MU-NLPC/Calc-aqua_rat huggingface dataset:
In how many ways can 5 boys be allotted four different study tables such that none of the study tables are empty and all the 5 boys are accommodated? Choose the correct choice:	A) 290	B) 280	C) 260	D) 240	E) 300

Solution: 4 boys can be selected from 5 boys in 5C4 ways = 5   4 boys can be arranged in 4 rooms in 4! ways   and since 1 boy has to share a room with one of the 4 boys, therefore total ways = 2! = 2   Hence total number of ways in which allocation can be done = 5C4 * 4! * 2! = 5*2*4! =240   240
Answer: D
The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square. Choose one:
A) 200 sq cm
B) 72 sq cm
C) 162 sq cm
D) Cannot be determined
E) None of these

Solution: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.   4a = 2(l + b)   2a = l + b   l . b = 480   We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .   Area of the square cannot be found.   ANSWER:Cannot be determined
Answer: D
What sum of money will produce Rs.90 as simple interest in 4 years at 4 1/2 percent?	Select the correct option:
A) Rs.550 B) Rs.650 C) Rs.600 D) Rs.500 E) Rs.700

Solution: Explanation:   90 = (P*4*9/2)/100   90 = 36P/100   P = 500   Answer: Option Rs.500
Answer: D
The mean of 50 observations was 36. It was found later that an observation 45 was wrongly taken as 23. The corrected new mean is?  Choose the correct choice from the following choices.
A) 36.7
B) 36.4
C) 36.5
D) 36.9
E) 36.3

Solution: Correct sum   = (36 * 50 + 45 - 23)= 
(36 * 50 + 45 - 23) = 1_822
1822.   Correct mean= 1822/50   = 36.4   Answer:36.4
Answer: B
Three friends Ravi, Baskar and Chandran divide $1200 amongs them in such a way that if $10, $20 and $15 are removed from the sums that Ravi, Baskar and Chandran received respectively, then the share of the sums that they got will be in the ratio of 10 : 12 : 13. How much did Chandran receive?
Choices.
A) $444 B) $445 C) $446 D) $447 E) $448

Solution: $444+B+C = 1200   Given ratio 10:12:13   Let us say the shares of $444,B,C deducting 10,20,15 be a,b,c   a+b+c = 1200-45= 
1200-45 = 1_155
1155= 35K   c share = (1155X13)/35 = 429   C = chandran share = 429+15= 
429+15 = 444
444   Option $444
Answer: A
At a conference, the only events scheduled for the day are seminars and breaks. All seminars are the same length and are 10 times as long as each break. A break must be between two consecutive seminars. If the first seminar begins at 9:00 a.m. and the third one ends at 11:40 a.m., how long D will the conference last if there are a total of 6 seminars that day? Pick:
A) 5 hours and 15 minutes B) 5 hours and 20 minutes C) 5 hours and 25 minutes D) 5 hours and 30 minutes E) 5 hours and 35 minutes

Solution: Shouldnt the answer be 5 hours 20 mins?   5 hours and 20 minutesreak = b   Seminar= 10b   9am to 11:40am= 160mins   3s+b=160   30b+b=160   b=160/31   6 seminar will take   6s+2b   =60b+2b   =62b   60 +2= 
60 +2 = 62
62b=62*160/31= 
62*160/31 = 320
320   D=5 hours 20 mins.5 hours and 20 minutes
Answer: B
Mr.Jones gave 40% of the money he had to his wife. He also gave 20% of the remaining amount to his 3 sons. and half of the amount now left was spent on miscellaneous items and the remaining amount of Rs.12000 was deposited in the bank. How much money did Mr.jones have initially?	Choose the most appropriate option.
A) 40000	B) 45000	C) 50000	D) 62000	E) None of these

Solution: Explanation :   Let the initial amount be x,   Amount given to his wife =(40/100)x=2x/5   Balance = (x-(2x/5)) = 3x/5   Amount given to his wife = (20/100)*(3x/5) = 3x/25   Balance = 3x/5-3x/25 = 12x/25   Amountt spent on miscellaneous items = (1/2)*(12x/25) = 6x/25 which is equal to 12000   Hence,   => 6x/25 = 12000   => x = 50000   Answer : 50000
Answer: C
A manufacturer sells a pair of glasses to a wholesale dealer at a profit of 18%. The wholesaler sells the same to retailer at a profit of 20%. The retailer in turn sells them to a customer for Rs. 30.09, there by earning a profit of 25%. The cost price for the manufacturer is:  Answers:	A) Rs. 15	B) Rs. 16	C) Rs. 17	D) Rs. 18	E) Rs. 19

