MU-NLPC/Calc-aqua_rat huggingface dataset:
A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?  Pick:
A) 621  B) 276  C) 236  D) 600  E) 211

Solution: Explanation:   Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6   And also given that, profit share of B is Rs. 1500   => 5 parts out of 15 parts is Rs. 1500   Now, required difference is 6 - 4= 
6 - 4 = 2
2 parts   Required difference= 2/5 (1500) = Rs. 600   Answer: 600
Answer: D
Gold is 19 times as heavy as water and copper 9 times as heavy as water. The ratio in which these two metals be mixed so that the mixture is 15 times as heavy as water is: Options:
A) 1 : 2  B) 2 : 3  C) 3 : 2  D) 19: 135  E) None of these

Solution: Explanation:   This question can be solved using weighted average formula. If two quantities of weights m, n have concentrations x, y are mixed then, final concentration = mx+ny/m+n   Take 1 unit of gold and x units of copper.   1×19+x×9/1+x=15⇒19+9x=15+15x   ⇒x=2/3   So they are to be mixed in the ratio 1 : x = 1:2/3 or 3 : 2   3 : 2orrect Option: 3 : 2
Answer: C
A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1 ?	Choose the correct choice from the following:
A) 4 months  B) 5 months  C) 6 months  D) 8 months  E) 9 months

Solution: Suppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 3. or x = (85000 * 12) / (42500 * 3)= 
(85000 * 12) / (42500 * 3) = 8
8.   So, B joined for 8 months.ANSWER 8 months
Answer: D
The length of the bridge, which a train 160 metres long and travelling at 45 km/hr can cross in 30 seconds, is: Choose the correct choice from the following
A) 200 m	B) 215 m	C) 245 m	D) 250 m	E) 270 m

Solution: Let the length of the bridge:L   The equation now is L+160/12.5m/s(45km/hr or12.5m/s)=30   Solving, L =215m   ANSWER:215 m
Answer: B
In 1950, John was 4 times as old as Tom. In 1955, Richard was 3 times as old as Tom. In which year was John twice as old as Tom? Answers
A) 1960  B) 1970  C) 1972  D) 1975  E) 1980

Solution: In 1950: Jo = 4 To-------------- eq1   In 1955: Jo +5 = 3(To+5)---------eq2   Thus in 1950, solving eq1 and eq2   Jo = 10 , Jo =40   Now for each year we can calculate:   1960: Jo = 50 , To=20   1965: Jo = 55, To=25   1970: Ri= 60, Ro = 30   Thus Ans:1970
Answer: B
In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of thesportformulation contains 5 ounces of corn syrup, how many ounces of water does it contain?	Choose the correct option:
A) 15
B) 30
C) 45
D) 75
E) 90

Solution: Standard:   Fl: Corn S: Water = 1:12:30   Sport:   Fl: Corn S: Water = 3:12:180   This simplifies to 1:4:60   If the large bottle has a capacity of x ounces, then   4x / 65 = 5.   So, x = 325 / 4 ounces.   Water = (60 / 65) * (325 / 4) = 60 * 3 / 4 = 75 ounces.   Ans 75
Answer: D
Alice has 3 times the number of stamps that Doris does and Jane has 7 stamps more than Doris does. If Alice, Doris, and Jane each increase their number of stamps by 4, which of the following must be true after each person increases her number of stamps?
Alice has more stamps than Jane.
Jane has 3 more stamps than Doris.
The sum of the numbers of stamps that Alice and Doris have is a multiple of 4.	Choose the correct choice from the following choices:  A) None  B) III only  C) I and III only  D) II and III only  E) I, II, and III

