MU-NLPC/Calc-aqua_rat huggingface dataset:
A rectangular lawn of dimensions 120 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? Choices:
A) s.5100	B) s.3900	C) s.3228	D) s.3922	E) s.3928

Solution: s.5100rea = (l + b – d) d   (120 + 60 – 10)10 => 1700 m2   1700 * 3   = Rs.5100   s.5100nswer:s.5100
Answer: A
How much water should be added to 15 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ? Choose the correct choice from the following
A) 25 liters  B) 27 liters  C) 30 liters  D) 32 liters  E) 35 liters

Solution: Let x ltr water to be added   2ltr alcohol to be represented as (20(1-3/4(new soln.=15+x)))   2=5%*(15+x)-------->x=25   25 litersns 25 liters
Answer: A
how many four digits numbers are formed such that the digits are in decreasing order
Choices
A) 170
B) 180
C) 190
D) 200
E) 210

Solution: START with 3 = 3_ _ _. You can fill in with digits 0,1,2. Hence 3C3 = 1   START with 4 = 4_ _ _. (0,1,2,3). hence 4C3= 4   START with 5, you have (0,1,2,3,4) to fill in the blanks behind 5, hence 5C3 = 10   START with 6, 6C3=20   7... = 7C3 = 35   8...=8C3 = 56   9...= 9C3 = 84   so ans=1+4+10+20+35+56+84= 
1+4+10+20+35+56+84 = 210
210   ANSW210R:210
Answer: E
If 6 coins are tossed, how many different coin sequences will have exactly 3 tails, if all tails have to occur in a row?	Choose one
A) 4  B) 8  C) 16  D) 20  E) 24

Solution: xactly 3 tails and have to occur in row   We have 6 coins we use the glue method so we say all 3 tails as 1   so we have 4! ways, however we need to reduce duplicate for 3 Heads as well   HHH{T} therefore using anagram method   4!/3! = 4   4nswer: 4
Answer: A
The average score of a cricketer in 10 matches is 60 and in other 15 matches is 70. Then find the average score in all the 25 matches?  Pick
A) 50 B) 48 C) 65 D) 66 E) 72

Solution: Average in 25 matches = (10*60 + 15*70)/10+15 = 66   Answer is 66
Answer: D
Ramu bought an old car for Rs. 43000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?  Choose the most appropriate option:
A) A)14%	B) B)16%	C) C)18%	D) D)22%	E) of these

Solution: Total CP = Rs. 43000 + Rs. 13000 = Rs. 56000 and SP = Rs. 64900   Profit(%) = (64900 - 56000)/55000 * 100 = 16%   ANSWER:16%
Answer: B
A shop keeper sell an article gets profit of 20% had he bought it for 20% less and sold it for Rs 120 less he would have still bought profit of 20% what is the cost price of article	Choose the correct choice from the following
A) 500 B) 600 C) 700 D) 750 E) 450

Solution: let c.p be x,   1st s.p =(120/100)x=6x/5   2nd s.p=(80/100)x=4x/5   filnal profit 20% so   120/100 * 4x/5   120 rs less so   6x/5 - 24x/25 =120   x=500   500NSWER:500
Answer: A
The area of a triangle will be when a = 1m, b = 2m, c = 5m, a, b, c being lengths of respective sides?
Pick one:
A) 3	B) 6	C) 4	D) 9	E) 1

Solution: S = (1 + 2 + 5)/2= 
(1 + 2 + 5)/2 = 4
4 Answer:4
Answer: C
If the speed of x meters per second is equivalent to the speed of Y mile per hour, what is y in terms of x? (1 mile = 1609.34 meter)	Select:
A) 1.21x
B) 1.33x
C) 2.23x
D) 2.84x
E) 3.13x

Solution: x meters per second -->   --> 3,600x meters per hour(as there are 3,600 seconds in one hour);   --> 3,600x/1,609.34=2.236x miles per hour (as there are 1,609.34 meters in one mile).   Answer: 2.23x.
Answer: C
Number X is 30% more than that of Number Y . Find what percent of Number Y is less than Number X ?
Choose the correct option.
A) 25 1/3%  B) 26 1/3%  C) 24 1/3%  D) 23 1/3%  E) 23 2/3%