Solution: Let the cost price for the manufacturer be Rs. x. Then, 125% of 120% of 118% of x = 30.09.   125/100 * 120/100 * 118/100 * x = 3009/100   177/100 x = 3009/100 => x = 17   ANSWER:Rs. 17
Answer: C
A invested $15000 in a business after 6months B invested $18000 in the business. End of the year if they got $16000 as profit. Find B shares?
Choose the correct choice from the following options:
A) $10000
B) $12000
C) $5000
D) $6000
E) $7500

Solution: A:B = 15000*12:18000*6   A:B = 5:3   A's share = 16000*5/8= 
16000*5/8 = 10_000
10000   B's share= 16000*3/8= 
16000*3/8 = 6_000
6000   Answer is $6000
Answer: D
For a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score W for the exam?
Pick
A) 74  B) 76  C) 78  D) 80  E) 82

Solution: A score of 58 was 2 standard deviations below the mean --> 58 = Mean - 2d   A score of 98 was 3 standard deviations above the mean --> 98 = Mean + 3d   Solving above for Mean W= 74.   74nswer: 74.
Answer: A
If x and y are both odd prime numbers and x < y, how many distinct positive integer W factors does 2xy have?
Pick:
A) 3	B) 4	C) 6	D) 8	E) 12

Solution: Since 2xy prime W factors are x^1*y^1*2^1, its total number or factors must be (1+1)(1+1)(1+1)=2^3=8. Thus, I think 8 would be the correct answer.
Answer: D
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?  Choose the correct option.
A) 2/28	B) 2/29	C) 2/21	D) 2/29	E) 2/20

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³2/21₂/¹⁵2/21₂ = (3 * 2)/(15 * 14) = 1/35   Probability that both are yellow = ²2/21₂/¹⁵2/21₂ = (2 * 1)/(15 * 14) = 1/105   Probability that one blue and other is yellow = (³2/21₁ * ²2/21₁)/¹⁵2/21₂ = (2 * 3 * 2)/(15 * 14) = 2/35   Required probability = 1/35 + 1/105 + 2/35   = 3/35 + 1/105 = 1/35(3 + 1/3)   = 10/(3 * 35) = 2/21   Answer: 2/21
Answer: C
There are 7 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?
Select the correct option:
A) 21	B) 30	C) 45	D) 60	E) 90

Solution: 7 players are there.   two players play one game with one another.   so 7C2=7*6/2= 
7*6/2 = 21
21   SO OPTION 21 is correct
Answer: A
In e is a positive integer smaller than 200 and (14e)/60 is an integer, then e has how many different positive prime factors?  Select:
A) 2  B) 3  C) 5  D) 6  E) 8

Solution: 7e/30 tells us that e is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3.   Answer: 3
Answer: B
A merchant marks his goods up in such a way that the profit made on selling 30 articles is equal to the cost price of 20 articles. What is the W % profit made by the merchant?
Choose the correct choice:
A) 66.67 %
B) 50 %
C) 200 %
D) 100 %
E) 33.33 %

Solution: C.P of 1 article= $30(say)   C.P of 20 articles=30*20= 
30*20 = 600
$600   Now, C.P of 20 articles=Profit on 30 articles   Therefore, profit on 1 article=$600/30= 
600/30 = 20
$20   Profit W%=(20/30)*100=66.67%   66.67 %nswer 66.67 %
Answer: A
A man fixed an appointment to meet the manager, Manager asked him to come two days after the day before the day after tomorrow. Today is Friday. When will the manager expect him?  Choose the correct choice from the following options
A) Sunday B) monday C) tuesday D) wednesday E) thursday

Solution: 1 2 3 4 5 6 7   sun mon tue wed thu fri sat   today is friday=6   by question   day after tommorrow i.e.sunday   day before sunday=saturday   now 2 days after saturday i.e.monday   hence answer is monday..   ANSWER:monday
Answer: B
Thirty men take 20 days to complete a job working 9 hours a day.How many hour a day should 40 men work to complete the job?
Select.
A) 8 hrs
B) 7 1/2 hrs
C) 7 hrs
D) 9 hrs
E) 19 hrs

