MU-NLPC/Calc-aqua_rat huggingface dataset:
An urn contains 5 red, 6 blue and 8 green balls. 4 balls are randomly selected from the urn, find the probability that the drawn ball are 1 blue and 3 red?	Choices.
A) 1/969  B) 2/969  C) 4/969  D) 5/323  E) 21/789

Solution: Sample space = no. of ways 4 balls were drawn from urn = 19C4 = 3876   No. ways 1 blue balls and 3 red were drawn from bag = 6C1 * 5C3 = 60   Probability = 60 / 3876 = 5/323   Ans - 5/323
Answer: D
45% of 750 - 25% of 480 = ?  Choices.
A) 216
B) 217.5
C) 236.5
D) 245
E) None

Solution: Sol.   Given expression = (45/100 x 750) - (25/100 x 480)   = (337.50 - 120)= 
(337.50 - 120) = 217.5
217.50   Answer 217.5
Answer: B
If a number between 0 and 1 is selected at random, which of the following will the number most likely be between?  Options.
A) 0 and 3/20
B) 3/20 and 1/5
C) 1/5 and 1/4
D) 1/4 and 3/10
E) 3/10 and 1/2

Solution: The number will most likely be between the largest range.   A. 0 and 3/20 --> range 3/20;   B. 3/20 and 4/20 --> range 1/20;   C. 4/20 and 5/20 --> range 1/20;   D. 5/20 and 6/20 --> range 1/20;   E. 6/20 and 10/20 --> range 4/20.   Answer: 3/10 and 1/2.
Answer: E
Sam bought 2Q steaks for W dollars. Jerome buys R steaks for a 50% discount, how much will the steaks cost him in cents? Options.
A) 50RW/Q.  B) 50QR/W.  C) 25RQ/W.  D) 25RW/Q.  E) RW/(4Q).

Solution: Sam bought 2Q steaks for W dollars, so 1 steak = W/2Q   Jerome buys R steaks for a 50% discount: r* (W/4Q)   in cents the answer will be : r* (100 W/4Q)= 25 RW/ Q=25RW/Q.
Answer: D
A man sells a car to his friend at 11% loss. If the friend sells it for Rs.54000 and gains 20%, the original C.P.of the car was :	Choose the correct choice from the following options
A) Rs.25561.80 B) Rs.37500.80 C) Rs.50561.80 D) Rs.60000 E) None of these

Solution: Explanation:   S.P = Rs.54,000. Gain earned = 20%   C.P = Rs.[100/120Ã—54000]   =Rs. 45000   This is the price the first person sold to the second at at loss of 11%.   Now S.P = Rs.45000 and loss = 11%   C.P. Rs.[100/89Ã—45000]= Rs.50561.80.   Rs.50561.80orrect Option : Rs.50561.80
Answer: C
Louie takes out a three-month loan of $3000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?  Choose the correct choice from the following answers
A) A)333	B) B)383	C) C)402	D) D)1206	E) E)483

Solution: Here's the calculation for that case, assume monthly payment is X.   After 1st month: (3000)(1.1)-X = 3300-X   After 2nd month: (3300-X)(1.1)-X = 3630-2.21X   After 3rd month: (3630-2.21X)(1.1)-X = 3993-3.31X   Now, the amount after the last payment in 3rd month must bring the total to 0. Hence:   3993-3.31X = 0   X = 3993/3.31 = 1206.34   Answer 1206
Answer: D
If rupee one produces rupees nine over a period of 30 years, find the rate of simple interest? Choose the correct choice from the following options.
A) 10 %	B) 20 %	C) 30 %	D) 22 %	E) 28 %

Solution: 9 = (1*30*R)/100   R = 30 %   ANSWER:30 %
Answer: C
A bag contains 6 white marbles and 6 black marbles. If each of 6 girls and 6 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?  Choose one.
A) 1/35 B) 1/10 C) 1/3 D) 1/462 E) 1/252

