MU-NLPC/Calc-aqua_rat huggingface dataset:
If the area of a circle is 36pi square feet, find its circumference.	Choose the correct choice from the following choices.
A) 65 pi feet
B) 43 pi feet
C) 12 pi feet
D) 18 pi feet
E) 64 pi feet

Solution: The area is given by pi * r * r. Hence   pi * r *r = 81 pi   r *r = 36 ; hence r = 36 feet   The circumference is given by   2 *pi *r = 2 * pi * 6 = 128 pi feet   correct answer 12 pi feet
Answer: C
A can do a job in 45 days and B can do it in 30 days. A and B working together will finish four times the amount of work in ------- days?
Choose the correct choice from the following choices.
A) 30days
B) 45 days
C) 80 days
D) 72 1/2 days
E) 72 days

Solution: 1/45+ 1/30 = 5/90 = 1/18   18/1= 
18/1 = 18
18*4= 
18*4 = 72
72 days   Answer:72 days
Answer: E
What is the smallest number by which 2880 must be divided in order to make it into a perfect square ?	Choose the correct choice from the following choices:  A) 3  B) 4  C) 5  D) 6  E) 7

Solution: 880/3=960 is not a perfect square   2880/4= 
2880/4 = 720
720 is not a perfect square   2880/5= 
2880/5 = 576
576 which is perfect square of 24   ANSWER:5
Answer: C
An art gallery has only paintings and sculptures. Currently, 1/3 of the pieces of art are displayed, and 1/6 of the pieces on display are sculptures. If 1/3 of the pieces not on display are paintings, and 1200 sculptures are not on display, how many pieces of art does the gallery have?
Select the correct option:
A) 360 B) 2700 C) 540 D) 640 E) 720

Solution: Too many words and redundant info there.   (i) 1/3 of the pieces of art are displayed, hence2/3 of the pieces of art are NOT displayed.   (ii) 1/6 of the pieces on display are sculptures, hence 5/6 of the pieces on display are paintings.   (iii) 1/3 of the pieces NOT on display are paintings, hence2/3 of the pieces NOT on display are sculptures.   1200 sculptures are not on display, so according to (iii) 2/3*{not on display} = 1200 --> {not on display} = 1800.   According to (i) 2/3*{total} = 1800 --> {total} = 2700.   Answer: 2700.
Answer: B
What will come in place of the x in the following Number series? 279936, 46656, 7776, 1296, 216, x  Select the correct option.
A) 2	B) 3	C) 5	D) 6	E) 8

Solution: Go on dividing by 6 to the next number   5)
Answer: C
In a group of 90 students, 36 are taking History, and 32 are taking Statistics. If 57 students are taking History or Statistics or both, then how many students are taking History but not Statistics?	Choose the correct answer
A) 9  B) 19  C) 25  D) 27  E) 31

Solution: Number of students taking history =H=36   Number of students taking statistics =S= 32   Total number of students =T= 90   Number of students taking History or Statistics or both =B= 57   Number of students taking neither history nor statistics =N= 90-57= 
90-57 = 33
33   LetXbe the number of students taking both history and statistics.   Then   T= H + S + N - X   or 90 = 36 + 32 +33 - X   or X = 11   Now,   Number of students taking only history will be   H-X   or  36-11= 
 36-11 = 25
25   Answer:- 25
Answer: C
A and B began business with Rs.7000 and Rs.15000 after 6 months, A advances Rs.3000 and B withdraws Rs.5000. At the end of the year, their profits amounted to Rs.2940 find the share of A and B respectively.	Select the correct option:
A) 1100, 1750	B) 1140, 1800	C) 940, 2000	D) 1190, 1750	E) 1000: 1690

Solution: 7*6 + 10*6):(15*6 + 10*6) =102 : 150 = 51 : 75 = 17 : 25   17 : 25   A's Share = 17/42 * 2940= 
17/42 * 2940 = 1_190
1190.   B's Share= 25/42 * 2940= 
25/42 * 2940 = 1_750
1750.   A and B shares respectively 1190 and 1750 . Answer: 1190, 1750
Answer: D
All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 150 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A?  Choose the most appropriate option.
A) 1200 B) 1723 C) 1129 D) 2613 E) 1372

