 hours in a certain point. So:   (2/3)XY= 4*y --> It took the car 4 hours to travel 2/3 of the distance at a constant speed y.   So if we solve this last equation:   2XY= 3*4*y= 6*y --> It will take this car 6 hours in total to reach its final destination.   6 hoursnswer: 6 hours
Answer: A
If 0.45: x : : 4 : 2, then x is equal to Choose the correct choice from the following:
A) 0.225	B) 0.228	C) 0.254	D) 0.256	E) None

Solution: Sol.   (x×4) = (0.45×2) ⇒ x = 0.9/4 = 0.225.   0.225nswer 0.225
Answer: A
The 480 students in a group are to be seated in rows so that there is an equal number of students in each row. Each of the following could be the number of rows EXCEPT  Select.
A) 4
B) 20
C) 30
D) 40
E) 90

Solution: Obviously the number of rows must be a factor of 480. The only option which is not a factor of 480 is E (90).   Answer: 90.
Answer: E
A man on tour travels first 160 km at 56 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:	Answers.
A) 31.11 km/hr	B) 35.55 km/hr	C) 65.9 km/hr	D) 36 km/hr	E) 71 km/hr

Solution: Total time taken = 160/56 + 160/80 = 2720/560 = 34/7 hours   --> Average speed = 320 x 7/34 = 65.9 km/hr.   Answer : 65.9 km/hr.
Answer: C
A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 800 m long?
Choose the correct choice from the following answers:
A) 200 Sec
B) 190 Sec
C) 167 Sec
D) 197 Sec
E) 179 Sec

Solution: L = S*T   S= 1200/120= 
1200/120 = 10
10 m/Sec.   Total length (D)= 2000 m   T = D/S   T = 2000/10= 
2000/10 = 200
200 Sec   200 Secnswer: 200 Sec
Answer: A
The present population of a town is 3888. Population increase rate is 20% p.a. Find the population of town before 2 years?	Choose the correct option.
A) 2500  B) 2100  C) 3500  D) 3600  E) 2700

Solution: P = 3888   R = 20%   Required population of town = P/(1 + R/100)^T   = 3888/(1 + 20/100)^2   = 3888/(6/5)^2   = 2700(approximately)   Answer is 2700
Answer: E
A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in? Pick
A) 25 days B) 24 C) 22 days D) 27 days E) 21 days

Solution: 24   24 days   24 = 1/8 – 1/2 = 1/24 => 24 days
Answer: B
A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?	Choose the correct option.
A) 33 1/7 %
B) 33 9/3 %
C) 33 1/3 %
D) 39 1/3 %
E) 23 1/3 %

Solution: The total number of mangoes bought by the shopkeeper be 12.   If he buys 4 a rupee, his 33 1/3 %P = 3   He selling at 3 a rupee, his SP = 4   Profit = SP - 33 1/3 %P = 4 - 3= 
4 - 3 = 1
1   Profit Percent= 1/3 * 100 = 33 1/3 %   Answer:33 1/3 %
Answer: C
if price of t.v set is reduced by 18%, then its sale increases by 72%, find net effect on sale value
Answers
A) 41	B) 45	C) 46	D) 47	E) 48

Solution: - a + b + ((-a)(b)/100)   = -18+72+(-18*72)/100   = -18+72-13= 
-18+72-13 = 41
41   41NSWER:41
Answer: A
If g, h, and i are each equal to 1 or 0, which of the following options will not be a correct value for e, given the equation e = g/5 + h/5^2 + i/5^3.	Choose the correct choice from the following:	A) 2/25	B) 1/5	C) 1/25	D) 6/25	E) 6/125

Solution: e = g/5 + h/5^2 + i/5^3   = g/5 + h/25+ i/125   = (25g + 5h + i ) /125   Depending on whether g, h and i take 0 or 1:   substitute 0 or 1 for the different values of g, h and i.   2/25nswer 2/25
Answer: A
If the speed of X meters per second is equivalent to the speed of Y meters per hour, what is Y in terms of X? (1 kilometer=1000 meters)  Select:
A) 15x/18	B) 3600x	C) 18x/5	D) 60x	E) 3600000x