Solution: As it is not given, in how many days 40 men have to complete the job, so considering same days(=20) in which 30 men completes the job.   So If 40 men works for 'x' hours/day for 20 days, then Total men hours=30*20*9 = 40*20*x   x=(30*20*9)/40*20)= 27/4= 6 3/4   ANSW19 hrsR:19 hrs
Answer: E
There are 10 teams in a certain league and each team plays each of the other teams exactly once. What is the total number of games played?	Select the correct option
A) 30 B) 36 C) 42 D) 45 E) 50

Solution: 10C2 = 45   The answer is 45.
Answer: D
A train 160 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?	Choose the correct choice from the following answers
A) 40 sec
B) 50 sec
C) 44 sec
D) 24 sec
E) 60 sec

Solution: Speed = 45 * 5/18 = 25/2 m/sec   Total distance covered = 160 + 140= 
160 + 140 = 300
300 m   Required time= 300 * 2/25= 
300 * 2/25 = 24
24 sec   Answer:24 sec
Answer: D
How many words can be formed by using all letters of the word ‘BEIJING’ ?	Choose the correct choice from the following options:
A) 4050
B) 720
C) 120
D) 5040
E) 770

Solution: Solution   The word BEIJING contains 7 different letters.   Required number of words = 7P7 = 7 ! = (7 x 6 x 5 x 4 x 3 x 2 x 1) = 5040   Answer 5040
Answer: D
Express 60 mps in kmph? Choose the most appropriate option:
A) 200 B) 182 C) 216 D) 127 E) 400

Solution: 60 * 18/5= 
60 * 18/5 = 216
216 kmph   Answer:216
Answer: C
Eight women can do a work in 10 days. Ten men can complete the same work in 6 days. What is the ratio between the capacity of a man and a woman? Choose the correct choice from the following.
A) 1:2	B) 2:1	C) 2:3	D) 4:3	E) None of these

Solution: Explanation:   (8Ã— 10) women can complete the work in 1 day.   âˆ´ 1 woman's 1 day's work = 1/80   (10 Ã— 6) men can complete the work in 1 day.   âˆ´ 1 man's 1 day's work = 1/60   so, required ratio =1/80 : 1/60= 4:3   Answer: 4:3
Answer: D
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is	Choose the correct option.
A) 22
B) 21
C) 28
D) 27
E) 31

Solution: Lot the total number of workers be v Then,   8OOOv = (12000 * 7) + 6000 (v - 7) <=> 2000v = 42000 <=> v = 21.   Answer: 21
Answer: B
Rita is twice as old as Rama. Three years ago, she was three
times as old as Rama. How old is Rita now?  Choices:
A) 11 years
B) 12 years
C) 13 years
D) 14 years
E) 15 years

Solution: If present age of Rita=x & Rama=y, then   x=2y ---(i) &   x-3=3*(y-3) or x-3y=-6 ---(ii)   On solving (i) & (ii), x=12, y=6   ANSWER:12 years
Answer: B
If a and b are positive integers such that a/b = 0.68, which of the following must be a divisor of a? Choose the correct choice from the following options:	A) 12	B) 13	C) 22	D) 25	E) 17

Solution: 1) A and B are positive INTEGERS   2) A/B = 0.68   A = 68   B = 100   68/100= 
68/100 = 17/25 = around 0.68
0.68   These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...   A= 34   B = 50   34/50= 
34/50 = 17/25 = around 0.68
0.68   This can be further reduced to:   A= 17   B = 25   There is no other way to reduce this fraction, so A must be a multiple of 17 and B must be an equivalent multiple of 25. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....   Since A is a multiple of 17, we have to 'factor-down' 17. This gives us only 17, apart from 1. So this integer MUST be a factor of A. You'll find the match in the answer choices.   Answer: 17
Answer: E
If the ratio of the roots of the equation x2+px+q=0 is equal to that of the roots x2+rx+s=0, then:
Pick
A) sq=pr
B) qp=sr
C) sq=p
D) ps=qr
E) none

