MU-NLPC/Calc-aqua_rat huggingface dataset:
A box contains 2 red chips and 2 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?  Choose the correct choice from the following answers:  A) 1/2  B) 4/3  C) 7/12  D) 2/3  E) 7/10

Solution: Total selection ways: 4C2=4!/2!2!=6   Selecting one blue chip out of two: 2C1=2!/1!1!=2   Selecting one red chip out of four: 2C1=2!/1!1!=4   Thus, (2C1*2C1)/4C2=(2*4)/6=8/6=4/3=4/3
Answer: B
What is the probability of getting only 1 head in a single throw of four fair coins?	Options: A) 1/2 B) 3/8 C) 1/4 D) 1/5 E) 5/8

Solution: One possible case is HTTT.   P(HTTT) = 1/2*1/2*1/2*1/2 = 1/16   There are 4C1 = 4 possible cases.   P(1 head) = 4*1/16 = 1/4   The answer is 1/4.
Answer: C
Can you find the missing number in the series below?
1 5 9 2 6 10 3 ? 11 4 8 12 Select.
A) 5 B) 6 C) 3 D) 8 E) 7

Solution: Series given in the problem :   1 5 9 2 6 10 3 ? 11 4 8 12   Let us break the series as :   1 5 9   2 6 10   3 ? 11   4 8 12   Now, read the numbers from left, top to bottom. The missing number is obviously 7.   correct answer is 7)7
Answer: E
The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ? Choose the correct choice from the following answers:
A) 250  B) 280  C) 240  D) 270  E) 230

Solution: Explanation:   Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 15   5x = 1350   x = 270   Smaller number = 270.   Answer 270
Answer: D
in a class of 25 students, 15 play hockey and 16 play basketball. if there are 4 students who play neither sport, determine the number of students who play both hockey and basketball?	Choose the correct option: A) 10 B) 11 C) 13 D) 14 E) 15

Solution: Let the number of who play both be x   Number of students who play sports 25-4= 
25-4 = 21
21   Use Venn diagram   (15-x)+x+(16-x)=21   Which gives x=10   10nswer is 10   10 play both sport
Answer: A
A clock loses a minute every three hours for 4 days and gains 2% in the subsequent 6 days. If it was set right on Friday at 11 AM, what will be the time at the end of 10 days? Select the correct option: A) 01:54:40 PM B) 01:56:24 PM C) 12:46:40 PM D) 11:54:24 AM E) 01:20:48 PM

Solution: Loses 8 minutes each day.   so total loss = 4×8 = 32min   subsequent 6 days = 6×48×60 minutes   1% gain = ( 6×24×60)/100 = 172.8 minutes   so, total gain = 172.8 - 32= 
172.8 - 32 = 140.8
140.8 min= 140 + 0.8 min = 2 Hours 20 minutes + 0.4 × 60 seconds = 2 Hours 20 min + 48 seconds   10 days later the clock should be 2 Hours 20 min + 48 seconds   so time , 01:20:48 pm (Answer 01:20:48 PM)
Answer: E
Which of the following is equal to the average (arithmetic mean) of (x+5)^2 and (x-5)^2?  Choose the correct option
A) x^2 B) x^2+2 C) x^2 +30 D) x^2+20 E) x^2+25

Solution: Avg = [(x+5)^2 + (x-5)^2] / 2   x^2+25xpanding and simplifying, (x^2 + 10x + 25 + x^2 - 10x + 25) / 2 = x^2 + 25   Answer x^2+25.
Answer: E
How many multiples of 9 are there between 1 and 50, exclusive?  Choose the correct choice from the following answers:	A) 5	B) 4	C) 6	D) 7	E) 3

Solution: 5   multiples of 9 between 1 and 50 exclusive.   from 9 * 1 upto 9*5, (1,2,3,4,5). Hence, 5 multiples !   correct option is 5
Answer: A
A certain number of workers can do a work in 85 days. If there were 10 workers more it could be finished in 10 days less. How many workers are there?
Answers
A) 75 B) 30 C) 28 D) 24 E) 32

Solution: number of workers = 10* (85-10)/10= 
10* (85-10)/10 = 75
75   75nswer is 75
Answer: A
If two of the four expressions x + y , x + 4y , x - y , and 4x - y are chosen at random, what is the probability that their product will be of the form of x^2-(by)^2, where b is an integer?	Choose one
A) 1/6	B) 1/8	C) 1/7	D) 1/5	E) 1/4