Solution: Explanation:   y=100 x=130   130---------30   100---------? => 23 1/3%   Answer 23 1/3%
Answer: D
A house of 4 rooms is designed from 4 types of bedrooms and 3 types of bathrooms. The house must have at least 2 types of bedrooms and at least 1 type of bathroom. How many ways can this house be designed? Pick one
A) 3  B) 4  C) 12  D) 30  E) 38

Solution: Solution: We have two possibilities 3Bed 1Bath or 2Bed 2Bath   (4C3)(3C1)+(4C2)(3C2)=30   30) 30
Answer: D
Ram and Krishna start from A and B respectively at the same time and travel towards each other at constant speeds along the same route. Ram meets Krishna at point C on the road which is 1000m away from starting point A and 500m away from point B. The time taken by Ram to reach point B is 10minutes. Find the time taken by krishna to go from B to A.?
Choose the correct choice from the following options:
A) 45 minutes	B) 35 minutes	C) 50 minutes	D) 52 minutes	E) None of the above.

Solution: total distance from A to B-   A - C = 1000m, B - C = 500m;   therefore A-B = 1500m;   Vr=1500/25= 
1500/25 = 60
60 m/m;   t-time taken by Ram for AB meet,   t=1000/60=16.67 minutes = Time taken by Krishna for AB meet.   therefore,   Vk=500/16.67=30m/m.   time taken by krishna for B-A = 1500/30= 
1500/30 = 50
50 minutes   option 50 minutes
Answer: C
Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 9 times the amount of the second solution?	Answers: A) 62 B) 65.5 C) 68 D) 70 E) 71.5

Solution: SOL:   Lets assume that 90L of sol1 was mixed with 10L of sol2.   Alcohol in Sol1: 90*3/4 = 67.5L   Alcohol in Sol2: 10*2/5 = 4L   Total Alcohol in the mixed solution of 100L = 67.5 + 4= 
67.5 + 4 = 71.5
71.5L   Alcohol concentration in the new sol: (71.5/100)*100= 
(71.5/100)*100 = 71.5
71.5%   ANSW71.5R:71.5
Answer: E
In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 130 marks, the no of questions he attempts correctly is :
Choose the correct choice from the following answers:
A) 33  B) 38  C) 99  D) 27  E) 71

Solution: Let the number of correct answers be X.   Number of incorrect answers = (60 – X).   4x – (60 – x) = 130   => 5x = 190   => x = 38   Answer: 38
Answer: B
The difference between two numbers is 1365. When the larger number is divided by the smaller one, the quotient is 6 and the remainder is 15. The smaller number is	Choose the correct choice from the following choices.
A) 240	B) 270	C) 295	D) 360	E) NOne

Solution: Sol.   Let the smaller number be x.   Then, larger number = (1365 + x).   ∴ 1365 + x = 6x + 15   ⇔ 5x = 1350   ⇔ x = 270.   Hence, the required number is 270.   Answer 270
Answer: B
Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 25% and 20% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of  Choose the correct choice from the following choices:
A) 18%
B) 20%
C) 21%
D) 25%
E) Cannot be determined

Solution: Answer: 25%.
Answer: D
How many odd 4-digit positive integers Q that are multiples of 5 can be formed without using the digit 3?
Choose the correct choice from the following choices.
A) 648 B) 729 C) 900 D) 1296 E) 3240

Solution: I choose A.   Possible n° of 1st digit: 8 (0 can't be the first number, or else it wouldn't have 4 digits. 3 is exlcuded)   Possible n° of 2nd digit: 9 (3 is excluded)   Possible n° of 3rd digit: 9 (3 is excluded)   Possible n° of 4th digit: 1 (a number is a multiple of 5 if it ends in 5 or 0, here we are asked for the odd numbers, hence the last digit can't be 0)   So, Q=8*9*9*1= 
8*9*9*1 = 648
648 (648)
Answer: A
A shopkeeper cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 20% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 10% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage. Select.
A) 20%  B) 32%  C) 23.365%  D) 22.109%  E) 2%