Solution: first, total ways to select for all boys and girls, i.e 12!/(6!*6!) = 12*11*10*9*8*7/6*5*4*3*2 =924   then there are one two way girls can have all same colors, either white or black.   The number of ways in which 6 girls can select 6 white balls = 6C6 = 1   The number of ways in which 6 girls can select 6 black balls = 6C6 = 1   Therefore, total favorable outcomes/total outcomes = 2/924 = 1/462   1/462
Answer: D
Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is?  Choose the correct option
A) 4:6	B) 4:3	C) 4:9	D) 4:4	E) 4:1

Solution: Let us name the trains A and B.   Then, (A's speed) : (4:3's speed)   = √b : √a = √16 : √9 = 4:3   Answer:4:3
Answer: B
Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 18 white marbles. How many red marbles could be in bag A?
Choose the correct choice from the following options
A) 2	B) 3	C) 4	D) 6	E) 8

Solution: 6 is the answer.   Bag 2-   R:W:B = 2:6:9   Let W in bag 2 be 6K   Bab B -   R:W = 1:4   Let W in bag B be 4P   W = 18 = 6K+4P   => K =1, P=3   Total Red's in bag 2 will be 2K = 2   2
Answer: A
A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/2 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?	Choose the correct option:
A) (a) 7/16  B) (b) 7/10  C) (c) 10/21  D) (d) 17/35  E) (e) 1/2

Solution: This problem is very good example how easy and quick plug-in method might be.   Let the total # of cups be 10.   # of small cups sold 3/5*10= 
3/5*10 = 6
6;   # of large cups sold  10-6= 
 10-6 = 4
4;   Let the price of small cup be $6, then the price of larges cup would be 7/2*6= 
7/2*6 = 21
$21;   Revenue from small cups: 6*$6=$36;   Revenue from large cups cups: 4*$21  6* 6= 
  6* 6 = 36
$36;   Revenue from large cups cups: 4*$21=$84;   Fraction of total revenue from large cups: 84/(36+84) 4* 21= 
 4* 21 = 84
$84;   Fraction of total revenue from large cups: 84/(36+84)=7/10.   Answer: (b) 7/10.
Answer: B
Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together?	Select.
A) 14 1/7 days B) 11 1/7 days C) 16 1/7 days D) 17 1/7 days E) 24 1/7 days

Solution: 17 1/7 days   17 1/7 days   1/30 + 1/40 = 7/120   120/7 = 17 1/7 days
Answer: D
The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 66 kg. What might be the weight of the new person?  Choices:  A) 56 kg  B) 90 kg  C) 86 kg  D) Data inadequate  E) None of these

Solution: C   86 kg   Total weight increased = (8 x 2.5) kg = 20 kg.   Weight of new person = (66 + 20)= 
(66 + 20) = 86
86 kg.
Answer: C
A vessel of capacity 90 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?	Choose the correct option:  A) 15.6 litres  B) 72.9 litres.  C) 22.8 litres  D) 16 litres  E) 92.3litres

Solution: Explanation:   Let the initial quantity of milk in vessel be T litres.   Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.   Quantity of milk finally in the vessel is then given by [(T - y)/T]n * T   For the given problem, T = 90, y = 9 and n = 2.   Hence, quantity of milk finally in the vessel   = [(90 - 9)/90]2 (90) = 72.9 litres.   Answer:72.9 litres.
Answer: B
In a card game, a combination of two kings beats all others. If Jose is the first to draw from a standard deck of 52 cards, what is the probability that he wins the game with the best possible combination? Choose the correct choice from the following options:
A) 1/221	B) 13/221 C	C) 2/52	D) 3/51	E) 4/51

Solution: The best possible combination is the case when he wins in his first two draws   There are 52 cards in a deck of cards with 4 kings in it.   Probability of first card to be king = 4/52   Probability of Second card to be king = 3/51   Probability of Best possible case = (4/52)*(3/51) = 1/221   1/221nswer: 1/221
Answer: A
Three numbers are in the ratio 1 : 3 : 6 and their average is 100. The largest number is : Answers.
A) 180	B) 98	C) 27	D) 21	E) 22

