MU-NLPC/Calc-aqua_rat huggingface dataset:
In the manufacture of a certain product, 9 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?	Choose the correct choice from the following choices:
A) 0.125%
B) 0.36%
C) 0.8%
D) 1.25%
E) 2.0%

Solution: Percent of defective produced = 9%   Percent of the defective units that are shipped for sale = 4%   Percent of units produced are defective units that are shipped for sale = (4/100)*(9/100)*100%   = (36/10000)*100%   = (36/100)= 
(36/100) = 9/25 = around 0.36
.36 %   Answer 0.36%
Answer: B
If Janice was 21 years old z years ago and Lisa will be 19 years old in p years, what was the average (arithmetic mean) of their ages 8 years ago?  Choose the correct option
A) (z + p)/2  B) (z - p + 24)/4  C) (z - p + 14)/4  D) (z + p + 34)/2  E) (z - p + 24)/2

Solution: Today, J = z+21 and L = 19-p   8 years ago, J = z+13 and L = 11-p   The average of their ages was (z-p+24) / 2   The answer is (z - p + 24)/2.
Answer: E
Find all positive integers n such that n^2
+ 1 is divisible by n+ 1. Choose the correct choice from the following options:  A) 1  B) 2  C) 3  D) 4  E) 5

Solution: There is only one such positive integer : n = 1.   In fact, n^2+1= n(n+1)-(n-1);   thus, if n+1|n^2+1, then n+1|n-1 which for positive integer n is possible only if n-1 = 0,   hence if n = 1.   1nswer is 1
Answer: A
5 men are equal to as many women as are equal to 7 boys. All of them earn Rs.90 only. Men’s wages are? Choose the correct choice.
A) 8Rs. B) 7Rs. C) 6Rs. D) 4Rs. E) 5Rs.

Solution: 5M = xW = 7B   5M + xW + 7B ----- 90 Rs.   5M + 5M + 5M ----- 90 Rs.   15M ------ 90 Rs. => 1M = 6Rs.   ANSWER:6Rs.
Answer: C
The height of the wall is 6 times its width and length of the wall is 7 times its height .if the volume of the wall be 6804 cu.m.its width is	Choose the correct choice.
A) 3m B) 5m C) 6m D) 7m E) 8m

Solution: Explanation:   Let width = x   Then, height=6x and length=42x   42x Ã— 6x Ã— x = 6804   x = 3   3mnswer: 3m
Answer: A
A boat can travel with a speed of 16 km/hr in still water. If the rate of stream is 5 km/hr, then find the time taken by the boat to cover distance of 168 km downstream.  Choose the correct option.
A) 4 hours	B) 5 hours	C) 6 hours	D) 7 hours	E) 8 hours

Solution: Explanation:   It is very important to check, if the boat speed given is in still water or with water or against water. Because if we neglect it we will not reach on right answer. I just mentioned here because mostly mistakes in this chapter are of this kind only.   Lets see the question now.   Speed downstream = (16 + 5)= 
(16 + 5) = 21
21 kmph   Time= distance/speed = 168/21= 
168/21 = 8
8 hours   Option 8 hours
Answer: E
In 1991, there are 28 days in February and there are 365 days in the year. In 1992, there are 29 days in February and there are 366 days in the year. If the date March 15, 1995 is a Tuesday, then which one of the following would the date March 15, 1996 be?  Choose the most appropriate option
A) Thursday	B) Friday	C) Saturday	D) Sunday	E) Monday

Solution: From the information given,March 15, 1992 is 366 days after March 15, 1991.   366 days = 52 weeks and 2 more days. Therefore if March 15, 1995 is a Tuesday, then March 15, 1996 is Tuesday + 2 days = Thursday   Thursdaynswer: Thursday
Answer: A
Look at this series: U32, V29, __, X23, Y20, ... What number should fill the blank?
Choose the correct choice from the following choices:
A) M43
B) D14
C) W26
D) F24
E) K81

Solution: W26   W26   In this series, the letters progress by 1; the numbers decrease by 3.
Answer: C
If the length of the longest chord of a certain circle is 22, what is the radius of that certain circle?  Choose the correct choice from the following:
A) 11
B) 5
C) 10
D) 15
E) 20