Solution: Anyways, one can infer that he 'steals' 20% from suppliers and then charges 10% extra to customers   So basically 1.2 * 1.1= 
1.2 * 1.1 = 1.32
1.32   Given that 1 is start point, we get 32% more   Hence answer is 32%
Answer: B
Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 10% of Listco's sales staff. Listco employs 72 level-1 employees, 20 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ?	Choose the correct choice from the following answers:	A) 46	B) 48	C) 56	D) 32	E) 58

Solution: I'm going in on this one.   So let's say that we have the following   So we know that L1 = 72 and that C and L1 = 0.10X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.1x = 20, therefore the grand total is 200. Now we know that L2 is  200 - 72= 
 200 - 72 = 128
128. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 52= 
100 - 52 = 48
48.   Thus 48 is the correct answer choice
Answer: B
A's salary is 50% more than B's. How much percent is B's salary less than A's?  Choose the correct choice: A) 25.5% B) 33.3% C) 45.6% D) 50% E) 25%

Solution: 33.3%'s salary is less than A's salary by 50/(100+50) * 100% = 100/3% = 33.3%   Answer is 33.3%
Answer: B
66 small identical cubes are used to form a large cube. How many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?  Choose one.
A) 64	B) 150	C) 152	D) 216	E) 256

Solution: 66 small cube will make a large cube with 4 cubes in each line i.e.   Adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line.   Total number of small cubes in new cube = 6^3 = 216   Extra cube required = 216 - 66= 
216 - 66 = 150
150   Hence, 150 is the answer.
Answer: B
If the sum of two numbers is 20 and the sum of their squares is 200, then the product of the numbers is
Pick one:
A) 40
B) 44
C) 100
D) 88
E) 48

Solution: according to the given conditions x+y = 20   and x^2+y^2 = 200   now (x+y)^2 = x^2+y^2+2xy   so 20^2 = 200 + 2xy   so xy = 200/2= 
200/2 = 100
100   ANSWER:100
Answer: C
A container contains 40 liters of milk, From this container 4 liters of milk was taken out and replaced by water. This process was repeated further 2 times. How much milk is now contained by the container?
Choose the correct choice from the following
A) 25.5 liters	B) 29.16 liters	C) 30.98 liters	D) 42.15 liters	E) 48.32 liters

Solution: Amount of milk left after 3 operations = 40 (1 - 4/40)^3 = 40 * 9/10 * 9/10 * 9/10= 
40 * 9/10 * 9/10 * 9/10 = 729/25 = around 29.16
29.16 liters   Answer is 29.16 liters
Answer: B
There are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?  Choices: A) 1800 B) 3200 C) 2600 D) 3600 E) None of these

Solution: There are 5 subjects and 6 periods. Each subject must be allowed in at least one period. Therefore, two periods will have same subject and remaining four periods will have different subjects.   Select the two periods where the same subject is taught. This can be done in 6C2 ways.   Allocate a subject two these two periods(5C1 ways).   Remaining 4 subjects can be arranged in the remaining 4 periods in 4! ways.   Required number of ways   = 6C2 × 5C1 × 4! = 1800   1800nswer : 1800.
Answer: A
In a 100 m sprint race Kelly was given a 3 m head start by Abel. If Abel lost the race to Kelly by a distance of 0.50 m, how many meters more would Abel need to overtake Kelly?	Choices.
A) 20.5  B) 18.4  C) 17.5  D) 19.9  E) 21.5

Solution: Distance Abel ran before completion of race---100 m-0.50m=99.5m   Distance gained on Kelly over 99.5m---3m-0.50m=2.50m   then Abel gains 99.5m/2.50m = 1m on Kelly every 39.8 meters.   Therefore 39.8 divided by half a meter ( i.e the 0.50 m Abel was defeated with)   ANSWER: D. 19.9m
Answer: D
Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are: Options: A) 39, 30 B) 41, 32 C) 42, 33 D) 43, 34 E) 41, 44