Solution: x2+px+q=0 for this eqn... roots are R1=-p R2=-q   x2+rx+s=0 for this eqn... roots are R3=-r R4=-s   As per Question, -p/-q=-r/-s   => ps=qr   ANSWER:ps=qr
Answer: D
A sum of money doubles in 12 years. In how many years, it will treble at S.I.	Choose the most appropriate option.
A) 12 years	B) 8 years	C) 6 years	D) 24 years	E) 36 years

Solution: Explanation :   Simple Interest, SI = PRT/100   i.e, SI ∝ T when rate(R) and principal (P) are constants   Let x be the sum of money and which will treble in n years   (Please note that when the money doubles, simple interest is 2x - x = x   and when the money trebles, simple interest is 3x - x = 2x)   (2x-x) ∝ 12   => x ∝ 12 -------------(1)   (3x-x) ∝ n   => 2x ∝ n -------------(2)   From (1) and (2),   x/2x=12/n 1/2=12/n⇒n = 24 years   i.e, in 24 years, the money will treble   Answer : Option 24 years
Answer: D
If the operation ∆ is defined by a ∆ b = (b - a)^2/a^2 for all numbers a and b, and a ≠ 0, then what is the result when we evaluate this expression: (-3) ∆ (3 ∆ −3) ?
Answers:
A) 47/6
B) 49/9
C) 36/25
D) 25/16
E) 16/9

Solution: (-3) ∆ (3 ∆ − 3) =   (-3) ∆ (6^2/3^2) =   (-3) ∆ (4) =   (-7^2) / (-3)^2 = 49/9   The answer is 49/9.
Answer: B
In how many ways, a committee of 5 members can be selected from 9 men and 5 ladies, consisting of 3 men and 2 ladies?	Options
A) 75
B) 552
C) 775
D) 840
E) 912

Solution: (3 men out 9) and (2 ladies out of 5) are to be chosen   Required number of ways = (9C3 * 5C2) = 840   Answer is 840
Answer: D
A certain plant was 11 feet long on the day it was plantedthe length grows by a constant amount everyday(inc. the first day it was planted).
if this plant grew by 70% b/w the 4th day and 10 th day after it was planted ,how many feet per day does the plant grow Choose one.
A) a) 2
B) b) 4.5
C) c) 2.41
D) d) 5.5
E) e) 3

Solution: If the plant is 11 feet tall when it is planted, it will be 11 + k feet tall at the end of the day (where k is the constant length it grows by every day).   Similarly, at the end of the 4th day the plant must be 11 + 4k feet tall and at the end of the 10th day it must be 11 + 10k feet tall.   Therefore 6k = 0.7 (11 + 4k)   => k = 2.41   Therefore the plant grows by 1 feet every day.   Option (c) 2.41)
Answer: C
A person bought 115 glass bowls at a rate of Rs. 18 per bowl. He sold 104 of them at Rs. 20 and the remaining broke. What is the percentage gain for A?
Choose the correct choice from the following options.
A) 40  B) 300/11  C) 243/7  D) 279/11  E) 100/207

Solution: CP=115*18= 
115*18 = 2_070
2070 and SP=104*20= 
104*20 = 2_080
2080   Gain %= 100*(2080-2070)/2070= 100/207   ANSW100/207R:100/207
Answer: E
When 242 is divided by a certain divisor the remainder obtained is 11. When 698 is divided by the same divisor the remainder obtained is 18. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 9. What is the value of the divisor? Select:
A) 11  B) 17  C) 13  D) 20  E) None of these

Solution: let that divisor be x   since remainder is 11 or 18 it means divisor is greater than 18.   now  242-11= 
 242-11 = 231
231=kx (k is an integer and 234 is divisble by x)   similarly  698-18= 
 698-18 = 680
680= lx (l is an integer and 689 is divisible by x)   adding both 698 and 242   = (231+680)+11+18   =x(k+l) + 29   when we divide this number by x then remainder will be equal to remainder of (29 divided by x) = 9 hence x = 29-9= 
29-9 = 20
20   hence 20
Answer: D
9 students bought burgers for $143 dollars. If the bill has to be divided among these students, how much amount should be added to the amound to make it
divided amoung them equally in dollars(in whole number of dollars)	Choose the correct answer:  A) $1  B) $2  C) $3  D) $4  E) $5