Solution: x=y/3600   y = 3600x   Answer : 3600x
Answer: B
What least number must be added to 1056, so that the sum is completely divisible by 23 ?
Options: A) 2 B) 1 C) 3 D) 23 E) 9

Solution: 1056/23 = 45.91   that is   23 * 45= 
  23 * 45 = 1_035
1035   Now,   1056 - 1035= 
1056 - 1035 = 21
21   To get completely divided by 23 add 2 to 1056   2ns -2
Answer: A
A car dealership has 40 cars on the lot, 20% of which are silver. If the dealership receives a new shipment of 80 cars, 50% of which are not silver, what percentage of total number of cars are silver?	Select the correct option.
A) 30%
B) 35%
C) 40%
D) 45%
E) 50%

Solution: The number of silver cars is 0.2*40 + 0.5*80= 
0.2*40 + 0.5*80 = 48
48   The percentage of cars which are silver is 48/120= 40%   The answer is 40%.
Answer: C
Of the votes cast on a certain proposal, 68 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.)  Options:
A) 300	B) 340	C) 380	D) 420	E) 460

Solution: Let x be the total number of votes cast.   0.6x = 0.4x + 68   0.2x = 68   x = 340   The answer is 340.
Answer: B
Using all the letters of the word "LIVE", how many words can be formed, which begin with L and end with E? Choose the correct choice from the following answers:	A) 3	B) 4	C) 5	D) 6	E) 2

Solution: There are four letters in the given word.   Consider 4 blanks ....   The first blank and last blank must be filled with L and E all the remaining two blanks can be filled with the remaining 2 letters in 2! ways.   The number of words = 2! = 2.   ANSW2R:2
Answer: E
Which of the following is satisfied with |x-4|+|x-3|<5?	Choose the correct choice from the following choices.
A) 1<x<6
B) 2<x<5
C) 2.5<x<4.5
D) 2.5<x<4
E) 3<x<4

Solution: --> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, |x-4|+|x-3|<5-> |x-4+x-3|<5 -> |2x-7|<5, -5<2x-7<5, 2<2x<12, 1<x<6   Therefore, the answer is 1<x<6.
Answer: A
Susan, Tim, Matt and Kim need to be seated in 4 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?	Choices: A) 360 B) 12 C) 80 D) 240 E) 60

Solution: Total # of arrangement of 4 people is 4!.   In half of the cases Susan will be seated left to Tim and in half of the cases Susan will be seated right to Tim (why should one seating arrangement have more ways to occur than another?).   So, # of arrangements to satisfy the given condition is 4!/2=12.   Answer: 12.
Answer: B
H.C.F of 136, 144 and a third number is 8 and their L.C.M is 2^4 * 3^2 * 17 * 7. The third number is:	Choose the correct choice from the following:	A) 154	B) 248	C) 360	D) 424	E) 168

Solution: 136 = 2^3 * 17;   144 = 2^4 * 3^2   H.C.F = 2^3 = 8   Since H.C.F is the product of lowest powers of common factors, so the third number must have (2^3 ) as its factor.   Since L.C.M is the product of highest powers of common prime factors, so the third number must have 3 and 7 as its factors.   Third number = 2^3 * 3 * 7   = 168   ANSW168R:168
Answer: E
Five balls of different colors are to be placed in three different boxes such that any box contains at least 1 ball . What is the maximum number of different ways in which this can be done?
Options.
A) 60  B) 90  C) 120  D) 150  E) 180

Solution: Since in each box there must be at least one ball, we have the possibilities of (2,2,1), (2,1,2), (1,2,2) OR (3,1,1), (1,3,1), (1,1,3) balls in the three boxes.   For the 2,2,1 type arrangements, we have [5!/(2!2!1!)]*3 = 90 possibilities. Inside a box, it doesn't matter the order of the balls.   For the 3,1,1 type arrangements, we have [5!/(3!1!1!)]*3 = 60 possibilities.   Total of 90 + 60= 
90 + 60 = 150
150 possibilities.   Answer 150.
Answer: D
In a school of 800 students, 44% wear blue shirts, 28% wear red shirts, 10% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)? Choose the correct choice from the following choices
A) 120
B) 132
C) 144
D) 156
E) 168