Solution: C   Let their marks be (x + 9) and x.   Then, x + 9 = 56/100(x + 9 + x)   25(x + 9) = 14(2x + 9)   3x = 99   x = 33   So, their marks are 42 and 33.
Answer: C
Rajesh, Sunil and Tarun enter into a partnership. Rajesh invested Rs.25000 and after one year he adds Rs.10,000 more. Sunil initially invests Rs.35,000 and after 2 years he withdraws Rs.10,000 and Tarun invests Rs.19,000 in the beginning only. Then ratio of their profits after 3 years will be  Select:
A) 05:30:00
B) 05:30:00
C) 05:30:00
D) 05:30:00
E) None

Solution: Ratio of their profits after 3 years   =25000×1+35000×2 :35000×2+25000×1:19000×3   =25×1+35×2:35×2+25×1:19×3   =95:95:57   =5:5:3   ANSWNoneR:None
Answer: E
What is the tens' digit Q of the sum of the first 40 terms of 1, 11, 111, 1111, 11111, 111111, ...?  Choose the correct choice.
A) Q=2  B) Q=3  C) Q=4  D) 8  E) 9

Solution: All of the first 40 terms have 1 at the units place.   Except the first term, the tens digit of all the remaining 39 terms is 1.   So now if you do the addition   1 1   1 1   . . .   . . .   . . .   1 1   0 1   3 0   Answer is Q=3
Answer: B
If q>0, which of the following must be true?	Choose the correct choice from the following options:
A) 1 <q
B) 0 < q < 2
C) -1 < q < 1
D) -10 < q
E) 1/100 < q

Solution: All we know is that q is some positive number. Right away we can see that D must be true: if q is positive then it MUST be true that it's greater than -10. Still let's check each option.   A. 1 < q. We don't know whether the number is greater than 1, it could be a positive number less than or equal to 1. Discard.   B. 0 < q < 2. The same here: we don't know whether the number is less than 2, it could be more than or equal to 2. Discard.   C. -1 < q < 1. The same as A. Discard.   E. 1/100 < q. We don't know whether the number is greater than 1/100, it could be a positive number less than or equal to 1/100. Discard.   Answer: -10 < q.
Answer: D
If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 7 children have two children of the same sex and one of the opposite sex?
Choices
A) 1/3  B) 2/3  C) 1/4  D) 7/64  E) 3/5

Solution: No of ways of selecting a gender - 2C1   No of ways of selecting any 2 children out of 7 = 7C2   Total possible outcomes - 2^7 (each child can be either a girl or a boy)   Probability=2C1*7C2/2^7= 2*7/2*2*2*2*2*2*2=7/64   Ans=7/64
Answer: D
Two whole numbers whose sum is 100 cannot be in the ratio	Choose the correct choice from the following answers:  A) 2:23  B) 5:45  C) 10:10  D) 2:6  E) 2:3

Solution: 2:6) 2:6
Answer: D
If Dale works at full efficiency he needs a break of 1 day after every 2 days of work and he completes a job in a total of 5 days. If he works at reduced efficiency, he can work without break and finish that same job in 5 days. Dale's output at reduced efficiency is what fraction of his output at full efficiency?  Choose the correct answer
A) 5/2
B) 4/1
C) 9/5
D) 4/5
E) 2/5

Solution: We're told that there are 2 ways for Dale to complete a job:   1) Full Efficiency: 2 days of work followed by 1 dayofffor a total of 5 days.   2) Reduced Efficiency: 5 straight days with no days off.   Working at Full Efficiency creates the following pattern:   2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on = 2+1+2= 
2+1+2 = 5
5 days   Totals: 4 days on, 1 days off   Reduced Efficiency means that Dale will do 6 days of work in 5 days, thus those Reduceddaysare 4/1 of Full Efficiency.   Answer : 4/1
Answer: B
If x is divisible by 2, 14, and 11, which of the following must be the least multiple of x?
Pick:	A) 308	B) 154	C) 70	D) 44	E) 0

Solution: We are looking for the LCM (which is not 0) of 2, 11, 14:    2 * 11 * 7= 
 2 * 11 * 7 = 154
154   ANSWER:154
Answer: B
To fill a cistern, pipes A,B and C take 20 minutes, 15 minute and 12 minutes resp. The time in minutes that the three pipes together will take to fill the cistern is	Choose the correct choice from the following answers
A) 5  B) 6  C) 8  D) 3  E) 9