Solution: Explanation:   Let the numbers be x, 3x and 6x, Then, (x + 3x + 6x ) / 3 = 100   => 10x = 100*3   => x = 30   Largest number 6x = 6*30= 
6*30 = 180
180   180nswer: 180
Answer: A
Sheela deposits Rs. 4500 in bank savings account. If this is 28% of her monthly income. What is her monthly income in?	Choose the correct choice from the following options:
A) 22000
B) 27000
C) 16071
D) 16789
E) None of these

Solution: Explanation :   28% of income = Rs. 4500   100% of income = 4500 X 100/28 = Rs. 16071   Answer : 16071
Answer: C
A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?	Choose the correct choice from the following.
A) 10 days
B) 11 days
C) 13 days
D) 15 days
E) 12 days

Solution: Let us assume the total work to be done is 60 units.   According to the question,   A and B finish the work in 12 days working together which implies 5 units of work is done by them in a single day, i.e,   A + B = 5 ----- (1)   Also, we know A alone can finish the work in 20 days which implies he can do 3 units of work in a single day.   Hence, B’s one day work is   3 + B = 5   => B = 2.   But B works half a day only which implies he is doing only 1 unit of work in a single day and hence only 4 units of work is done in a single day.   Thus, total number of days taken by A and B working together to complete the work is   60/4= 
  60/4 = 15
15 days.   ANSWER:15 days
Answer: D
What is the average of 1/2, 1/5 and 3/10?	Choose the correct choice.
A) 1/5
B) 3/10
C) 2/5
D) 1/3
E) 6/5

Solution: Sum of 1/2,1/5,3/10 =10/10= 
10/10 = 1
1   Average= 1*1/3 =1/3   Answer 1/3 1/3
Answer: D
One hour after Yolanda started walking from X to Y, a distance of 40 miles, Bob started walking along the same road from Y to X. If Yolandaâs walking rate was 2 miles per hour and Bobâs was 4 miles per hour, how many miles had Bob walked when they met?  Choose the correct option:
A) 24
B) 23.5
C) 22
D) 21.2
E) 25.32

Solution: Let t be the number of hours that Bob had walked when he met Yolanda. Then, when they met, Bob had walked 4t miles and Yolanda had walked 2(t + 1) miles. These distances must sum to 40 miles, so 4t + 2(t + 1) = 40, which may be solved for t as follows   4t + 2(t + 1) = 40   4t + 2t + 2 = 40   6t = 38   T = 6.33 (hours)   Therefore, Bob had walked 4t = 4(7.6) = 25.32 miles when they met. The best answer is 25.32.
Answer: E
Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?	Choose the correct choice from the following answers:
A) 2:3:4 B) 6:5:9 C) 3:3:4 D) 11:12:14 E) 5:6:7

Solution: Mathematics, Physics and Biology be 5x, 7x and 8x   increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).   =>(140/100*5X) (150/100*7X) 2:3:4ND (175/100*8X)   =>7X, 21X/2 2:3:4ND 14X   REQ R2:3:4TIO = 7X:21X/2:14X   14x:21x:28x   2:3:4   2:3:4NSWER 2:3:4
Answer: A
The average of first 10 even numbers is?
Choose the most appropriate option:
A) 18	B) 16	C) 15	D) 11	E) 19

Solution: Sum of 10 even numbers = 10 * 11= 
10 * 11 = 110
110   Average= 110/10= 
110/10 = 11
11   Answer: 11
Answer: D
Mary can do a piece of work in 26 days. Rosy is 30% more efficient than Mary. The number of days taken by Rosy to do the same piece of work is?
Choose the correct option
A) 22  B) 20  C) 24  D) 26  E) 30

Solution: Ratio of times taken by Mary and Rosy = 130:100 = 13:10   Suppose Rosy takes x days to do the work.   13:10 :: 26:x => x= 20 days.   Hence, Rosy takes 20 days to complete the work.   Answer: 20
Answer: B
A number consists of 3 digit whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:
Select:
A) 145  B) 253  C) 140  D) 200  E) 160