Solution: Total number of expressions if 2 are multiplied = 4C2 = 4!/2!*2! = 6   now we have to find the expressions that are in form of x^2 - (by)^2   one is (x+y)(x-y) = x^2 - (1y)^2   If you see any other combination we are always going to have one term of xy since 4x and 4y are there, so there can be only one type of combination like this.   therefore, probablity is 1/6   1/6nswer : 1/6
Answer: A
In a Question paper there are 4 multiple choice questions. Each question has 5 choices with only one choice as the correct answer. What is the total number of ways in which a candidate will not get all the four answers correct? Choose the correct choice from the following choices:
A) 19
B) 85
C) 120
D) 624
E) 1024

Solution: A candidate can answer the test in 5*5*5*5=5^4 number of ways (each question has 5 choices and we have total of 4 questions). Now, out of these cases there will be only one case when the candidate answered all the four questions correct. Therefore the total number of ways in which a candidate will NOT get all the four answers correct is 5^4-1=624.   Answer: 624.
Answer: D
A batsman makes a score of 87 runs in the 17th inning and thus increases his avg by 3. Find his average after 17th inning.  Answers:
A) 15
B) 26
C) 41
D) 32
E) 39

Solution: Sol. Let the average after 17th inning = x.   Then, average after 16th inning = (x - 3).   :. 16 (x - 3) + 87 = 17x or x = (87 - 48)= 
(87 - 48) = 39
39.   ANSW39R 39
Answer: E
Rebecca's yearly income is $15,000 and Jimmy's annual income is $18,000. By how much must Rebecca's yearly income increase so that it constitutes 55% of Rebecca and Jimmy's combined income?	Choices:
A) 7000
B) 8000
C) 9000
D) 10000
E) 11000

Solution: total rebecca = x+15000 ; total = x+15000+18000;   x+15000/x+33000 = 55/100 therefore x =7000   7000
Answer: A
You hold some gold in a vault as an investment. Over the past year the price of gold increases by 40%. In order to keep your gold in the vault, you must pay 5% of the total value of the gold per year. What percentage has the value of your holdings changed by over the past year.  Choices
A) 35%
B) 33%
C) 36%
D) 38%
E) 40%

Solution: (100%+40%)*(100%-5%) = 140*0.95= 
140*0.95 = 133
133% an increase of 33%   Your gold holdings have increased in value by 33%.   The Answer is 33%
Answer: B
Determine the ratio of the number of people having characteristic X to the number of people having characteristic Y in a population of 100 subjects from the following table
People having X and Y are 20
People having X but not Y are 10
People having Y but not X are 30
People having neither X nor Y are 40.	Choose the correct answer:
A) 3 : 5  B) 3 : 4  C) 4 : 3  D) 5 : 3  E) 1 : 2

Solution: Number of people having characteristic X = 10 + 20= 
10 + 20 = 30
30   Number of people having characteristic Y= 20 + 30= 
20 + 30 = 50
50   Therefore Required ratio= 30 : 50 = 3 : 5   3 : 5NSWER:3 : 5
Answer: A
A patient was given four pills which he is required to take one after every twenty-five minutes.
How long can the pills run for him?
Select.
A) 1 hour 15 minutes
B) 1 hour 35 minutes
C) 1 hour 30 minutes
D) 1 hour 40 minutes
E) 1 hour 37 minutes

Solution: Explanation:   He took the first pill at the zero minute.   He took the second pill after 25 minutes = 0+25= 
0+25 = 25
25   He took the third pill after 25 minutes= 25+25= 
25+25 = 50
50   He took the fourth pill after 25 minutes= 50+25= 
50+25 = 75
75   Then it will last for 75 minutes or an hour and 15 minutes   1 hour 15 minutesnswer 1 hour 15 minutes
Answer: A
If x:y=7:5, y:z= 8:9, find x:y:z =? Select:
A) 56:40:43
B) 56:40:42
C) 56:40:40
D) 56:40:45
E) 56:40:41