Solution: Longest chord of a circle is the diameter of the circle   diameter = 2 * radius   If diameter of the circle is given as 22 = 2 * 11   so radius of the circle = 11   correct answer - 11
Answer: A
What is the smallest number Y which when increased by 5 is completely divisible by 8, 11 and 24?
Pick one.
A) 264
B) 259
C) 269
D) 270
E) 282

Solution: This question includes a number of great Number Property shortcuts that you can take advantage of:   1) The question asks for the SMALLEST number that, when increased by 5 is divisible by 8, 11 and 24. Since the answers are numbers, we can TEST THE ANSWERS.   2) Any number that is divisible by 24 is ALSO divisible by 8, so we really just need to consider the 11 and the 24.   3) To be divisible by 24, the end number MUST be EVEN. Since we're adding 5 to get to that end number, the starting number MUST be ODD.   The last shortcut allows us to eliminate Answers A, D and E. Between Answers B and C, TESTING B first will prove that, when increased by 5, the end sum is divisible by both 11 and 24.   Final Answer:   259
Answer: B
The average monthly salary of 25 employees in an organisation is Rs. 2500. If the manager's salary is added, then the average salary increases by Rs. 200. What is the manager's monthly salary?  Pick: A) Rs.7700 B) Rs.3618 C) Rs.3600 D) Rs.3619 E) Rs.3610

Solution: Manager's monthly salary   = Rs. (2700 * 26 - 2500 * 25)   = Rs. 7700 Rs.7700nswer:Rs.7700
Answer: A
Mary, Peter, and Lucy were picking chestnuts. Mary picked three times as much as much chestnuts than Peter. Lucy picked 4 kg more than Peter. Together the three of them picked 29 kg of chestnuts. How many kilograms of chestnuts did Mary, Peter, and Lucy pick respectively?  Select:
A) 9, 5 and 15  B) 5, 15 and 9  C) 15, 5 and 9  D) 9, 15 and 5  E) 5, 9 and 15

Solution: M = 3P   L = P+4   M + P + L = 29   3P + P + (P+4) = 29   P = 5, M = 15, L = 9   Therefore, Mary, Peter, and Lucy picked 15, 5, and 9 kg, respectively.   The answer is 15, 5 and 9.
Answer: C
Each shelf of a bookcase contained 11 books. If the librarian took out 18 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 17 books, how many shelves does the bookcase have?	Choose the correct choice from the following options.
A) 5	B) 6	C) 7	D) 8	E) 9

Solution: Let x be the number of shelves.   11x - 18 = 7(x-1) + 17   4x = 28   x= 7   The answer is 7.
Answer: C
A company seeks to hire a sales manager, a shipping clerk, and a receptionist. The company has narrowed its candidate search and plans to interview all remaining candidates including 7 persons for the position of sales manager, 5 persons for the position of shipping clerk, and 10 persons for the position of receptionist. How many different hirings of these three people are possible?	Options:	A) 7 + 5 + 10	B) 7 × 5 × 10	C) 21 × 20 × 19	D) 7! + 5! + 10!	E) 7! × 5! × 10!

Solution: 1 sales manager can be selected out of 7 in 7 ways   1 clerk can be selected out of 5 in 5 ways   1 receptionist can be selected out of 10 in 10 ways   total no. of ways these 3 can be selected = 7 *4 * 10   Ans. 7 × 5 × 10) 7 × 5 × 10
Answer: B
Eight animals of a circus has to be placed inside in eight cages one in each cage. If 4 of the cage are too small for 6 of the animal then find the number of ways of caging the animal.	Pick one
A) A.604 B) B.2880 C) C.502450 D) D.784200 E) E.302400

Solution: ways for cages that are too small = 5*4*3*2= 
5*4*3*2 = 120
120   since we have 4 cages and 4 animal left therefore ways for 4 cages=4!   total ways =120*4!=2880   Answer B.2880
Answer: B
Sum of the squares of three numbers is 414 and the sum of their products taken two at a time is 131. Find the sum?  Choose the correct choice from the following answers:
A) 20
B) 22
C) 25
D) 26
E) 29

Solution: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 414 + 2* 131   a + b + c = √676 = 26   26
Answer: D
A certain animal shelter has 26 horses and 36 cows. How many horses must be taken away from the animal shelter so that 75 percent of the animals in the shelter will be cows?  Answers:
A) 12
B) 13
C) 14
D) 15
E) 16