Solution: A   B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k.   Quantity of milk in B = 8k - 5k = 3k.   Quantity of milk in container C 8  - 5= 
8  - 5 = 3
3k.   Quantity of milk in container C= 8k - 3k = 5k   Container: A B C   Quantity of milk: 8k 3k 5k   It is given that if 150 liters was transferred from container C to container B, then both the containers would have equal quantities of milk.   5k - 1508  - 3= 
8  - 3 = 5
5k   Container: A B C   Quantity of milk: 8k 3k 5k   It is given that if 150 liters was transferred from container C to container B, then both the containers would have equal quantities of milk.   5k - 150= 3k + 150 => 2k = 300 => k = 150   The initial quantity of milk in 1200 = 8k = 8 * 150= 
8 * 150 = 1_200
1200 liters.
Answer: A
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 80 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?	Pick:
A) 20	B) 34	C) 58	D) 40	E) 46

Solution: Nice question +1   We have that X/24 - (60-X)/2R = 40   Also X/R - (60-X)/2R = 120   So we get that 2x - 60 = 80R   3x - 60 = 240R   Get rid of R   120 = 3x   x = 58   Hence answer is 58
Answer: C
If 15 students in a class average 75% on an exam and 10 students average 90% on the same exam, what is the average in percent for all 25 students? Choose the correct answer.
A) 80%  B) 81%  C) 82%  D) 83%  E) 84%

Solution: (15*75 + 10*90) / 25= 
(15*75 + 10*90) / 25 = 81
81%   The answer is 81%.
Answer: B
The bus that travels from St. Louis to Chicago and back comes to St. Louis every 2 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 3 hours. If at 12:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?  Choose one
A) 16:00.
B) 18:00.
C) 20:00.
D) 22:00.
E) 24:00.

Solution: Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 2 hours   Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 3 hours   Time taken by both buses to meet again in St. Louis will be LCM of 2 and 3 = 6   If the buses start at 12:00 o'clock from St. Louis , they will meet again in St. Louis at 18:00 hours   Answer 18:00.
Answer: B
If a is Negative integers and b is positive integers and a ≠ 0 which of the following equal 0 ?
Choose the correct choice from the following options
A) a-b B) a^2+b^2 C) a*b D) a/b E) a^2-b^2

Solution: All options Except E gives Non-zero answer.   a should be negative integers and b should be an positive integers.   (E)a^2-b^2   If b=0,a^2-b^2=a^2.   a is negative integers. Any square of the negative integers gives us a positive numbers.   So The option a^2-b^2 is answer
Answer: E
The sum of three consecutive even numbers is 63, Find the last one ?
Choose the correct choice
A) 26  B) 24  C) 21  D) 23  E) 19

Solution: Let the first number be n   Let the second number be n + 2   Let the third number be n + 4   n + n + 2 + n + 4 = 63   Combine like terms:   3n + 6 = 63   3n = 63 - 6   3n = 57   n = 19   n + 2 = 21   n + 4 = 23   The last number is 23   Answer: 23
Answer: D
If difference between compound interest and simple interest on a sum at 5% P.a. for 2 years is Rs.60, then what is the sum?	Choose the most appropriate option.
A) Rs.8000 B) Rs.4000 C) Rs.5000 D) Rs.6000 E) Rs.24000

Solution: C.I-S.I=60   SI=(x*2*5)/100=x/10   CI={x*(1+5/100)^2-x} = 41x/400   CI-SI= 41x/400 - x/10 =60   x=24000   ANSWRs.24000R:Rs.24000
Answer: E
In how many no. between 10 and 20 exactly Two of the digits is 1? Choose the correct choice from the following choices.
A) 25
B) 35
C) 10
D) 1
E) 15

Solution: It's simple can be solved by elimination of answer choices.   Option A and B are too large, not possible. Even CE are large to have correct choice.   Ans : 1
Answer: D
The sum of the two numbers is 11 and their product is 24. What is the sum of the reciprocals of these numbers ? Pick:  A) 11/24  B) 11/25  C) 13  D) 13/15  E) None