Solution: In order to divide the sum in 9 parts, the amount must be divisible by 9   Divisibility rule of 9: The sum of the digits must be divisible by 9   Sum of digits of 143 = 8 and 9 is divisible by 9.   Hence, we need to add 1 to this number for it to be divisible by 9   Correct Option: $1
Answer: A
In what time will a train 125 m long cross an electric pole, it its speed be 130 km/hr? Choose the most appropriate option: A) 3.5 B) 2.7 C) 2.9 D) 2.3 E) 2.1

Solution: Speed = 130 * 5/18 = 36 m/sec   Time taken = 125/36   = 3.5 sec.   3.5nswer: 3.5
Answer: A
Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one? Answers.
A) 22
B) 88
C) 48
D) 99
E) 22

Solution: Relative speed = 45 + 30= 
45 + 30 = 75
75 km/hr.   75 * 5/18= 125/6 m/sec.   Distance covered = 500 + 500= 
500 + 500 = 1_000
1000 m.   Required time= 1000 * 6/125= 
1000 * 6/125 = 48
48 sec   Answer: 48
Answer: C
In the quadrilateral PQRS d=10 cm, h1=4.6 cm and
h2=2.3 cm. Find the area  Choose the correct answer.
A) 21 B) 22 C) 23 D) 34.5 E) 25

Solution: area of quad.=1/2*any diagonal*(sum of 2 perpendiculars which is drawn on that diagona)   so 1/2*10*(4.6+2.3)= 
1/2*10*(4.6+2.3) = 34.5
34.5   ANSWER:34.5
Answer: D
Which of the following numbers is two more than the square of an odd integer?  Choose the most appropriate option
A) 14,173
B) 14,361
C) 15,253
D) 15,737
E) 16,131

Solution: If a square has an odd unit's digit, then its ten's digit must be even.   Only 16,131-2 = 16,129 satisfies this condition.   The answer is 16,131.
Answer: E
Find the odd man out. 6, 13, 18, 25, 30, 37, 40 Choices:
A) 40
B) 30
C) 37
D) 25
E) 15

Solution: Explanation :   The difference between two successive terms from the beginning are 7, 5, 7, 5, 7, 5   Hence, in place of 40, right number is   37 + 5= 
  37 + 5 = 42
42, 40nswer : Option 40
Answer: A
In the infinite sequence 2, 4, 6, 8, 10, . . . , where each term is 2 greater than the previous term, the 72th term is  Choose the correct choice from the following:	A) 144	B) 263	C) 176	D) 344	E) 287

Solution: T(n) = a + (n-1) d   Here d =2, a=2, n=72   Solving we get T(n) =144.   144nswer: 144
Answer: A
A and B go around a circular track of length 600 m on a cycle at speeds of 24 kmph and 60 kmph. After how much time will they meet for the first time at the starting point?  Choose the most appropriate option:
A) 120 sec
B) 176 sec
C) 178 sec
D) 180 sec
E) 189 sec

Solution: Time taken to meet for the first time at the starting point   = LCM { length of the track / speed of A , length of the track / speed of B}   = LCM { 600/ (24 * 5/18) , 600/ (60 * 5 /18) }   =180 sec.   Answer: 180 sec
Answer: D
3 candidates in an election and received 3136, 7636 and 11628 votes respectively. What % of the total votes did the winning candidate got in that election? Choose the correct choice from the following.
A) 45%
B) 49%
C) 52%
D) 59%
E) 61%

Solution: Total number of votes polled = (3136 + 7636 + 11628)= 
(3136 + 7636 + 11628) = 22_400
22400   So, Required percentage= 11628/22400 * 100 = 52%   52%
Answer: C
By selling 22 pens for a rupee a woman loses 10%. How many for a rupee should he sell in order to gain 50%?	Choose the correct choice:
A) 12 B) 14 C) 45 D) 13 E) 65

Solution: 13   90% --- 22   150% --- ?   90/150 * 22 = 13
Answer: D
The edges of three iron cubes are 6cm; 8cm; 10cm respectively. A new cube was made by melting them. Find the edge of the new cube?
Choose the most appropriate option:  A) 8 cm  B) 12 cm  C) 14 cm  D) 10 cm  E) 15 cm