Solution: Suppose x horses need to be removed from the shelter.   After x horses are removed, the shelter shall have (26 - x) horses and the same 36 cows; and the total number of animals shall be (26 - x) + 36 = 62 - x   Now we want the 75 percent of animals in the shelter to be cows.   This means 75 percent of (62 - x) should be equal to the number of cows which is 36.   This means,   75 % of (62 - x) = 36   Solving above equation we get x = 14   x=14   Ans 14
Answer: C
Walking 7/6 of his usual rate, a boy reaches his school 2 min early. Find his usual time to reach the school?  Answers.
A) 14
B) 28
C) 99
D) 77
E) 66

Solution: Speed Ratio = 1:7/6 = 6:7   Time Ratio = 7:6   1 -------- 7   2 --------- ? 14 m   14nswer:14
Answer: A
Company Z has 61 employees. If the number of employees having birthdays on Wednesday is more than the number of employees having birthdays on any other day of the week, each of which have same number of birth-days, what is the minimum number of employees having birthdays on Wednesday.
Options
A) 6 B) 7 C) 13 D) 9 E) 12

Solution: Say the number of people having birthdays on Wednesday is x and the number of people having birthdays on each of the other 6 days is y. then x + 6y =61.   Now, plug options for x. Only C and E give an integer value for y. But only for C x > y as needed.   Answer: 13.
Answer: C
John is three times as old as Sam. If John will be twice as old as Sam in six years, how old was Sam four years ago?	Select the correct option:
A) 2 B) 4 C) 6 D) 8 E) 16

Solution: j= 3s   after 6 years   j +6 = 2(s+6)   j= 2s+6   2s +6 = 3s   s= 6   four years ago   s= 6-4= 
6-4 = 2
2   2 is the answer
Answer: A
A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train?	Select the correct option:
A) 120 m  B) 190 m  C) 115 m  D) 110 m  E) 250 m

Solution: Speed = 60 * 5/18 = 50/3 m/sec   Length of the train = speed * time = 50/3 * 15= 
50/3 * 15 = 250
250 m   Answer: 250 m
Answer: E
In 2008, the profits of Company M were 5 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 15 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
Choose the correct choice from the following options.
A) 80%	B) 105%	C) 124%	D) 240%	E) 138%

Solution: the profit 0f 2009 in terms of 2008 = 0.8*15/5*100= 
0.8*15/5*100 = 240
240%   240%
Answer: D
The speed of a car is 85 km in the first hour and 45 km in the second hour. What is the average speed of the car?
Choose the correct choice from the following
A) 72 kmph B) 65 kmph C) 30 kmph D) 80 kmph E) 82 kmph

Solution: S = (85 + 45)/2= 
(85 + 45)/2 = 65
65 kmph   ANSWER:65 kmph
Answer: B
A bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 64 ounces of nuts, representing a mixture of both brands, and 14 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used? Pick
A) 14	B) 20	C) 32	D) 44	E) 48

Solution: lets say x ounces of P is mixed with Q.   => 64-x ounces of Q is present in the mixture (as the total = 64 ounces)   given total almond weight = 14 ounces   (20x/100)+(25/100)(64-x) = 14   => x = 40   => 64-40 = 14 ounces of Q is present in the mixture.   14nswer is 14.
Answer: A
If x is a prime number, and x-1 is the median of the set {x-1, 3x+3, 2x-4}, then what is the average (arithmetic mean) of the set?  Pick one:
A) 2
B) 5/3
C) 3
D) 10/3
E) 14/3

Solution: If x is a prime number, and x-1 is the median of the set {x-1, 3x+3, 2x-4}, then what is the average (arithmetic mean) of the set?   A. 2   B. 5/3   C. 3   D. 10/3   E. 14/3   Solution:   x-1 is the median of the set, implies if we arrange the set in ascending order, the set would be [2x-4, x-1, 3x+3]. This means that:   2x-4<x-2<3x+3 gives="" inequality="" solving="" x="">-2 and x<3. Since x is prime number and the only prime number <3 is 2, so put x</x-2<3x+3>=2.   Hence set becomes: [ 0, 1, 9] and avg = 10/3.10/3
Answer: D
The H.C.F. of two numbers is 12 and their L.C.M. is 600. If one of the number is 60, find the other? Choose the correct answer:
A) 100  B) 240  C) 120  D) 200  E) 150