Solution: Let the numbers be   x   x and   y   y Then   x   +   y   =   11   x   y   =   24   x+y=11xy=24   Hence,   x   +   y   x   y   =   11   24   x+yxy=1124   ⇒   1   y   +   1   x   =   11   24   11/24nswer is 11/24
Answer: A
A car covers a distance of 1932 km in 7 hours. Find its speed? Choose one
A) 104 B) 288 C) 271 D) 276 E) 128

Solution: 1932/7= 
1932/7 = 276
276 kmph   Answer: 276
Answer: D
If point A coordinates are (-4, -3) point B coordinates are (8 ,4 ) if C is along the line A-B so that AC = 1/2 CB. What are the coordinates of point C. Choose the correct choice from the following answers.
A) (-2, - 2/3) B) (2, -2/3) C) (2/3, -2) D) (0, 2) E) (2, 2/3)

Solution: Look at the diagram below:   Line segment.pngSince, AC= 1/2 CB, then AC = 1/3 AB. This implies that point C is closer to A than to B, which on the other hand implies that the x-coordinate of C must be less than (-4+8)/2=0.5. Only D and A fits, but as (0 , 2) is clearly not on line segment AB, then the answer must be A.   (-2, - 2/3)nswer: (-2, - 2/3).
Answer: A
Kim purchased n items from a catalog for $8 each. Postage and handling charges consisted of $4 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?	Select:
A) 8n + 2	B) 8n + 4	C) 9n + 2	D) 9n + 3	E) 9n + 4

Solution: its C   n items for $8 each   total price $8n   postage and handling of $3 for 1st item and $1 for the rest   total postage and handling = $ [4+ (n-1)]   = $ n+3   total cost   8n+n+3 = 9n+3   9n + 3
Answer: D
Mr. Hanson has a pool of money from which to give out Christmas bonuses to his 5 employees. He wants all his employees to have identical bonuses, but when he divides them out, he finds he has 2 dollars left over, as the payroll system will only accept whole dollar amounts. The next Christmas, Mr. Hanson discovers the pool for the bonuses is 3 times the size. This time, how much money will be left over?	Choose the correct option:
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: Set x = to amount of money for bonuses, and y to be the amount of each individual bonus.   x = 5*y +2.   3x = 15*y+6   3x = 3*5*y + 6   3x = 5(3(y+1))+1   Remainder is then 1, so option 1.
Answer: B
In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability E at least one of the shirts he draws will be blue?  Choose the correct choice from the following answers.
A) 25/153	B) 28/153	C) 5/17	D) E=4/9	E) E=12/17

Solution: P(at least one blue) = 1 - P(0 blue) = 1 - 10/18*9/17 = 12/17.   Answer: E=12/17.
Answer: E
Katie has 9 employees that she must assign to 3 different projects. If 3 employees are assigned to each project and no one is assigned to multiple projects, how many different combinations L of project assignments are possible?  Options:
A) 252 B) 1,680 C) 2,340 D) 362,880 E) 592,704

Solution: The ways to select three employees out of 9 for first project = 9C3   The ways to select three employees out of Remaining 6 for Second project = 6C3   Third Project already has the group of three to be assigned to it so need to select that   So total ways to assign 3 employees to each of 3 projects L= 9C3 * 6C3 * 1 = 1,680   Answer: Option 1,680
Answer: B
A lady grows cabbage in her garden that is in the shape of a square. Each cabbage takes 1 square foot of area in her garden. This year, she has increased her output by 127 cabbages when compared to last year. The shape of the area used for growing the cabbage has remained a square in both these years. How many cabbages did she produce this year?  Choices.
A) 4096	B) 4098	C) 5000	D) 5096	E) Cannot be determined