Solution: 44 + 28 + 10= 
44 + 28 + 10 = 82
82%   100 – 82= 18%    800 * 18/100= 
 800 * 18/100 = 144
144   The answer is 144.
Answer: C
If 10 gallons of grape juice are added to 30 gallons of a mixture, which contains 10 percent grape juice then what percent of the resulting mixture is grape juice? Options.
A) 14%  B) 25%  C) 28%  D) 32.5%  E) 50%

Solution: OFFICIAL SOLUTION:   If we start with 40 gallons of a mixture that is 10% grape juice, then we have:   30 × 0.10 = 3 gallons of grape juice.   30 × 0.90 = 27 gallons of other components.   If we add 10 gallons of grape juice, we will end up with 13 gallons of grape juice and 36 gallons of other components, and we will have a total of 40 gallons of the mixture.   So 13/40 of the new mixture is grape juice. Now we convert this to a percent:Percent Grape Juice = 32,5%.   The correct answer is choice (32.5%)
Answer: D
The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly copied. The first is 17 greater than the actual number and the second number added is 13 instead of 31. Find the correct average. Choices: A) 40.3 B) 40.4 C) 40.6 D) 40.8 E) None of the above

Solution: Sum of 10 numbers = 402   Corrected sum of 10 numbers   = 402 – 13 + 31 – 17 = 403   Hence, new average = 403⁄10 = 40.3   40.3nswer 40.3
Answer: A
In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected? Answers:
A) 400
B) 500
C) 600
D) 20
E) 25

Solution: We can select one boy from 20 boys in 20 ways.   We select one girl from 25 girls in 25 ways   We select a boy and girl in 20 * 25 ways i.e., = 500 ways.   ANSWER:500
Answer: B
A man gains 40% by selling an article for a certain price. If he sells it at double the price, the percentage of profit will be. Select the correct option:
A) 130%
B) 180%
C) 150%
D) 160%
E) 170%

Solution: Explanation:   Let the C.P. = x,   Then S.P. = (140/100)x = 7x/5   New S.P. = 2(7x/5) = 14x/5   Profit = 14x/5 - x = 9x/5   Profit% = (Profit/C.P.) * 100   => (9x/5) * (1/x) * 100 = 180 %   Option 180%
Answer: B
Replace The Asterisk Mark Below With Correct Number ?
2 {38} 3
4 {1524} 5
6 {3548} 7
8 {****} 9  Select
A) 7291
B) 6380
C) 7298
D) 8332
E) 3829

Solution: 6380   6380   2*2-1 3*3-1 =>38   4*4-1 5*5-1 =>1524 and so on
Answer: B
On a certain farm the ratio of horses to cows is 6:1. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 3:1. After the transaction, how many more horses than cows would the farm own?
Choose the correct choice from the following answers: A) 40 B) 50 C) 60 D) 70 E) 80

Solution: Originally, there were 6k horses and k cows.   (6k-15) = 3(k+15)   6k-3k = 45+15   3k = 60   k = 20   The difference between horses and cows is (6k-15)-(k+15) = 5k-30 = 70   The answer is 70.
Answer: D
The forth proportional to 12,8,15 is?	Select.
A) 15 B) 12 C) 18 D) 10 E) 24

Solution: Let the fourth proportional to 12,8,15 be x   then 12:8::15:x   12x = 8*15   x = 10   Answer is 10
Answer: D
A raffle is being held at a party with 25 guests. Each guest has a numbered ticket (1 through 25). Three numbers will be randomly chosen and prizes given out. Paul and Jane have numbers 22 and 23. What is the probability both will win a prize? Choose the correct choice from the following options:	A) 1/2	B) 1/3	C) 1/100	D) 1/10	E) 3/25