Solution: Other number = 12*600/60= 
12*600/60 = 120
120   Answer is 120
Answer: C
A car salesman earns a base salary of $1,000 per month plus a commission of $200 for each car he sells. If the car salesman earned $2000 in March, how many cars does he need to sell in April in order to double his March earnings?	Choose the most appropriate option:  A) 14  B) 15  C) 16  D) 17  E) 18

Solution: 1000+200x=4000   x=15 cars.   The answer is 15.
Answer: B
The average weight of a group of boys is 30 kg. After a boy of weight 37 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
Choose the correct option.
A) 4 B) 8 C) 5 D) 2 E) 6

Solution: Let the number off boys in the group originally be x.   Total weight of the boys = 30x   After the boy weighing 37 kg joins the group, total weight of boys = 30x + 37   So 30x + 37 + 31(x + 1) = > x = 6.   Answer: 6
Answer: E
Manoj borrowed Rs.3900 from Anwar at 6% p.a. simple interest for three years. He then added some more money to the borrowed sum and lent it to Ramu for the same time at 9% p.a. simple interest. If Manoj gains Rs.824.85 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Ramu?	Select: A) 22877 B) 5655 C) 2778 D) 6787 E) 1771

Solution: Let the sum lent by Manoj to Ramu be Rs.P.   Amount gained by Manoj = P. 3.9 /100 = 3900.3.6/100 = Rs.824.85   27P = 70200 = 82485   P = (82485 + 70200)/27 = 3055 + 2600 = Rs.5655   Answer: 5655
Answer: B
Buses A and B start from a common bus stop X. Bus A begins to travel in a straight line away from bus B at a constant rate of 60 miles per hour. One hour later, bus B begins to travel in a straight line in the exact opposite direction at a constant rate of 80 miles per hour. If both buses travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes bus B to cover the exact distance that bus A has covered and the amount of time it takes bus B to cover twice the distance that bus A has covered?	Options
A) 36	B) 72	C) 132	D) 144	E) 180

Solution: 1st part: - In 1hr, Bus A covers 30 miles.   Relative speed of bus ABus B is   (80-30)= 
  (80-30) = 50
50mph.   So time required for Bus B to cover the exact distance as A is   50*t= 30   t=3/5 = 36min   2nd part   80*t=2d - B has to cover twice the distance   30*(t+1) = d - A traveled 1hr more and has to travel only only d   so   d/30 - 2d/80 = 1   D=120   T= 3hrs = 180 min   Question asks for +ve difference between part 1 and part 2 in minutes   = 180-36 = 180min   180
Answer: E
The sum of two numbers is 40 and their product is 350. What will be the sum of their reciprocals? Choose one.
A) 4/35	B) 8/75	C) 75/4	D) 75/8	E) 75/6

Solution: (1/a)+(1/b)=(a+b)/ab=40/350=4/35   4/35NSWER:4/35
Answer: A
A person purchases 90 clocks and sells 40 clocks at a gain of 10% and 50 clocks at a gain of 20%. If he sold all of them at a uniform profit of 15%, then he would have got Rs. 40 less. The cost price of each clock is:  Choose the correct choice from the following choices.
A) Rs.50 B) Rs.60 C) Rs.80 D) Rs.90 E) Rs.100

Solution: Let C.P. of clock be Rs. x.   Then, C.P. of 90 clocks = Rs. 90x.   [(110% of 40x) + (120% of 50x)] - (115% of 90x) = 40   44x + 60x - 103.5x = 40   0.5x = 40 => x = 80   ANSWER:Rs.80
Answer: C
If p/q = 3/5 , then 2p+q= ?
Pick.
A) 12 B) 11 C) 13 D) 15 E) 16

Solution: let p=3, q=5 then 2*3+5= 
2*3+5 = 11
11   so 2p+q=11.   ANSWER:11
Answer: B
Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?	Choose one.
A) 299
B) 277
C) 266
D) 992
E) 188