Solution: 5   5
Answer: A
A factory produces x widgets per day. The factory's fixed costs are $8000 per day. The price per widget is $70 and the variable costs are $30 per widget. How many widgets need to be produced for profits of $5440 a day? Choose the correct answer:
A) 42.33  B) 90.33  C) 168  D) 224  E) 311

Solution: profits=5440=40x-8000 --> x=311   Answer 311.
Answer: E
Excluding stoppages, the speed of a bus is 58 kmph and including stoppages, it is 40 kmph. For how many minutes does the bus stop per hour? Select:	A) 19	B) 19.13	C) 10.5	D) 11.35	E) None of these

Solution: Due to stoppages, it covers 18 km less.   Time taken to cover 18 km = ((18/58)Ã—60) = 19 min.   Option(19) is correct
Answer: A
If f(x)=4x−1 and g(x)=2x+6 for all integers, which of the following is a possible value of g(f(x))?	Choose the correct choice from the following answers:
A) -23  B) -17  C) 0  D) 8  E) 20

Solution: g(f(x)) = 2*f(x)+6 = 2*(4x-1)+6 = 8x+4   Of these five options, only 20 has the form 8x+4.   The answer is 20.
Answer: E
Two whole numbers whose sum is 24 is the ratio
Choose the correct choice
A) 1:3  B) 2:8  C) 1:6  D) 2:3  E) 2:5

Solution: 1:3) 1:3
Answer: A
Reena took a loan of 1200 with simple interest for as many years as the rate of interest. If she paid 432 as interest at the end of the loan period, what was the rate of interest? Choose the correct choice from the following answers:
A) 6
B) 3
C) 7
D) 8
E) 9

Solution: A   6   Let rate = R% and time = R years.   Then, (1200 x R x R)/100 = 432   12R² = 432   R² = 36   R = 6.
Answer: A
In a recent election, Ms. Robinson received 3200 voters cast by independent voters, that is, voters not registered with a specific political party. She also received 10 percent of the votes cast by those voters registered with a political party. IF N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Mrs. Robbins received?	Choose the correct choice from the following answers.
A) 0.06N+3200  B) 0.1N+7200  C) 0.4N+7200  D) 0.1N+8000  E) 0.06N+8000

Solution: 40% of N are independent voters, hence 60% of N are not independent voters. From this group she received 10% votes so, 0.1*0.6*N plus 3,200 votes from independents: total=0.1*0.6*N+3,200=0.06*N+3,200.   0.06N+3200nswer: 0.06N+3200.
Answer: A
If Leo gains 10 pounds, he will weigh 50% more than his sister Kendra. Currently their combined weight is 140 pounds. What is Leo's current weight?
Pick one.
A) 80	B) 90	C) 100	D) 110	E) 120

Solution: L+K = 140 and so K = 140-L   L+10 = 1.5K = 1.5(140-L)   2.5L = 200   L = 80   The answer is 80.
Answer: A
Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?  Pick one.
A) 8
B) 7
C) 6
D) 9
E) 5

Solution: 1/10 + 1/15 - 1/x = 1/18   x = 9   Answer:9
Answer: D
One side of a triangle has length 6 and a second side has length 4. Which of the following could be the area of the triangle?
I. 15
II. 12
III. 5  Choose the correct choice from the following answers:	A) I only	B) II only	C) III only	D) II and III only	E) I, II and III

Solution: The triangle will have a maximum area when it is a right angled triangle   The largest triangle will be formed when 6 and 4 are the base and height of triangle .   Area = 1/2 * 6 * 4= 
1/2 * 6 * 4 = 12
12   There is no lower limit on the area of any triangle whose only 2 sides are known.   Then 0 < Area <= 12   The answer is II and III only.
Answer: D
A train 280 m long, running with a speed of 63 km/hr will pass a tree in?	Pick one:
A) 22 sec
B) 16 sec
C) 17 sec
D) 88 sec
E) 12 sec