Solution: Explanatory Answer   The shape of the area used for growing Cabbage has remained a square in both the years.   Let the side of the square area used for growing Cabbage this year be X ft.   Therefore, the area of the ground used for cultivation this year = X2 sq.ft.   Let the side of the square area used for growing Cabbage last year be Y ft.   Therefore, the area of the ground used for cultivation last year = Y2 sq.ft.   As the number of cabbage grown has increased by 127, the area would have increased by 127 sq ft because each cabbage takes 1 sq ft space.   Hence, X2 - Y2 = 127   (X + Y)(X - Y) = 127.   127 is a prime number and hence it will have only two factors. i.e., 127 and 1.   Therefore, 127 can be expressed as product of 2 numbers in only way = 127 * 1   i.e., (X + Y)(X - Y) = 127* 1   So, (X + Y) should be 127 and (X - Y) should be 1.   Solving the two equations we get X = 64 and Y = 63.   Therefore, number of cabbage produced this year = X2 = 642 = 4096.   Alternative Approach : Use answer choices   The area in both the years are squares of two numbers.   That rules out choice B,C and D. as 4098,5000 and 5096 are not the square of any number.   Check Choice A: If this year's produce is 4096, last year's produce would have been  4096 - 127= 
 4096 - 127 = 3_969
3969   3969 is the square of 63.   So, 4096 is the answer.   Choice 4096
Answer: A
The total age of A and B is 13 years more than the total age of B and C. C is how many years younger than A.? Options:
A) 16
B) 12
C) 15
D) 20
E) 13

Solution: (A+B)-(B-C)=13   A-C=13   Answer is 13
Answer: E
Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is? Choose the correct answer
A) 1/2
B) 1/7
C) 1/8
D) 1/1
E) 1/3

Solution: A leap year has 52 weeks and two days   Total number of cases = 7   Number of favourable cases = 1   i.e., {Saturday, Sunday}   Required Probability = 1/7   Answer:1/7
Answer: B
What is the probability that when a hand of 5 cards is drawn from a well shuffled deck of 52 cards,
it contains all Queens?  Choose the correct choice:
A) 192/379017	B) 192/379015	C) 379015/192	D) 1/379015	E) 2/379015

Solution: nCr = n!/(n-r)!r!   Total number of possible hands = 52C5   52C5 = 2274090   Number of hands with 4 Queens = 4C4 × 48C1   4C4 = 24   48C1 = 48   (other 1 card must be chosen from the rest 48 cards)   Hence P (a hand will have 4 Queens) = (4C4 × 48C1)/52C5 = 192/379015.   192/379015
Answer: B
Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?  Choose the correct choice from the following answers:
A) 10
B) 16
C) 15
D) 15
E) 12

Solution: Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.   x + y = 7 --- (1) ; 2x = 4 --- (2)   solving both the equations, we get y = 5   So, time taken to cover both ways by cycle = 2y hours = 10 hours.   10nswer: 10
Answer: A
For the past n days, the average (arithmetic mean) daily production at a company was 60 units. If today's production of 90 units raises the average to 65 units per day, what is the value of n ? Choose the correct choice from the following answers:
A) 30  B) 18  C) 10  D) 9  E) 5

Solution: (average production for n days) * n = (total production for n days) --> 60n=(total production for n days);   (total production for n days) + 90 = (average production for n+1 days) * (n+1) --> 60n + 90 = 65 * (n+1) --> n=5.   Or as 30 extra units increased the average for n+1 days by 5 units per day then 30/(n+1)=5 --> n=5.   Answer: 5.
Answer: E
Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 15 miles behind the slower one. How far apart are the two trains at 5 o'clock? Answers
A) 60 miles B) 80 miles C) 75 miles D) 120 miles E) 400 miles

Solution: Answer = C. 75 miles   Relational speed = 130 - 100= 
130 - 100 = 30
30 miles per hour   In 3 hours, difference= 30 * 3= 
30 * 3 = 90
90 miles   Fast train trailing 15 miles, so effective difference= 90 - 15= 
90 - 15 = 75
75 miles
Answer: C
Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.	Choose the correct choice from the following answers:
A) 873
B) 838
C) 960
D) 838
E) 939