Solution: Let Alice, Doris and jane have A, D and J stamps initially.   We know that   A =3D   and   J=d+7   After addition of 4 stamps they'll have A+4, D+4, and J+4 stamps respectively.   Lets analyze each statements:   Alice has more stamps than Jane.   this can be written as   A+4 > J+4   => 3D+4 > D+7+4   =>D >7/3   It may not be true for many values of D.. D could very well be equal to 1,2 etc for which D<7/3. Not correct.   Jane has 3 more stamps than Doris.   this can be written as   J+4 = (D+4)+3   => D+7+4 = D+4+3   Clealy not correct for any value of D.   The sum of the numbers of stamps that Alice and Doris have is a multiple of 4.   (A+4)+(D+4) = 4k, where k is any integer   => 3D+4+D+4 =4k   => 4D+8 = 4K   => 4(D+2) = 4K   or K = D+2 .. clearly possible for any value of D. Hence Correct.   Hence Ans B. Only iii is correct.
Answer: B
What is the thousandths digit in the decimal equivalent of 43/5000?	Choose the correct choice:
A) 0  B) 1  C) 3  D) 5  E) 8

Solution: 43/5000 = 43 /(5*10^3)   = (43/5) *10^-3   =8.6 * 10^-3   =.0086   Thousandths digit = 8   Answer 8
Answer: E
Eesha bought two varities of rice costing 50Rs per kg and 60 Rs per kg and mixed them in some ratio.Then she sold that mixture at 70 Rs per kg making a profit of 20 % What was the ratio of the micxture?	Select the correct option
A) 1 : 9	B) 1 by 5	C) 1 : 7	D) 1 : 3	E) 1 : 1

Solution: Selling price of the mixture = 70 and profit = 20%   Cost price of the mixture = 70×100120=70×5670×100120=70×56   1 by 5y applying alligation rule:   So ratio = 60−1753:1753−5060−1753:1753−50 = 1 : 5   Answer:1 by 5
Answer: B
A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
Choose one.
A) 999  B) 279  C) 120 metre  D) 99  E) 21

Solution: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/ sec = 20 m/sec.   Length of the train = 20 * 6= 
20 * 6 = 120
120 m.   Answer: 120 metre
Answer: C
A certain experimental mathematics program was tried out in 2 classes in each of 34 elementary schools and involved 40 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are  Choose the most appropriate option.
A) 0 and 13	B) 0 and 14	C) 1 and 10	D) 1 and 9	E) 2 and 8

Solution: One may notice that greatest possible values differ in each answer choice in contrast to the least values, which repeat.   To find out the greatest value you should count the total classes (34*2=68), then subtract the total #of teachers since we know from the question that each teacher taught at least one class (68-40=28). Thus we get a number of the available extra-classes for teachers, and all that we need is just to count how many teachers could take 2 more classes, which is  28/2= 
 28/2 = 14
14. So the greatest possible value of the # of teachers who had 3 classes is 14.   Only answer 0 and 14 has this option.
Answer: B
In a pair of fractions, fractions A is twice the fraction B and the product of two fractions is 2/25. What is the value of fraction A?	Choose the correct choice from the following.
A) 1/5	B) 1/25	C) 2/5	D) 3/5	E) Data inadequate

Solution: a=2b   ab=2/25   2b*b=2/25   b^2=1/25   b=1/5   a=2/5   ANSWER:2/5
Answer: C
A boat running downstream covers a distance of 22 km in 4 hours while for covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water?
Options:
A) 5 kmph B) 4 kmph C) 4.75 kmph D) 4.95 kmph E) 4.65 kmph

Solution: Speed 4.95 kmphownstream = 22/4= 
22/4 = 11/2 = around 5.5
5.5 kmph   Speed Upstream= 22/5= 
22/5 = 22/5 = around 4.4
4.4 kmph   Speed of the boat in still water= 5.5+4.4/2=4.95 kmph   Answer : Option 4.95 kmph
Answer: D
What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?  Choose the correct choice from the following answers:
A) 814 tiles	B) 800	C) 100	D) 200	E) 456

Solution: Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.   Area of each tile = (41 x 41) cm2.   Required number of tiles = (1517 x 902)/41 x 41 = 814.   814 tilesnswer:814 tiles
Answer: A
The product X of two prime numbers is between 17 and 55. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then X = Select the correct option.
A) 18	B) 29	C) 37	D) 44	E) 51