Solution: x:y=7:5   y:z= 8:9   x:y:z =56:40:45   Answer : 56:40:45
Answer: D
A sum of money at simple interest amounts to $ 645 in 3 years and to $690 in 4 years. The sum is:
Select:
A) $153
B) $510
C) $598
D) $549
E) $675

Solution: B   $510   S.I. for 1 year = $(690 - 645)= 
(690 - 645) = 45
$45.   S.I. for 3 years= $(45 x 3) = $135.   Principal = $(645 - 135)= 
(645 - 135) = 510
$510.
Answer: B
Tough and Tricky questions: Combinations.
Eight contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?
Answers:
A) 6 B) 7 C) 12 D) 16 E) 24

Solution: Number of ways First-place medal can be awarded to four contestants = 8   Number of ways Second-place medal can be awarded to contestants after awarding First-place medal =3   Therefore number of possibilities = 8 *3= 
8 *3 = 24
24   Answer:24
Answer: E
Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 4 litres from vessel P is mixed with 6 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
Select the correct option.
A) 31:1	B) 31:4	C) 31:8	D) 31:9	E) 31:2

Solution: Quantity of alcohol in vessel P = 62.5/100 * 4 = 5/2 litres   Quantity of alcohol in vessel Q = 87.5/100 * 6 = 21/4 litres   Quantity of alcohol in the mixture formed = 5/2 + 21/4 = 31/4= 
31/4 = 31/4 = around 7.75
7.75 litres   As 10 litres of mixture is formed, ratio of alcohol and water in the mixture formed= 7.75 : 2.25 = 31:9.   Answer: 31:9
Answer: D
A can finish a work in 24days, B in 9days and C in 2days, B and C start the work but are forced to leave after 3 days. The remaining work was done by A in?  Choose the most appropriate option:  A) 10days  B) 12days  C) 6days  D) 7days  E) 8days

Solution: B+C 1day work = 1/9 + 1/12 +  1= 
+  1 = 1
1/9 + 1/12= 7/36   work done by B and C in 3days = 7/36 * 3 = 7/12   Remaining work = 1 - 7/12 = 5/12   1/24 work is done by 10days in 1day   5/12 work is done by 10days in   24*5/12= 
  24*5/12 = 10
10days   10daysnswer is 10days
Answer: A
The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg. What might be the weight of the new person?	Choose the correct choice from the following answers:  A) 70kg  B) 80kg  C) 85kg  D) 90kg  E) 95kg

Solution: Total weight increased = (8 x 2.5) kg = 20 kg.   Weight of new person = (50 + 20)= 
(50 + 20) = 70
70 kg.   70kg)
Answer: A
When the positive integer x is divided by 9,the remainder is 5.What is the remainder when 5x is divided by 9?  Options:
A) 0  B) 1  C) 3  D) 4  E) 7

Solution: i tried plugging in numbers   x = 9q+5   x = 14   5x 9 +5= 
9 +5 = 14
14   5x= 70   5x/9= 63 + 7   remainder is 7.   Answer is 7.
Answer: E
The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square? Choose the correct choice from the following answers:
A) 80 cm	B) 800 cm	C) 287 cm	D) 718 cm	E) 86 cm

Solution: Area of the square = s * s = 5(125 * 64)   => s = 25 * 8= 
25 * 8 = 200
200 cm   Perimeter of the square= 4 * 200= 
4 * 200 = 800
800 cm.   Answer: 800 cm
Answer: B
If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is Options
A) 48 km	B) 50 km	C) 40 km	D) 22 km	E) 70 km

Solution: B   50 km.   Let the actual distance travelled be x km.   Then x/10=(x+20)/14   --> 14x = 10x + 200   --> 4x = 200   --> x = 50 km.
Answer: B
At exactly what time past 9:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time? Options:	A) 20 13/21 minutes past 7:00	B) 20 13/17 minutes past 9:00	C) 21 3/23 minutes past 7:00	D) 21 9/11 minutes past 7:00	E) 22 4/9 minutes past 7:00