Solution: (800*3*3)/100= 
(800*3*3)/100 = 72
72   920 + 72= 
920 + 72 = 992
992   Answer:992
Answer: D
The sum of the digits of a two-digit number is 12. The difference of the digits is 6. Find the number?
Choose one.
A) 93
B) 39
C) 75
D) 48
E) Either (a) or (b)

Solution: Let the two-digit number be 10a + b   a + b = 12 --- (1)   If a>b, a - b = 6   If b>a, b - a = 6   If a - b = 6, adding it to equation (1), we get   2a = 18 => a =9   so b = 12 - a = 3   Number would be 93.   if b - a = 6, adding it to the equation (1), we get   2b = 18 => b = 9   a = 12 - b = 3.   Number would be 39.   There fore, Number would be 39 or 93.   Either (a) or (b)
Answer: E
X men can do a work in 120 days. If there were 20 men less, the work would have taken 60 days more. What is the value of X?	Choices
A) 60  B) 77  C) 26  D) 66  E) 281

Solution: We have M1 D1 = M2 D2   120X = (X - 20)180   => 2X = (X - 20) 3 => 2X = 3X - 60   => X = 60   60nswer:60
Answer: A
What number has a 5:1 ratio to the number 10?  Choose the correct choice from the following choices
A) 36	B) 50	C) 76	D) 56	E) 62

Solution: 5:1 = x: 10   x = 50   Answer: 50
Answer: B
How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? Select the correct option:
A) 11  B) 30  C) 99  D) 88  E) 61

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18 = 50/3 m/sec.   Time taken to pass the man = 500 * 3/50= 
500 * 3/50 = 30
30 sec.   Answer: 30
Answer: B
How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
Choose the most appropriate option.
A) 2	B) 4	C) 6	D) 8	E) 10

Solution: 132 = 4 x 3 x 11   So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.   264 11,3,4 (/)   396 11,3,4 (/)   462 11,3 (X)   792 11,3,4 (/)   968 11,4 (X)   2178 11,3 (X)   5184 3,4 (X)   6336 11,3,4 (/)   Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.   Required number of number = 4.   4
Answer: B
If the wheel is 14 cm then the number of revolutions to cover a distance of 1056 cm is?	Choose the correct choice from the following answers:
A) 15	B) 10	C) 14	D) 12	E) 11

Solution: 2 * 22/7 * 14 * x = 1056 => x = 12   ANSWER:12
Answer: D
From a total of 4 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls? Select
A) 16  B) 36  C) 60  D) 120  E) 240

Solution: Answer=36=36   No of 4 person committees that can be formed=4C2*4C2=36   Answer 36
Answer: B
A train 650 m long is running at a speed of 81 km/hr. In what time will it pass a bridge 340 m long?	Choose the correct choice from the following:  A) 42  B) 43  C) 44  D) 45  E) 46

Solution: Speed = 81 * 5/18 = 45/2 m/sec   Total distance covered = 650 + 340= 
650 + 340 = 990
990 m   Required time= 990 * 2/45= 
990 * 2/45 = 44
44 sec   Answer: 44
Answer: C
A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 20% less than the price each head sold for the day before.what was the gross profit on this shipment? Choose the correct choice.
A) $100	B) $115	C) $125	D) $130	E) $135

Solution: Sol:   1500 heads -> $600   1 head -> $600/1500   1 head -> $(2/5)   25% more of (2/5) -> 125/100 * 2/5 = $(1/2)   He sold   2/3*1500= 
  2/3*1500 = 1_000
1000 heads for $(1/2) per head   Total revenue by selling 1000 heads= 1000 * 1/2= 
1000 * 1/2 = 500
$500   Heads left: 500   Cost per head: 80% of the previous price: 80/100 * 1/2= $(2/5)   Total revenue by selling 500 heads = 2/5 * 500= 
2/5 * 500 = 200
200   Total revenue after selling 1500 cabbage heads - 200+500= $700   Money spent on the purchase: $600   Profit = 700-600= 
700-600 = 100
$100   $100ns: $100
Answer: A
A man started a business investing Rs.70,000. Rakhi joined him after six months with an amount of Rs.1,05,000 and Sagar joined them with Rs.1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?	Choose the correct choice from the following answers.
A) 7 : 6 : 10  B) 12 : 15 : 16  C) 42 : 45 : 56  D) cannot be determined  E) None

Solution: Solution   Aman : Rakhi : Sagar	=(70,000 x 36):(1,05,000 x 30):(1,40,000 x 24)   = 12 : 15 : 16.   Answer 12 : 15 : 16
Answer: B
The probability of pulling a black ball out of a glass jar is 1/X. The probability of pulling a black ball out of a glass jar and breaking the jar is 1/Y. What is the probability of breaking the jar?
Choose one.
A) 1/(XY).	B) X/Y.	C) Y/X.	D) 1/(X+Y).	E) 1/(X-Y).