Solution: Explanation:   60(x + 1) = 64x   X = 15   60 * 16= 
60 * 16 = 960
960 km   Answer: Option 960
Answer: C
The average earning of amechanic for the first 4days of a week is Rs.18 and for the last four days is Rs.22. If heearns Rs.20 on the fourth day, his average earning forthe whole week is? Choose the correct choice from the following answers
A) Rs. 10
B) Rs. 20
C) Rs. 30
D) Rs. 40
E) Rs. 50

Solution: Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day   = 4 x18 + 4 x 22 -20   = Rs. 140   ∴ Average earning = 140 / 7   = Rs. 20   Rs. 20
Answer: B
By selling 50 meters of cloth. I gain the selling price of 20 meters. Find the gain percent? Choose the correct choice from the following choices:
A) 42 7/7%  B) 42 5/8%  C) 42 6/4%  D) 42 6/8%  E) 66 2/3%

Solution: SP = CP + g   50 SP = 50 CP + 20 SP   30 SP = 50 CP   30 --- 20 CP gain   100 --- ? => 66 2/3%   Answer: 66 2/3%
Answer: E
A Sum of Rs.2600, is lent out in 2 parts SI at 10% for 5yrs is equal to SI on 2nd part at 9% rate for 6 yrs. find the ratio of parts.	Pick:
A) 23:21
B) 27:25
C) 25:27
D) 23:29
E) 21:19

Solution: Solution :   Given SI1 = SI 2   P1 : P2 = 1/R1T1 : 1/R2T2   = 1/(10*5) : 1/(9:6)   27:25   27:25
Answer: B
In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
Pick.
A) 347	B) 190	C) 388	D) 277	E) 281

Solution: Time taken by B run 1000 meters = (1000 * 10)/50= 
(1000 * 10)/50 = 200
200 sec.   Time taken by A= 200 - 10= 
200 - 10 = 190
190 sec.   Answer: 190
Answer: B
In a park there are two ponds with both brown ducks and green ducks. In the smaller pond there are 20 ducks and in the larger pond there are 80 ducks. If 20% of the ducks in the smaller pond are green and 15% of the ducks in the larger pond are green, then what percentage of ducks are green?  Choose one
A) 13%
B) 14%
C) 15%
D) 16%
E) 17%

Solution: Number of ducks in small pond = 20   green ducks in small pond = 20 % of 20 = 4 ducks   Number of ducks in large pond = 80   green ducks in large pond = 15 % of 80 = 12 ducks   Total number of ducks = 20 + 80= 
20 + 80 = 100
100   total number of green ducks= 4 + 12= 
4 + 12 = 16
16 ducks   percentage of green ducks= 16/100 * 100= 
16/100 * 100 = 16
16%   Answer: 16%
Answer: D
At a party, everyone shook hands with everybody else. There were 66 handshakes.
How many people were at the party?  Choices.
A) 15	B) 18	C) 11	D) 12	E) 19

Solution: D   12   If there are n people,   the first person will shake hand with n-1 persons,   the second with n-2,   the third with n-3,   and   the (n-1)th person with n-(n-1)=1 person means the last person.   Hence, total handshakes are (n-1)+(n-2)+(n-3)+….+3+2+1   Which can be equated using n(n-1)/2 -( -1)= 
 -( -1) = 1
1 person means the last person.   Hence, total handshakes are (n-1)+(n-2)+(n-3)+….+3+2+1   Which can be equated using n(n-1)/2=66   Hence, n=12
Answer: D
Find the area of the square, one of whose diagonals is 5.9 m long ?
Options:
A) 37.14m^2
B) 17.4m^2
C) 8.96m^2
D) 7.8m^2
E) 27.14m^2

Solution: Area of the square= 1/2(diagonal)^2   =(1/2*5.9*5.9)m^2   = 17.4 m^2   Answer (17.4m^2)
Answer: B
During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 40 miles per hour for the entire trip? Choose the correct answer
A) 8.5%
B) 50%
C) 200/x%
D) 60/x%
E) 500/x%