Solution: A1 = hour angle   A2 = minute angle   A1-A2 = 90   Assume the minutes = M   A1 = (9*60+M)/12*60 )*360   A2 = M*360/60   Solving all three equation , results in the answer 20 13/17 minutes past 9:00
Answer: B
One millisecond is 0.001 of a second. The costs for a single run of a computer program are $1.07 for operating-system overhead, $0.027 per millisecond of computer time, and $4.35 for the mounting of a data tape. What is the total of these three costs for 1 run of a program that requires 1.5 seconds of computer time ? Choose the correct answer
A) $57.15  B) $45.92  C) $37.96  D) $31.57  E) $25.92

Solution: Operating system overhead for 1 run = 1.07 $   Mounting of data tape = 4.35$   Cost per 1 millisecond of computer time = .027 $   Total cost of 1 run of a program that requires 1.5 seconds of computer time   = 1.07 + (.027*1500) + 4.35   =1.07 + 40.5 + 4.35= 
1.07 + 40.5 + 4.35 = 45.92
45.92$   Answer $45.92
Answer: B
A man spends Rs. 1900 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income?	Choose the correct choice: A) 2075 B) 2175 C) 2275 D) 2375 E) 2475

Solution: Explanation:   Total expenditure for the first 3 months = 3 Ã— 1900 = 5700   Total expenditure for 4 months = 4 Ã— 1550 = 6200   Total expenditure for 5 months = 5 Ã— 1800 = 9000   Total expenditure and saving (which is income for one year)   = 5700 + 6200 + 9000 + 5200 = Rs. 25200   So, Average monthly income = 26100/12 = Rs. 2175   Answer 2175
Answer: B
If a town of 45,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to?
Choose the correct option
A) a.46000  B) b.47000  C) c.48000  D) d.49000  E) e.50000

Solution: 1% is quite small and hence the answer is a.46000)
Answer: A
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? Choose the most appropriate option
A) 210 B) 1050 C) 25200 D) 21400 E) None of these

Solution: Number of ways of selecting 3 consonants out of 7 and 2 vowels out of 4 = 7C3 x 4C2 = (7x6x5)/(3x2x1) x (4x3)/(2x1) = 210.   Number of groups, each having 3 consonants and 2 vowels = 210.   Each group contains 5 letters.   Number of ways of arranging 5 letters among themselves   = 5! = 5x4x3x2x1 = 120   Therefore the required number of words = 210 x 120 = 25200.   Answer 25200.
Answer: C
P can do a certain work in 18 days. Q is 60% more efficient than P. How many days does Q alone take to do the same job?  Pick
A) 14.25	B) 13.75	C) 12.5	D) 11.25	E) 10.5

Solution: Each day, P can do 1/18 of the work.   Each day, Q can do 1.6/18 of the work = 16/180 of the work   The time taken by B alone to complete the total work is   180/16= 
  180/16 = 45/4 = around 11.25
11.25 days.   The answer is 11.25.
Answer: D
Determine the value of 3*27/31+81/93	Choose one: A) 0 B) 156/31 C) 123/31 D) 151/31 E) none

Solution: Solution:   Both fractions should be reduced before performing arithmetic operations. We get 3*27/31+3.27/3.31=3*27/31+27/31=4*27/31=151/31   Answer 151/31
Answer: D
If it is assumed that 70 percent of those who receive a questionnaire by mail will respond and 300 responses are needed, what is the minimum number of questionnaires that should be mailed?  Options
A) 400  B) 428.5  C) 480  D) 500  E) 600

Solution: Minimum no of mail to be sent for getting 300 responses at 70%   = 300/0.7 = 428.5   Option 428.5
Answer: B
If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 6 kmph, then the speed of the boat in still water is :	Choose the correct choice from the following options
A) 2.5 km/hr  B) 4 km/hr  C) 5 km/hr  D) 10.5 km/hr  E) None of these

Solution: Solution   Speed of stream = 1/2 (16-8) km/hr= 4kmph . Answer 4 km/hr
Answer: B
The ratio of a to b is 4 to 5, where a and b are positive. If x equals a increased by 25 percent of a, and m equals b decreased by 80 percent of b, what is the value of m/x?	Options
A) 1/5 B) 3/4 C) 4/5 D) 5/4 E) 3/2

Solution: a/b = 4/5   m/x = (1/5)*5 / (5/4)*4 = 1/5   The answer is 1/5.
Answer: A
Jim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renee have an equal chance of choosing any one of the hand signs, what is the probability that Jim will win?
Choose the correct choice from the following answers:
A) 5/6  B) 2/3  C) 1/2  D) 5/12  E) 1/3