Solution: Let the probability of breaking the jar= n   n*1/X = 1/Y   n= X/Y   X/Y. is the answer
Answer: B
In how many different number of ways 8 boys and 3 girls can sit on a shopa which can accommodate 4 persons?
Choose the correct choice from the following choices.
A) 7900  B) 7800  C) 5200  D) 6400  E) None

Solution: Option 'None'   11p4= 11x10x9x8 = 7920
Answer: E
Marts income is 30 percent more than Tims income and Tims income is 40 percent less than Juans income. What percentage of Juans income is Marts income  Pick
A) 124%  B) b) 120 %  C) c) 78 %  D) d) 80 %  E) e) 64 %

Solution: M = (130/100)T   T = (60/100)J   => M = (78/100)J   Answer c) 78 %.
Answer: C
On a map, 1 inch represents 28 miles. How many X XXinches would be necessary to represent a distance of 383.6 miles?  Choose one:
A) 5.2
B) 7.4
C) 13.7
D) 21.2
E) 28.7

Solution: X inches necessary to represent a distance of 383.6 miles = 383.6/28= 
383.6/28 = 13.7
13.7   Answer 13.7
Answer: C
There are 6 people and 6 chairs. In how many different ways people can occupy the chairs?  Select:
A) 12	B) 15	C) 720	D) 36	E) 120

Solution: number of ways =6! = 720   Answer is 720
Answer: C
When two coins are tossed, Find the probability of getting all t ails?	Pick one.
A) 1/3	B) 3/4	C) 1/8	D) 3/8	E) P(E) =1/4

Solution: When two coins are tossed,   S = {HH, HT, TH, TT} where H = Head and T = Tail   Let P( =1/4 = event of getting all tails   Then P( =1/4 = {TT}   so, P(P( =1/4) = n(P( =1/4)/n(S) =1/4
Answer: E
A, B and C start swimming in a pool simultaneously from the same end. To complete 12 laps, A takes 10 minutes, B takes 8 minutes and C takes 6 minutes. What is the ratio of speeds A:B:C?  Options: A) 3:4:5 B) 10:15:20 C) 5:4:3 D) 4:6:5 E) 12:15:25

Solution: The slowest one is A, then comes B and the fastest one is C. So, the the ratio of speeds A:B:C must be in ascending order. Eliminate options C, D, and E.   A's speed (distance)/(time) = 12/10 = 6/5 lap per minute = 10 laps in 10 minute;   B's speed (distance)/(time) = 12/8 = 3/2 lap per minute = 15 laps in 10 minutes;   C's speed (distance)/(time) = 12/6= 
12/6 = 2
2 lap per minute= 20 laps in 10 minutes/   Therefore, the the ratio of speeds A:B:C is 12:15:20.   Answer: 10:15:20.
Answer: B
A woman complete a journey in 15 hours. She travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.  Choose one.
A) 336 km.	B) 216 km.	C) 314 km.	D) 224 km.	E) 544 km.

Solution: 0.5x/21 + 0.5x/24 = 15   --> x/21 + x/24 = 30   --> x = 336 km.   336 km.
Answer: A
P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 50 days to complete the same work. then Q alone can do it in  Pick one
A) 30 days  B) 25 days  C) 20 days  D) 15 days  E) 10days

Solution: Explanation :   Work done by P and Q in 1 day = 1/10   Work done by R in 1 day = 1/50   Work done by P, Q and R in 1 day = 1/10 + 1/50 = 6/50   But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as   Work done by P in 1 day × 2 = 6/50   => Work done by P in 1 day = 3/50   => Work done by Q and R in 1 day = 3/50   Hence work done by Q in 1 day = 3/50 – 1/50 = 2/50 = 1/25   So Q alone can do the work in 25 days   Answer : Option 25 days
Answer: B