Solution: Say x = 5 miles (so no remainder of the trip).   Time to cover x = 5 miles at 30 miles per hour = (time) = (distance)/(rate) = 5/30 = 1/6 hours = 10 minutes.   Time to cover x = 5 miles at 60 miles per hour = (time) = (distance)/(rate) = 5/60 = 1/12 hours = 5 minutes.   (Or simply, half rate will result in doubling the time.)   So, we can see that the time to cover x = 5 miles at 30 miles per hour (10 minutes) is 100% greater than the time to cover x = 2 miles at 40 miles per hour (5 minutes).   Now, plug x = 2 miles into the answer choices to see which one yields 100%. Only answer E works.   Answer: 200/x%.
Answer: C
ACME’s manufacturing costs for sets of horseshoes include a $22,450 initial outlay, and $30per set. They can sell the sets $70. If profit is revenue from sales minus manufacturing costs, and the company producessells 1000 sets of horseshoes, what was their profit?  Answers
A) $16550
B) $18550
C) $17000
D) $20550
E) $17550

Solution: Total Manufacturing cost = 22,450+1000*30 = 52450   Total Selling cost = 1000*70= 
1000*70 = 70_000
70000   Profit= 70000-52450= 
70000-52450 = 17_550
17550   Answer : $17550
Answer: E
The price of a commodity was raised by 25%. So what is % amount of commodity would be reduced by family so that the amount spent on the commodity remains same  Options
A) 10%	B) 20%	C) 30%	D) 40%	E) 50%

Solution: say price of commodity is 100   after raising price by 25% new price=125   to make it 100 again,   25=125*x/100, x% has to be reduced ie:20%   ANSWER:20%
Answer: B
An investor bought 200 shares of stock in ABCD company in 1990. By 1992, the investment was worth only 2/3 of its original value. By 1995, the 200 shares were worth only 1/4 of their value in 1990. By what percent did the value of the investment drop from 1992 to 1995?	Choose the correct option
A) 62.5%  B) 25%  C) 33 1/3%  D) 50%  E) 66 2/3%

Solution: Let price of each share in 1990 = X.   Total cost in 1990 = 200X   Now Price in 1992 = 2/3 * 200X = 400/3 * X   Now price in 1995 = 1/4 *200= 
1/4 *200 = 50
50X   %Change in 1995 from 1992= [(400/3* X -50X) / (400/3 *X) ] *100 = 62.5%   62.5%nswer 62.5%
Answer: A
A train 300 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?	Choose the correct choice:
A) 5 sec	B) 9 sec	C) 12 sec	D) 18 sec	E) 19 sec

Solution: Speed of the train relative to man = (68 - 8) kmph   = (60* 5/18) m/sec = (50/3)m/sec   Time taken by the train to cross the man   = Time taken by It to cover 300 m at 50/3 m / sec = 300 *3/ 50= 
300 *3/ 50 = 18
18 sec   Answer : 18 sec.
Answer: D
A trader has 1600 kg of sugar. He sells a part at 8% profit and the rest at 12% profit. If he gains 11% on the whole , find the quantity sold at 12%?
Choose the correct choice from the following answers:
A) 1000
B) 1200
C) 1400
D) 1450
E) 1500

Solution: 1200y rule of alligation,   % Profit by selling part1	% Profit by selling part2   8	12   Net % Profit   11   12 - 11= 
12 - 11 = 1
1	11 - 8= 3   => Quantity of part1 : Quantity of part2 = 1 : 3   Given that total quantity = 1600 kg   Hence, quantity of part2 (quantity sold at 12% profit)   =   1600   ×   3   4   =1200   1200)
Answer: B
The price of the jewel, passing through three hands, rises on the whole by 65%. If the first and the second sellers 20% and 25% profit respectively find the percentage profit earned by the third seller.	Choose the correct choice from the following answers:
A) 20  B) 10  C) 15  D) 25  E) 30

Solution: Let the original price of the jewel be $ p and let the profit earned by the third seller be x% Then, (100+x)% of 125% of 120% of P =165% Of P ((100+X)/100*125/100*120/100*P)=(165/100*P)   ==> (100+X)=(165*100*100)/(125*120)= 
(165*100*100)/(125*120) = 110
110=>X=10%   Answer 10) 10
Answer: B