Solution: 63 + 83 + 103 = a3 => a = 12   ANSWER:12 cm
Answer: B
Sheik Abdullah decides to buy 3 new cars for his collection. If he has to choose between nine different cars, what is the number of purchasing possibilities he has?  Choose one.
A) A)304
B) B)404
C) C)504
D) D)604
E) E)704

Solution: Sheik Abdullah decides to buy 3 new cars for his collection. He has to choose between nine different cars   85043= 9*8*7*6/(3*2*1)= 
9*8*7*6/(3*2*1) = 504
504 ANS:504
Answer: C
A string of 25 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.06, what is the probability that the string of light bulbs will fail during the time period T?
Options:
A) 0.06	B) (0.06)^25	C) 1 - (0.06)^25	D) 1 - (0.94)^25	E) (0.94)^25

Solution: The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1.   The opposite event is when none of the 25 light bulbs fails, since the probability of each light bulb not to fail is 1-0.06= 
1-0.06 = 0.94
0.94 the probability that none of the 25 light bulbs fails is 0.94^25.   Hence, the probability that at least one light bulb fails is 1-0.94^25.   Answer: D.   Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 25, then according to your logic the probability that the string of light bulbs will fail would be 100*0.06= 
100*0.06 = 6
6, which is not possible since the probability of an event cannot be more than 1 (100%).
Answer: D
The distance between A&B is 750km. A person is traveling from A to B at 80km/hr started at 10AM and another person is traveling from B to A at 70km/hr and started at same time. Then at what time they meet together.? Pick:
A) A)2PM	B) B)4PM	C) C)3PM	D) D)1PM	E) E)5PM

Solution: Let x hours be they will meet together   distance covered by 1st person+distance covered by 2nd person = 750km   70x+80x = 750   x= 5 hr   They will meet = 10AM +5hr = 3PM   Answer is 3PM
Answer: C
A milk man has 40 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk.If the cost of pure milk is Rs.18 per liter,then the profit of the milkman, when he sells all the mixture at cost price is: Select:  A) 20%  B) 25%  C) 45%  D) 18%  E) None of these

Solution: Explanation:   when the water is freely available and all the water is sold at the price of the milk, then the water gives the profit on the cost of 40 liters of milk.   Therefore, profit percentage = 45 %. Answer: 45%
Answer: C
In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?  Choose one:
A) 65	B) 44	C) 86	D) 29	E) 26

Solution: Let the capacity of the can be T litres.   Quantity of milk in the mixture before adding milk = 4/9 (T - 8)   After adding milk, quantity of milk in the mixture = 6/11 T.   6T/11 - 8 = 4/9(T - 8)   10T = 792 - 352 => T = 44.   Answer: 44
Answer: B
The juice stall at the circus stocked just 2 brands of orange juice tetra packs. Brand A costs $1 per pack and brand B costs $1.5 per pack. Last week , brand A contributed to a% of stall’s revenue and accounted for b% of sales of juice tetra packs. Which of the following expresses a in terms of b?
Pick one:  A) 100b/(150 – b)  B) 200b/(250-b)  C) 200b/(300-b)  D) 250b/(400-b)  E) 300b/(500-b)

Solution: 1. Let the number of units sold be 100. Then n units of A are sold and (100-n) units of B are sold.   Total revenue= Revenue due to A + Revenue due to B   = (No.of units of A sold * Cost/unit of A) + (No.of units of B sold * cost/unit of B)   = b *1 + (100-b) *1.5   = b + (150-1.5b) --- (1)   2. But we know, revenue due to A = a%. of the total revenue --- (2)   3. To express a in terms of b we need to relate (1) and (2)   4. a% = b / ( b + (150-1.5b))   or a= 100b / 150-0.5b = 200b/(300-b)   200b/(300-b)
Answer: C
Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 10% profit?	Pick:  A) 13.86  B) 16.33  C) 16.35  D) 16.3  E) 16.32

Solution: C.P. of 50 kg wheat = (30 * 11.50 + 20 * 14.25) = Rs. 630.   S.P. of 50 kg wheat = 110% of Rs. 630 = 110/100 * 630 = Rs.693   S.P. per kg = 693/50 = Rs. 13.86   13.86nswer: 13.86
Answer: A