Solution: Option B & C can be ruled out as they themselves are prime numbers   18 = 2*9 = 3*6 >> Ignore   44 = 2 * 22 = 4 * 11 >> Ignore   51 = 3*17 >> Answer   Answer 51
Answer: E
In how many different ways can the letter of the word 'BOTTLE ' be arranged in such a way that the vowels occupy the odd positions?
Select the correct option.
A) 63	B) 48	C) 85	D) 52	E) 47

Solution: In the given word there 6 letters in that there are 2 vowels and 4 consonants   no of ways of arranging the vowels=2p2=2   no of ways of arranging the consonants=4p4=24   total number of ways 24*2= 
24*2 = 48
48   Answer(48)
Answer: B
Evaluate (51 + 52 + 53 + ... + 100)
Pick:
A) 3775	B) 3665	C) 3456	D) 3459	E) 3569

Solution: Sn = (1 + 2 + 3 + ... + 50 + 51 + 52 + ... + 100) - (1 + 2 + 3 + ... + 50)   = (50 x 101) - (25 x 51)   = (5050 - 1275)= 
(5050 - 1275) = 3_775
3775.   Option 3775
Answer: A
The sum of two consecutive integers is 31. Find the numbers.	Choose the correct option:	A) 17, 18	B) 7, 8	C) 15, 16	D) 1, 2	E) 8, 9

Solution: n + (n + 1) = 31   2n + 1 = 31   2n = 30   n = 15   Answer: 15, 16
Answer: C
There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is: Options:
A) 20
B) 80
C) 100 students
D) 200
E) 120

Solution: Let the number of students in rooms A and B be x and y respectively.   Then, x - 10 = y + 10   x - y = 20 .... (i)   and x + 20 = 2(y - 20)   x - 2y = -60 .... (ii)   Solving (i) and (ii) we get: x = 100 , y = 80.   The required answer A = 100.   ANSWER:100 students
Answer: C
A number lock on a suitcase has 3 wheels each labelled with 10 digits from 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible?	Choose the correct choice.
A) 720  B) 760  C) 680  D) 780  E) 880

Solution: On first wheel there can be 10 digits. On the second wheel there will be one of the 9 digits and on the third wheel there will be 8 digits. Therefore, the number of numbers is   10 x 9 x 8 = 720   720NSWER:720
Answer: A
The original price of a camera was displayed as a whole dollar amount. After adding sales tax of 8 percent, the final price was also a whole dollar amount. Which of the following could be the final price of the camera?
Answers:	A) $115	B) $101	C) $100	D) $108	E) $109

Solution: Final price = (1+8/100) * Original Price   = 1.08* Original Price   From options given only 108 is divisible by 1.08 as it is stated OP is whole dollar amount.   Hence $108
Answer: D
A candidate who gets 30% of the marks fails by 50 marks. But another candidate who gets 45% marks gets 25 marks more than necessary for passing. Find the number of marks for passing?	Pick one
A) 276 Marks  B) 200 Marks  C) 186 Marks  D) 187 Marks  E) 167 Marks

Solution: 30% ------------ 50   45% ------------ 25   ----------------------   15% ------------- 75   30% -------------- ?     150 + 50= 
  150 + 50 = 200
200 Marks   Answer: 200 Marks
Answer: B
In a barrel of juice there is 30 liters; in a barrel of beer there are 50 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer?
Choose the correct choice: A) 3:2. B) 2:1. C) 3:1. D) 4:3. E) 15:4

Solution: Price of 30 L juice= 3x   1L= 3x/30   Price of 50 L beer= 4x   1L= 4x/50   Ratio of 1 L price = 3x/30/4x/50= 15:4   15:4 is the answer
Answer: E
If four coins are tossed, the probability of getting two heads and two tails is? Choose the correct answer:	A) 3/8	B) 3/9	C) 3/7	D) 3/56	E) 3/1