Solution: Let the middle digit be x. Then, 2x = 10 or x = 5.   So, the number is either 253 or 352. Since the number increases on reversing the digits, so the hundred's digit is smaller than the unit's digit. Hence, required number = 253.   ANSWER 253
Answer: B
Evaluate: 98612 / 22*11*70 = ?  Choose one
A) 700.4 B) 704.4 C) 740.4 D) 744.4 E) 700.0

Solution: According to order of operations, 22?11?70 (division and multiplication) is done first from left to right   22/11= 
22/11 = 2
2* 70= 
2* 70 = 140
140   Hence   98612 / 24*11*70= 98612 / 140 = 704.4   correct answer 704.4
Answer: B
Six years ago, the ratio of ages of Kunal and Sagar was 6:5. Four years hence, the ratio of their ages will be 11:10. What is Sagar's age at present?	Choose the correct choice from the following answers:
A) 16 years	B) 18 years	C) 88 years	D) 17 years	E) 13 years

Solution: Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.   Then, [(6x + 6) + 4] / [(5x + 6) + 4] = 11/10   10(6x + 10) = 11(5x + 10) => x = 2   Sagar's present age = (5x + 6) = 16 years.   16 yearsnswer: 16 years
Answer: A
In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of:	Choose the correct answer:  A) Rs. 3100  B) Rs. 6240  C) Rs. 6500  D) Rs. 9600  E) Rs. 10120

Solution: To obtain Rs. 10, investment = Rs. 96   To obtain Rs. 650, investment = Rs. (96/10 * 650) = Rs. 6240.   Answer = Rs. 6240
Answer: B
If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004? Choose the correct option.
A) Sunday	B) Saturday	C) Tuesday	D) Wednesday	E) Monday

Solution: The year 2004 is a leap year. So, it has 2 odd days.   But, Feb 2004 not included because we are calculating from March 2004 to March 2005. So it has 1 odd day only.   The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004.   Given that, 6th March, 2005 is Monday.   6th March, 2004 is Sunday (1 day before to 6th March, 2005).   Sundaynswer Sunday
Answer: A
A pump can be operated both for filling a tank and for emptying it. The capacity of the tank is 2400 m3. The emptying capacity of the pump is 10m3 per minute higher than its filling capacity. Consequently, the pump needs 8 minutes less to empty the tank than to fill it. Find the filling capacity of the pump.	Choose the correct answer
A) 45 m3/min
B) 40 m3/min
C) 50 cubic metre per minute
D) 55 m3/min
E) None of these

Solution: 2400/x - 2400/x+10=8,solving this we get x,   =50m3/min   Answer: 50 cubic metre per minute
Answer: C
There are 624 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?  Choose the correct choice from the following.
A) 320
B) 345
C) 375
D) 390
E) 400

Solution: In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 624. Hence   3x + 5x = 624   Solve for x   8x = 624   x = 78   Number of boys   3x = 3 × 78 = 234   Number of girls   5x = 5 × 78 = 390   390
Answer: D
Ben is driving on the highway at x miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of t feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour? Choices
A) 5,280(x/t)	B) 5,280(y/x)	C) 5,280(xy)	D) 5,280/(xy)	E) (xy)/5,280

Solution: In one hour, at the rate of x miles per hour, Ben covers x miles, so 5,280x feet.   The number of revolutions = distance/circumference = 5,280x/t.   5,280(x/t)nswer: 5,280(x/t).
Answer: A
The average of seven numbers is 4. The average of first three numbers is 2 and the average of last three numbers is 6. What is the middle number?  Choose the correct option:
A) 3
B) 4
C) 6
D) 7
E) 8

Solution: The total of seven numbers = 7X4 = 28   The total of first 3 and last 3 numbers is = 3 X 2+3 X 6 = 24   So, the middle number is  (28 - 24 )= 
 (28 - 24 ) = 4
4   4
Answer: B
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.  Pick.
A) 150 meter	B) 145 meter	C) 140 meter	D) 135 meter	E) None of these