Solution: There are 3*3= 
3*3 = 9
9 combinations (cases) possible. In 3 cases there will be a tie (rock-rock, scissors/scissors, paper/paper). Now, out of 6 cases left Jim and Renee have equal chances of winning, so in 3 cases Jim will win and in other 3 Renee will win. So the probability Jim winning the game is (favorable outcomes) / (total # of outcomes)= 3/9 = 1/3.   Or: no matter what sign Renee will select Jim can select 1 sign to win, 1 sign to get tie and 1 sign to loose, so the probability Jim winning the game is 1/3.   Answer: 1/3.
Answer: E
Cricket match is conducted in US. The run rate of a cricket game was only 3.2 in first 10 over. What should be the run rate in the remaining 40 overs to reach the target of 262 runs? Pick one.
A) 6 B) 6.25 C) 5.75 D) 7.5 E) 8

Solution: Required run rate = 262 - (3.2 x 10) =	230 = 5.75   40	40   5.75
Answer: C
A first grade teacher uses eight playing cards, each numbered from 1 to 8 to teach her students to order numbers correctly. She has students choose four flash cards randomly, then arrange the cards in ascending order. One day, she removes the cards '2' and '4' from the deck. On that day, how many different correct arrangements of four randomly selected cards are possible?	Choose the correct choice from the following: A) 40 B) 30 C) 15 D) 10 E) 20

Solution: problem of combination 6154 = 6!/4!*(6-4)! = 6*5*4!/4!*2! =15   15
Answer: C
Out of first 30 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is -.  Choose the most appropriate option
A) 1/2  B) 16/19  C) 4/5  D) 24/30  E) 3/5

Solution: n(S) = 30   n(Even no) = 15 = n(E)   n(Prime no) = 10 = n(P)   P(EᴜP) = 15/30 + 10/30 - 1/30 = 24/30   ANSWER:24/30
Answer: D
A computer wholesaler sells six different computers and each is priced differently. If the wholesaler chooses three computers for display at a trade show, what is the probability (all things being equal) that the two most expensive computers will be among the three chosen for display?
Choose the correct choice from the following options:  A) 15/56  B) 3/28  C) 1/28  D) 1/5  E) 1/168

Solution: Since, two of the choices are prefixed, we are free to choose 1 from the rest of the 4 avilable. so 4C1 is the numerator.   Total no of ways we can choose 3 from 6 is 6c3, which is the denominator.   So, the probability: 4c1/6c3= 1/5 ans is 1/5.
Answer: D
Ages of two persons differ by 22 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present age	Choose the correct choice from the following choices.
A) 12,28	B) 14,30	C) 17,39	D) 18,34	E) 19,34

Solution: Explanation:   Let the age of younger person is x,   Then elder person age is (x+22)   => 3(x-6) = (x+22-6) [6 years before]   => 3x-18 = x+16   => x =17.   So other person age is x + 22 = 39   Answer: Option 17,39
Answer: C
A car traveled 65% of the way from Town A to Town B at an average speed of 65 mph.
The car traveled at an average speed of v mph for the remaining part of the trip.
The average speed for the entire trip was 50 mph. What is v in mph?
Choose the correct choice from the following
A) 65  B) 50  C) 45  D) 40  E) 35

Solution: Assume total distance = 100miles   Time taken for 65 miles = 65/65= 
65/65 = 1
1 hour   Time taken for the rest of the 35 miles= 35/v hours.   Average speed = 50   Therefore the total time needed = 2 hours.   2 = 1 + 35/v   Hence v = 35 mph   Correct Option: 35
Answer: E
The prices of tea and coffee per kg were the same in june. In August the price of coffee shot up by 20% and that of tea dropped by 20%. if in August , a mixture containing equal quantities of tea and coffee costs 50/kg. how much did a kg of coffee cost in june ? Choose the correct answer:  A) 45  B) 50  C) 40  D) 35  E) 30

Solution: Let the price of tea and coffee be x per kg in June.   Price of tea in August = 1.2x   Price of coffee in August = 0.8x .   In July the price of 1/2 kg (500gm) of tea and 1/2 kg (500gm) of coffee (equal quantities) = 50   1.2x(1/2) + 0.8x(1/2) = 50   => x =50   50
Answer: B
A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is 12, what is the value of x?  Choose the correct choice from the following answers: A) -4 B) -2 C) 2 and 6 D) 4 E) Cannot be determined.