Solution: Since four coins are tossed, sample space = 24   Getting two heads and two tails can happen in six ways.   n(E) = six ways   p(E) = 6/24 = 3/8   3/8nswer: 3/8
Answer: A
Barbara has 8 shirts and 10 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants? Choices.
A) 41 B) 66 C) 36 D) 70 E) 84

Solution: 8 shirts   9 pants   we can combine 2 shirts with (10-3) pants   2*7= 
2*7 = 14
14   we can combine the other shirts (6) with any pants (9)   7*10= 
7*10 = 70
70   Thus total :70+14= 
70+14 = 84
84	ANS:84
Answer: E
A tour group of 25 people paid a total of $630 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices Pick one.
A) $22
B) $23.94
C) $24
D) $25.20
E) $30

Solution: Soln:-   630/25=x+0.05x   630/25=1.05x   x=(630*100)/(25*105)   =63*10*4/21*5=24   ANSWER:$24
Answer: C
After getting 2 successive discounts, a shirt with a list price of Rs 150 is available at Rs 105. If the second discount is 12.55,find the first discount Choose the correct choice from the following options
A) 38% B) 15% C) 20% D) 12% E) 36%

Solution: Let the first discount be x%   Then,87.5% of (100-x)% of 150= 105   87.5/100*(100-x)/100*450=150=>105=>100-x=(105*100*100)/(150*87.5)= 
(105*100*100)/(150*87.5) = 80
80   x=(100-80)= 
(100-80) = 20
20   first discount= 20%   Ans: 20%
Answer: C
A father can do a certain job in x hours. His son takes twice as long to do the job. Working together, they can do the job in 6 hours. How many hours does the father take to do the job?  Choose the correct choice from the following answers:
A) 9
B) 18
C) 12
D) 20
E) 16

Solution: Explanatory Answers   The father completes the job in x hours.   So, the son will take 2x hours to complete the same job.   In an hour, the father will complete 1/x of the total job.   In an hour, the son will complete 1/2x of the total job.   So, if the father and son work together, in an hour they will complete 1/x + 1/2x of the job.   i.e., in an hour they will complete 3/2x of the job.   The question states that they complete the entire task in 6 hours if they work together.   i.e., they complete 1/6<sup>th</sup> of the task in an hour.   Equating the two information, we get 3/2x = 1/6   Cross multiplying and solving for x we get 2x = 18 or x = 9.   The father takes 9 hours to complete the job.   9nswer 9
Answer: A
A 2-year certificate of deposit is purchased for Q dollars. If the certificate earns interest at a n annual rate of 6 percent compound quarterly, which of the following represents the value, in dollars, of the certificate at the end of 2 years? Choose the correct choice from the following choices: A) k(1.06)^2 B) k(1.06)^8 C) k(1.015)^2 D) Q(1.015)^8 E) k(1.03)^4

Solution: Annual Rate of interest= 6%   Quaterly rate of interest= 6/4= 
6/4 = 3/2 = around 1.5
1.5%   Now, periods of compounding in 2 years= 8 (8 quarters)   Thus Q(1.015)^8   Answer: Q(1.015)^8
Answer: D
Walking 6/5 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school? Answers.
A) 22  B) 99  C) 27  D) 24  E) 20

Solution: Speed Ratio = 1:6/5 = 5:6   Time Ratio = 6:5   1 -------- 6   4 --------- ? 24 m.Answer:24
Answer: D
12 persons can complete the work in 18 days. after working for 6 days, 4 more persons added to complete the work fast. in how many more days they will complete the work?
Pick
A) 10 days B) 9 days C) 8 days D) 7 days E) 6 days

Solution: total work 12*18= 
12*18 = 216
216 units   after 6 days work finished   6*12= 
  6*12 = 72
72 units   remaining work 216-72= 
216-72 = 144
144 units   remaing days=144(12+4)=9 days   ANSWER:9 days
Answer: B
An investor invests in a new fund. The fund averages 20% growth annually for the first three years, but it loses 25% of its value in the fourth year. At the end of four years, the value of the fund is approximately what percent of the original amount?	Choose the correct choice from the following:  A) 135.7%  B) 129.6%  C) 123.5%  D) 117.4%  E) 112.6%