Solution: Explanation:   Speed = 60*(5/18) m/sec = 50/3 m/sec   Length of Train(Distance) = Speed * Time   =50/3∗9=150meter   Option 150 meter
Answer: A
A researcher computed the mean, the median, and the standard deviation E for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change?
Choose the correct choice from the following answers:
A) The mean only
B) The median only
C) The standard deviation only
D) The mean and the median
E) The mean and the standard deviation

Solution: If we add or subtract a constant to each term in a set the standard deviation E will not change..   If we add (or subtract) a constant to each term in a set the mean and the median will increase (decrease) by the value of that constant.   Answer: The mean and the median.
Answer: D
A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is ? Choose the correct choice from the following choices.
A) 25/42
B) 25/49
C) 25/47
D) 25/44
E) 25/41

Solution: Total fruits = 9   Since there must be at least two apples,   = 25/42.   25/42nswer: 25/42
Answer: A
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?  Choices.
A) 299 B) 778 C) 150 D) 888 E) 132

Solution: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9)= 
(50/3 * 9) = 150
150 m.   Answer: 888
Answer: D
A trader wants 10% profit on the selling price of a product whereas his expenses amount to 15% on sales. What should his rate of mark up be on an article of Rs. 9?
Choose the correct choice from the following:
A) 20%
B) 25%
C) 30%
D) (100/3) %
E) none

Solution: Let S.P. = Rs X   Therefore, expenses = 15% of X = 0.15 X   Profit = 10% of X = 0.10X   C.P. = Rs 9 (Given)   Therefore, 9 + 0.15X + 0.1X = X => X = 12   Markup % = 3/9 x 100 = 100/3 %   Therefore, the rate of mark up on the article should be 100/3 %   ANSWER:(100/3) %
Answer: D
The milk level in a rectangular box measuring 56 feet by 25 feet is to be lowered by 6 inches. How many gallons of milk must be removed? (1 cu ft = 7.5 gallons)	Pick
A) 100  B) 250  C) 750  D) 5250  E) 5635

Solution: 6 inches = 1/2 feet (there are 12 inches in a foot.), so  56*25*1/2= 
 56*25*1/2 = 700
700 feet^3 of milk must be removed, which equals to   700*7.5= 
  700*7.5 = 5_250
5250 gallons.   Answer: 5250.
Answer: D
If the true discount on a sum due 2 years hence at 14% per annum be Rs.168,the sum due is :	Choose one.
A) Rs. 768
B) Rs. 968
C) Rs. 1960
D) Rs. 2400
E) None

Solution: Solution   P.W = 100 x T.D/Rx T = 100 x168/14x2= 600.   ∴ Sum = (P.W. + TD.) = Rs. 768.   Rs. 768nswer Rs. 768
Answer: A
The average of numbers 0.64205, 0.64203, 0.64202 and 0.64201 is ?
Select the correct option.
A) 0.64202	B) 0.64204	C) 0.642022	D) 0.642028	E) None

Solution: Answer   Average = (0.64205 + 0.64203 + 0.64202 + 0.64201)/ 4   =2.56811/ 4   =0.642028   Correct Option: 0.642028
Answer: D
A group of 630 children is arranged in rows for a group photograph session. Each row contains three fewer children than the row in front of it. What number of rows is not possible? Choices.
A) 3  B) 4  C) 5  D) 6  E) 7

Solution: Explanation :   Let the last row contain x seats. So, the rows in front have x + 3, x + 6 , x + 9 , …   Total no: of students are 630. So, x + (x + 3) + (x + 6) + (x + 9) + ……… = 630.   There are 2 ways of approaching the problem. You can consider it as an Arithmetic Progression, substitute the options and find the answer, else a simple “less time consuming” way explained. We know that the number of students in each row needs to be a “natural number” and not a decimal, since there cannot be 3.5 or 1.2 or any other decimal number of students/row. We exploit this condition to get the solution quickly.   1st option : 3 rows So, x, x + 3, x+ 6 are the students in 3 rows. Sum = 3x + 9 = 630. We get a natural number as value of x. So it is fine.   2nd option : 4 rows x + (x +3) + (x+6) + (x+9) = 630, x = (630 – 18)/4 = natural number.   3rd option : 5 rows x + (x +3) + (x+6) + (x+9) + (x + 12)= 630 x = (630 – 30)/5, again natural number.   4th option : 6 rows x + (x +3) + (x+6) + (x+9) + (x + 12) + (x+15) = 630   x = (630 – 45)/6 is not a natural number, and is a decimal.   Hence, we cannot have 6 rows.   Answer : 6
Answer: D
A is half good a work man as B and together they finish a job in 12 days. In how many days working alone B finish the job?  Choose the correct choice from the following answers:
A) 28 days
B) 22 days
C) 20 days
D) 18 days
E) 19 days