Solution: Speed = 63 * 5/18 = 35/2 m/sec   Time taken = 280 * 2/35= 
280 * 2/35 = 16
16 sec   Answer:16 sec
Answer: B
What is the smallest no. that should be added to 27452 to make it exactly divisible by 9? Choose the correct choice from the following options:
A) 1 B) 3 C) 5 D) 6 E) 9

Solution: If a number is divisible by 9, the sum of its digits must be a multiple of 9.   Here, 2+7+4+5+2=20, the next multiple of 9 is 27.   7 must be added to 27452 to make it divisible by 9   9
Answer: E
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 720 sq. feet, how many feet of fencing will be required?	Choose the correct choice from the following.
A) 34	B) 40	C) 68	D) 88	E) 92

Solution: Given that length and area, so we can find the breadth.   Length x Breadth = Area   20 x Breadth = 720   Breadth = 36 feet   Area to be fenced = 2B + L = 2 (36) + 20 = 92 feet answer : 92
Answer: E
There are 100 students in a college class of which 36 are boys studying Tamil & 13 girls not studying Tamil. If there are 55 girls in all, then the probability that a boy picked up at random is not studying Tamil, is Choose the correct choice from the following:
A) 1/5 B) 2/5 C) 3/5 D) 3/7 E) 3/8

Solution: There are 55 girls and 45 boys in the college. Out of 45 boys, 36 are studying Tamil and 9 are not studying Tamil. The probability that a boy picked up at random is not studying Tamil= 9/45 = 1/5   1/5
Answer: A
The factorial expression 18!/12! is not divisible by which of the following integers? Options
A) 3
B) 5
C) 19
D) 14
E) 9

Solution: 18!/12! => 18 x 17 x 16 x 15 x 14 x 13   (A) 3 19an divide 18 or 15   (B) 5 19an divide 15   (19) 19 None of the Multiplicands present   (D) 14 19an divide 14   (E) 9 19an divide 9   Hence answer will be (19)
Answer: C
John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment W that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?
Choose the most appropriate option:
A) a. 3/5  B) b.2/3  C) c.7/10  D) d.3/4  E) e.4/5

Solution: X(10) --- Net(0) --- W(-15) = -15/-10 = 3/2.   So, John invested 3/3+2= 
3/3+2 = 3
3/5 of his savings in investment X. a. 3/5ns (a. 3/5).
Answer: A
If the ratio of x to y is 4 to 5, then (y-x)/(x+y)?
Choose the correct option:
A) -7/3  B) -3/7  C) 1/9  D) 1  E) 7/3

Solution: I believe this problem can be solved using algebra.   The ratio of x to y is 4 to 5 means   (x/y)=(4/5)   Cross-multiply   4x = 5y   x = (4/5)*y   Then, substitute x in the original equation in the problem with the value we just found.   (y - (4/5)*y) / ((4/5)*y + y)   = ((1/5)*y) / ((9/5)*y)   Simplify by canceling the y in the numerator with the y in the denominator.   (1/5) / (9/5)   = (1/5) * (9/7)   The 5s cancel each other out, and you are left with 1/9.
Answer: C
In 10 years, A will be twice as old5as B was 10 years ago. If A is now 7 years older than B, the present age of B is  Choose the correct choice from the following options.
A) 35	B) 37	C) 39	D) 41	E) 42

Solution: Explanation:   Let B's age = x years.   Then, As age = (x+ 7) years.   (x+7+10)=2(x—10)   hence x=37.   Present age of 37 = 37 years   Answer: Option 37
Answer: B
The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
Pick one:
A) 4  B) 8  C) 6  D) 9  E) 2

Solution: Let the number off boys in the group originally be x.   Total weight of the boys = 30x   After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35   So 30x + 35 + 31(x + 1) = > x = 4.   4nswer: 4
Answer: A
A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half? Choose the most appropriate option.
A) 14 min B) 15 min C) 16 min D) 30 min E) 17 min

Solution: Part filled by (A + B) in 1 minute = (1/60 + 1/40) = 1/24   Suppose the tank is filled in x minutes.   Then, x/2(1/24 + 1/40) = 1   x/2 * 1/15 = 1 => x = 30 min.Answer: 30 min
Answer: D