Solution: 0.75*1.2^3 = 1.296   The answer is 129.6%.
Answer: B
A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.78 less, he could have gained 25%. What is the cost price? Choose the most appropriate option
A) s.370	B) s.375	C) s.375	D) s.390	E) s.300

Solution: CP1 = 100 SP1 = 120   CP2 = 80 SP2 = 80 * (125/100)= 
80 * (125/100) = 100
100   20 ----- 100   78 ----- ?=> 390   ANSWER:s.390
Answer: D
If 25% of a number exceeds 8% of it by 11.9, then find the number?	Answers:
A) 76
B) 70
C) 55
D) 65
E) 22

Solution: Use the elimination method to find the correct option.   Of all the options only 70 fits   25% of 70 = 17.5   8% of 70 = 5.6   17.5 - 5.6= 
17.5 - 5.6 = 11.9
11.9   Required number is 70.   ANSWER:70
Answer: B
A CAR MOVES AT THE SPEED OF 80KM/HR. WHAT IS THE SPEED OF THE CAR IN METRES PER SECOND? Choose the correct choice from the following options:  A) 8 m/sec  B) 20 1/9 m/sec  C) 22 2/0 m/sec  D) Cannot be determined  E) None of these

Solution: SPEED = (80*5/18)M/SEC=200/9 M/SEC = 22 2/9 M/SEC.   22 2/0 m/secORRE22 2/0 m/secT OPTION: 22 2/0 m/sec
Answer: C
Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ?  Choose one: A) 5/8 B) 5/9 C) 5/1 D) 5/3 E) 5/2

Solution: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.   Thus   6 * 5 * 4= 
  6 * 5 * 4 = 120
120 favourable cases.   The total cases are   6 * 6 * 6= 
  6 * 6 * 6 = 216
216.   The probability= 120/216   =5/9.   Answer:5/9
Answer: B
Parameshwaran invested an amount of 12,000 at the simple interest rate of 10 pcpa and another amount at the simple interest rate of 20 pcpa. The total interest earned at the end of one year on the total amount invested became 14 pcpa. Find the total amount invested Choose the correct option
A) 22,000	B) 25,000	C) 20,000	D) 24,000	E) None of these

Solution: Let the amount invested at 20% rate be x. According to the question,   12000 × 10⁄100 + x × 20⁄100 = (12000 + x) × 14⁄100   or, 1200 + x⁄5 = 1680 + 7⁄50x   or, x⁄5 - 7⁄50x = 480   or, 3⁄50x = 480   \ x = 8000   \ Total amount invested = (12000 + 8000)= 
(12000 + 8000) = 20_000
20000   Answer 20,000
Answer: C
P can do a work in 60 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days.  Choose one.
A) 7  B) 8  C) 9  D) 15  E) 25

Solution: Work done by P in 1 day = 1/60   Work done by Q in 1 day = 1/9   Work done by R in 1 day = 1/12   Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36   Work done by Q and R in 3 days = 3Ã—7/36 = 7/12   Remaining work = 1 â€“ 7/12 = 5/12   Number of days in which P can finish the remaining work = (5/12) / (1/60)= 
(5/12) / (1/60) = 25
25   Option 25
Answer: E
If the price of 25 toys is 500, then what will the price of 10toys ?	Pick:
A) 144 B) 361 C) 117 D) 287 E) 200

Solution: One toy price = 500/25= 
500/25 = 20
20   10 toy price= 10 * 20= 
10 * 20 = 200
200   Answer : 200
Answer: E
There are 10 members from that a total of 6 men & 4 ladies a committee of 3 is to be formed. If Mrs. A is not willing to join the committee in which Mr. B is a member, whereas Mr.B is willing to join the committee only if Mrs C is included, how many such committee are possible?  Choose the correct choice from the following options
A) 43  B) 54  C) 65  D) 91  E) 99