Solution: WC = 1:2   2x + x = 1/12 => x = 1/36   2x = 1/18 => 18 days   ANSWER:18 days
Answer: D
On a ranch, a rancher can place a loop of rope, called a lasso, once in every 3 throws around a cow’s neck. What is the probability that the rancher will be able to place a lasso around a cow’s neck at least once in 4 attempts?  Select: A) 4/9 B) 5/9 C) 17/27 D) 23/27 E) 65/81

Solution: P(missing all 3)=(2/3)^4=16/81   P(success on at least one attempt)=1-16/81=65/81   The answer is 65/81.
Answer: E
A and B can do a piece of work in 2 days and 6 days respectively. Both work for 1 days and then A goes away. Find how long will B take to complete the remaining work?
Choose the correct answer
A) 1 days  B) 2 days  C) 3 days  D) 4 days  E) 5 days

Solution: 1/2 + (1 + x)/6 = 1   x = 2 days   ANSWER:2 days
Answer: B
Integers 3n+2 and 8n+7 are divisible by an integer p. If p is not equal to 1, then p equals to?	Choose the correct choice from the following options:
A) 2
B) 3
C) 5
D) 7
E) 11

Solution: If p divides 3n+2, then p divides 24n+16.   If p divides 8n+7, then p divides 24n+21.   Then p must equal 5.   The answer is 5.
Answer: C
For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 100 units raises the average to 55 units per day, what is the value of n?
Choose the correct choice from the following.
A) 6
B) 7
C) 8
D) 9
E) 10

Solution: The daily production was raised by 5 units for n days, which has a weighting of 5n.   5n = 100-55= 
100-55 = 45
45   n= 9   The answer is 9.
Answer: D
Pipe A, B and C are kept open and together fill a tank in t minutes. Pipe A is kept open throughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes after pipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equal share of the tank. Furthermore, it is known that if pipe A and B are kept open continuously, the tank would be filled completely in t minutes. How long will C alone take to fill the tank?
Select the correct option:
A) 18	B) 36	C) 27	D) 24	E) 32

Solution: A is kept open for all t minutes and fills one-third the tank. Or, A should be able to fill the entire tank in '3t' minutes.   A and B together can fill the tank completely in t minutes. A alone can fill it in 3t minutes.   A and B together can fill 1t of the tank in a minute. A alone can fill 1/t of the tank in a minute. So, in a minute, B can fill 1/t−1/t=2/t. Or, B takes 3/2 minutes to fill an entire tank.   To fill one-third the tank, B will take t/2 minutes. B is kept open for t - 10 minutes.   t/2 = t - 10, t = 20 minutes.   A takes 60 minutes to fill the entire tank, B takes 30 minutes to fill the entire tank. A is kept open for all 20 minutes. B is kept open for 10 minutes.   C, which is kept open for 8 minutes also fills one-third the tank. Or, c alone can fill the tank in 24 minutes. Choice (24)
Answer: D
The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 10% p.a. was Rs.420. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.  Choose the correct option:	A) Rs.2530	B) Rs.2430	C) Rs.2420	D) Rs.2410	E) Rs.2440

Solution: Let the sum be Rs.P   P{ [ 1 + 10/100]2 - 1 } = 420   P(10/100)(2 + 10/100) = 420 [a2 - b2 = (a - b) ( a + b)] P = 420 / (0.1)(2.1) = 2000. Amount =2000+420=Rs.2420 Answer : Rs.2420
Answer: C