Solution: Combination Formula: nCr = n!/(r!(n - r)!), where n is the population/set, and r is the sample/subset.   Total number possible = 251/1003 - 5!/(3!(5 - 3)!) = 2,300   Number 22 possible = 11/1001 = 1   Number 23 possible = 11/1001 = 1   Number other possible = 231/1001 = 23   Probability Formula: P(A) = (Number Favorable Outcomes)/(Total Number Possible Outcomes)   P(22, 23) = (11/1001)(11/1001)(231/1001)/251/1003 = 23/2,300 = 1/100   Answer: 1/100
Answer: C
A train 200 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 10 km/hr in the direction opposite to that in which the train is going?	Choose the correct choice:
A) 5
B) 6
C) 10
D) 9
E) 5

Solution: Speed of train relative to man = 60 + 10= 
60 + 10 = 70
70 km/hr.= 70 * 5/18 = 175/9 m/sec.   Time taken to pass the men = 200 * 9/175 = 10 sec.Answer: 10
Answer: C
If w is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of w ?
Choose the most appropriate option: A) 10 B) 12 C) 14 D) 16 E) 18

Solution: Answer is C.   numbers in format of 3^k in the series from 1 to 30 inclusive w are: 3*1, 3*2, 3*3, 3*4, 3*5, 3*3*2, 3*7, 3*8, 3*3*3, 3*10. Total number of 3 = 13. So k=14.
Answer: C
Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
Choose the correct answer:
A) 19
B) 17
C) 12
D) 15
E) 18

Solution: T = 9/45 * 60= 
9/45 * 60 = 12
12.Answer:12
Answer: C
The overall age of X and Y is 10 year greater than the overall age of Y and Z. Z is how many decades younger that X?  Choose the correct answer.
A) 11 B) 10 C) 12 D) 17 E) 19

Solution: 10   10   (X + Y) â€“ (Y + Z) = 10   X â€“ Z = 10
Answer: B
A survey was conducted to find out how many people in a housing colony of 144 residents could swim, dance and drive a car. It was found that the number of people who could not swim was 89, the number of people who could not dance was 105 and that the number of people who could not drive a car was 91. If the number of people who could do at least two of these things, was found to be 37 and the number of people who could do all these things was found to be 6, how many people could not do any of these things? Options
A) 52
B) 46
C) 40
D) 35
E) 38

Solution: T=n(A)+n(B)+n(40)-n(Exactly two of the events)-2*n(All 3 Events)+n(None of the events)   T=144   n(A)=T-n(A')=144-89= 
144-89 = 55
55   n(B)=T-n(B')=144-105= 
144-105 = 39
39   n(40)=T-n(40')=144-91= 
144-91 = 53
53   n(Exactly two of the events)=n(At least 2 Events)-n(All 3 Events)=37-6= 
37-6 = 31
31   n(All 3 Events)=6   144=55+39+53-31-2*6+n(None of the events)   n(None of the events)=144-55-44-53+31+12=40   Ans:40
Answer: C
A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 5 employees to 3 different offices?  Choose the correct choice:
A) 234
B) 243
C) 273
D) 284
E) 325

Solution: Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 3*3*3*3*3=3^5=243.   Answer: 243.
Answer: B
A 120 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?	Choose the correct answer
A) 220 meter  B) 225 meter  C) 380 meter  D) 435 meter  E) None of these

Solution: Explanation:   As trains are running in opposite directions so their relative speed will get added   So, Relative speed = 120 +80= 
120 +80 = 200
200 kmph= 200*(5/18) = 500/9 m/sec   Let the length of other train is x meter then   x+120 /9=500 /9   =>x+120=500   =>x=380   So the length of the train is 380 meters   Option 380 meter
Answer: C
If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
Select: A) Rs.8082 B) Rs.7800 C) Rs.8100 D) Rs.8112 E) none of these