Solution: A number x is multiplied with itself --> X^2   added to the product of 4 and x --> X^2+4X   If the result of these two operations is -4 --> X^2+4X=4   i.e X^2+4X-12=0 is the Quadratic equation which needs to be solved.   (X-2)(X+6) = 0   Hence X=2, X=-6   IMO 2 and 6
Answer: C
The average temperature of the town in the first four days of a month was 57 degrees. The average for the second, third, fourth and fifth days was 60 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day ?
Choose the correct choice from the following choices.
A) 62 degrees
B) 64 degrees
C) 65 degrees
D) 66 degrees
E) 96 degrees

Solution: Explanation:   Sum of temperatures on 1st, 2nd, 3rd and 4th days = (57 * 4)= 
(57 * 4) = 228
228 degrees ... (1)   Sum of temperatures on 2nd, 3rd, 4th and 5th days - (60 * 4)= 240 degrees ....(2)   Subtracting (1) From (2), we get :   Temp, on 5th day - Temp on 1st day = 12 degrees.   Let the temperatures on 1st and 5th days be 7x and 8x degrees respectively.   Then, 8x - 7x = 12 or x = 12. Answer: 96 degrees   Temperature on the 5th day = 8x = 96 degrees.
Answer: E
Tom purchased 8kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? Pick one.
A) 1040	B) 1045	C) 1055	D) 1060	E) 1075

Solution: Cost of 8 kg apples= 70 × 8 = 560.   Cost of 9 kg of mangoes = 55 × 9 = 490.   Total cost he has to pay = 560 + 490 = 1055.   c)
Answer: C
P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 10 days. How many days more will P take to finish the work?  Select:
A) 10  B) 15  C) 18  D) 22  E) 25

Solution: Explanation :   Let work done by P in 1 day = p,   Work done by Q in 1 day = q,   Work done by R in 1 day = r   p + q = 1/30   q + r = 1/24   r + p = 1/20   Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8   => p + q + r = 1/16   => Work done by P,Q and R in 1 day = 1/16   Work done by P, Q and R in 10 days = 10 × (1/16) = 10/16 = 5/8   Remaining work = 1 = 5/8 = 3/8   Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day   = 1/16 – 1/24 = 1/48   Number of days P needs to work to complete the remaining work = (3/8) / (1/48)= 
(3/8) / (1/48) = 18
18   Answer : Option 18
Answer: C
A grocer has a sales of Euro 6435, Euro 6927, Euro 6855, Euro 7230 and Euro 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Euro 6500?
Choose the correct answer:
A) Euro 4991
B) Euro 5991
C) Euro 6001
D) Euro 6991
E) None

Solution: Explanation: Total sale for 5 months = Euro (6435 + 6927 + 6855 + 7230 + 6562)= 
(6435 + 6927 + 6855 + 7230 + 6562) = 34_009
Euro 34009.   Required sale= Euro [ (6500 x 6) - 34009 ]   = Euro (39000 - 34009)= 
(39000 - 34009) = 4_991
Euro 4991.   Euro 4991nswer: Option Euro 4991
Answer: A
The ratio between the sale price and the cost price of an article is 7:4. What is the ratio between the profit and the cost price of that article?	Choose the most appropriate option:
A) 3:4	B) 1:2	C) 2:5	D) 3:5	E) 25

Solution: C.P. = Rs. 4x and S.P. = Rs. 7x.   Then, Gain = Rs. 3x   Required ratio = 3x : 4x = 3:4   3:4
Answer: A
A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?
Choose the correct choice from the following:
A) 2400	B) 2882	C) 2277	D) 2656	E) 2778

Solution: 1200 * 12: x * 9 = 2:3   x = 2400   2400nswer: 2400
Answer: A
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%? Choices.
A) 20%
B) 29%
C) 90%
D) 90%
E) 112%

Solution: SP2 = 2/3 SP1   CP = 100   SP2 = 80   2/3 SP1 = 80   SP1 = 120   100 --- 20 => 20%   20%nswer:20%
Answer: A