Solution: We first count the number of committee in which   (i). Mr. Y is a member   (ii). the ones in which he is not   case (i): As Mr. Y agrees to be in committee only where Mrs. Z is a member.   Now we are left with (6-1) men and (4-2) ladies (Mrs. X is not willing to join).   We can choose 1 more in5+\inline {\color{Blue} 2C_{1}}=7 ways.   case (ii): If Mr. Y is not a member then we left with (6+4-1) people.   we can select 3 from 9 in \inline {\color{Blue} 9C_{3}}=84 ways.   Thus, total number of ways is  7+84= 
 7+84 = 91
91 ways.   91
Answer: D
The average of five integers is 71, and none of these integers is greater than 100. If the average of three of the integers is 76, what is the least possible value of one of the other two integers? Choose the correct answer
A) 5	B) 15	C) 20	D) 21	E) 27

Solution: When it comes to averages, we know thataverage value = (sum of n values)/n   We can rewrite this into a useful formula:sum of n values = (average value)(n)   The average of five integers is 71   So, the sum of ALL 5 integers = (71)(5) =355   The average of three of the integers is 65   So, the sum of the 3 integers = (76)(3) =228   So, the sum of the 2 REMAINING integers =355-228= 
355-228 = 127
127   If the sum of the 2 REMAINING integers=127, and we want to minimize one value, we must MAXIMIZE the other value.   100 is the maximum value so let 1 integer = 100, which means the other must equal 27   Answer: 27
Answer: E
There are 8 books on a shelf that consist of 3 paperback books and 5 hardback books. If 4 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?
Choose the correct choice from the following options.
A) 35  B) 45  C) 50  D) 55  E) 65

Solution: The total number of ways to select 4 books is 8C4 = 70   The number of ways which do not include any paperbacks is 5C4 = 5   The number of combinations with at least one paperback is  70-5= 
 70-5 = 65
65   The answer is 65.
Answer: E
In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is?  Select the correct option.
A) 1 hr  B) 3 hr  C) 2 hr  D) 6 hr  E) 8 hr

Solution: A   1 hr   Let the duration of the flight be x hours. Then,   600/x - 600/(x + 1/2) = 200   x(2x + 1) = 3 2x2 + x - 3  (2  + 1)= 
 (2  + 1) = 3
3 2x2 + x - 3= 0   (2x + 3)(x - 1) = 0   x = 1 hr
Answer: A
The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 40 per cent. The two reductions together are equal to a single reduction of
Select:  A) 45%  B) 55%  C) 35%  D) 32.5%  E) 30%

Solution: Price = p   initially price reduced by 25% which means new price is 3/4P   Now on this new price further 40percent is reduced which means the new price is merely 60percent of 3/4P   ==> (3/4)x(3/5)P = 9/20P is the new price after both deduction which is 45percent of the original value P. This implies this entire series of deduction is worth having discounted 55% of P. So answer is 55% = 55%
Answer: B
One pump drains one-half of a pond in 8 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone?	Choose the correct choice from the following.
A) 1 hour  B) 1.1 hour  C) 3 hours  D) 5 hours  E) 6 hours

Solution: First pump drains 1/2 of the tank in 8 hours   so 16 hours it will take to drain the full tank.   Let, 2nd pump drains the full tank in a hours   so both together can drain (1/16+1/a) part in 1 hour   son in 1/2 hour they drain 1/2*(1/16+1/a) part of the tank   given that in 1/2 hour they drain 1/2 of the tank   hence we can say   1/2*(1/16+1/a) = 1/2   solving u get a = 16/15=1.1   Hence answer is 1.1 hour
Answer: B
At what rate of compound interest per annum will a sum of $1200 becomes 1348.32 in 2 years?  Choose the correct choice from the following
A) 5%
B) 6%
C) 7%
D) 8%
E) 10%

Solution: Let the rate be R% p.a.   1200*(1+R/100)^2 = 1348.32   (1+R/100)^2 = 134832/120000 = 11236/10000   (1+R/100)^2 = (106/100)^2   1+R/100 = 106/100   R = 6%   Answer is 6%
Answer: B