Solution: A = 7500(26/25)2 = 8112   ANSWER:Rs.8112
Answer: D
The CITY club has exactly 5 new members at the end of its first week. Every subsequent week, each of the previous week's new members (and only these members) brings exactly P new members into the club. If y is the number of new members brought into the club during the twelfth week, which of the following could be y?	Choose the correct choice from the following answers.
A) 5^1/12
B) 3^11 * 5^11
C) 3^12 * 5^12
D) 3^11 * 5^12
E) 60^12

Solution: At the end of the first week, there are 5 new members;   At the end of the second week, there are 5P new members (since each 5 new members from the previous week brings P new members);   At the end of the third week, there are 5P^2 new members (since each 5P new members from the previous week brings P new members);   ...   At the end of the twelfth week, there are 5P^11 new members (since each 5P^10 new members from the previous week brings P new members).   We are given that 5P^11=y. Out of the answers only D yields integer value for P: 5P^11=3^11 * 5^12 --> P=3*5= 
3*5 = 15
15.   Answer: 3^11 * 5^12.
Answer: D
If the average marks of three batches of 55, 60 and 65 students respectively is 50, 46, 60, then the average marks of all the students is	Choose the correct choice from the following options.
A) 54.48  B) 54.68  C) 52.27  D) 54.58  E) None of these

Solution: Explanation:   (55Ã—50)+(60Ã—46)+(65Ã—60) / 55+60+65   9410 / 180=52.27   Option 52.27
Answer: C
Jeff received a 10% raise each month for three consecutive months. What was his starting salary if after the three raises his salary is $1331? Choose the correct choice from the following options
A) $1,000  B) $1,100  C) $1,200  D) $1,300  E) $1,400

Solution: S * 1.1 * 1.1 * 1.1 = 1331 thus,   S = 1000   $1,000nswer: $1,000
Answer: A
Ajay and Balu together can do a piece of work in 12 days. Balu and Charan together can do the same work in 16 days. After Ajay has been working at it for 5 days and Balu for 7 days, Charan finishes it in 13 days. In how many days will Charan alone be able to do the work?	Choose the correct option.
A) 16 days	B) 24 days	C) 36 days	D) 48 days	E) 58 days

Solution: Let the total work be 48 units.   Ajay and Balu’s One day work = 48/12= 
48/12 = 4
4 units.   Balu and Charan’s one day work= 48/16= 
48/16 = 3
3 units.   Ajay’s one day work= 4 - Balu’s one day work.   Balu’s one day work = 3 - Charan’s one day work.   Therefore, Ajay’s one day work = 1 + Charan’s one day work.   Also given,   5 x Ajay’s one day work + 7 x Balu’s one day work + 13 x Charan’s one day work = 48   Equating all the equations formed, we get Charan’s one day work is 2 units .   Hence, Charan can finish the whole work in  48/2= 
 48/2 = 24
24 days.   ANSWER:24 days
Answer: B
If 10 spiders make 5 webs in 5 days, then how many days are needed for 1 spider to make 1 web?
Options
A) 10  B) 9  C) 5  D) 15  E) 20

Solution: Explanation:   Let, 1 spider make 1 web in x days.   More spiders, Less days (Indirect proportion)   More webs, more days (Direct proportion)   Hence we can write as   (spiders)10:1   (webs) 1:5}::x:5   â‡’10Ã—1Ã—5=1Ã—5 Ã— x   â‡’x=10   10nswer: Option 10
Answer: A
The cost of cultivating a square field at the rate of Rs.135 per hectare is Rs.1215. The cost of putting a fence around it at the rate of 75 paise per meter would be :	Choose the correct choice from the following options.
A) s.360  B) s.810  C) Rs.900  D) s.1800  E) s.1900

Solution: Area= Total cost/ Rate= (1215/135) hectares= (9*10000) sq.m.   Therefore, side of the square= Ö90000=300m.   Perimeter of the field= (300*4)= 
(300*4) = 1_200
1200m   Rs.900ost of fencing= Rs.(1200*3/4)= Rs.900   ANSWER:Rs.900
Answer: C