MU-NLPC/Calc-aqua_rat huggingface dataset:
The ratio between the speeds of two persons is 7:8.If the second main runs 400 km in 4 hours,then find the speed of the another person? Select the correct option.
A) 91.6km/hr  B) 87.5km/hr  C) 80.5 km/hr  D) 92 km/hr  E) 120.1 km/hr

Solution: Let the speed of two persons be 7x and 8x km/hr   8x=400/4= 
400/4 = 100
100/8= 
100/8 = 25/2 = around 12.5
12.5   Speed of first person=(7*12.5)km/hr   =87.5 km/hr   Answer is option 87.5km/hr
Answer: B
The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?	Select:
A) 08 a.m.	B) 09 a.m.	C) 12 a.m.	D) 10 a.m.	E) 07 a.m.

Solution: D   10 a.m.   D = 110 – 20 = 90   RS = 20 + 25= 
20 + 25 = 45
45   T= 90/45= 
90/45 = 2
2 hours   8 a.m. + 2= 10 a.m.
Answer: D
In a certain group of 10 members, 4 members teach only French and the rest teach only Spanish or German. If the group is to choose 4-member committee, which must have at least 1 member who teaches French, how many different committee can be chosen ? Choose the correct choice from the following.
A) 174  B) 171  C) 186  D) 196  E) 200

Solution: Case 1   1french 3either German or Spanish: 4C1 * 6C3 = 80   Case 2   2french 2either German or Spanish: 4C2 * 6C2 = 90   Case 3   4french 4C4 = 1   Answer is 171 = 171
Answer: B
Rectangular tile each of size 80cm by 40cm must be laid horizontally on a rectangular floor of size 130cm by 230cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:  Choose the correct option:
A) 6	B) 2	C) 8	D) 9	E) 7

Solution: Area of tile = 80*40= 
80*40 = 3_200
3200   Area of floor= 130*230= 
130*230 = 29_900
29900   No of tiles= 29900/3200 = 9.34   So, the no of tile = 9   ANSWER:9
Answer: D
There are two numbers. If 60% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?  Options:	A) 5/12	B) 5/7	C) 5/3	D) 5/8	E) 5/1

Solution: Let the two numbers be x and y.   60/100 * x + y = 5/4y   => 3/5 x = 1/4 y => x/y   = 5/12   5/12nswer: 5/12
Answer: A
At what rate percent per annum will a sum of money double in 9 years.  Answers.
A) 12.5%
B) 13.5%
C) 11.5%
D) 11.1%
E) 21.5%

Solution: Let principal = P, Then, S.I.=P and Time=8 years   Rate = [(100 x P)/ (P x 9)]% = 11.1% per annum. Answer: 11.1%
Answer: D
A dishonest dealer professes to sell goods at the cost price but uses a weight of 600 grams per kg, what is his percent?  Pick one
A) 11  B) 25  C) 66  D) 88  E) 11

Solution: 600 --- 400   100 --- ? => 66%   Answer:66
Answer: C
A certain car dealership offers its newest model in ten exterior and nine interior colors. If the ten interior colors are identical to the nine exterior colors, and the dealership sells every pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible? Choose the correct choice from the following answers.
A) 45 B) 81 C) 90 D) 10!/2! E) 10!

Solution: I lined up the 10 different colours for Exterion and Interior like this:   E: A B C D E F G H I J   I: A B C D E F G H I J   I calculated the number of combinations:   10*10= 
  10*10 = 100
100 combinations.   But, from these 100 we need to delete sth: the same colours.   There are 10 possible pairs of coulours that will be the same. So, I deleted these 10 pairs from 100, resulting in 81.   Mind here, that the 10 do not result in 20 colours, because 1 pair is one unit that is not allowed. So, 10 units are not allowed (surprised that 80 wasn't among the answer options to confuse test takers...).   81
Answer: B
Sum of the squares of three numbers is 363 and the sum of their products taken two at a time is 131. Find the sum? Choose the correct answer:
A) 20 B) 22 C) 25 D) 27 E) 29

Solution: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 363 + 2* 131   a + b + c = √625 = 25   25
Answer: C
If a is a positive number and 1/4 the square root of a is equal to 2a, then a =
Answers.
A) 1/64	B) 1/16	C) 1/2	D) 4	E) 16

Solution: 1/4 of sqrt(a) = 2a, which means that sqrt(a) = 8a   or a = 64a^2 -> divide by a   1=64a   a=1/64   1/64.
Answer: A
In March, Bill ran an average of 1 mile an hour. If by June he had increased his pace by 10 seconds per mile, then which of the following expresses the number of hours it would take Bill to complete one mile in June?	Choices:
A) 3590/60^2
B) 2410/60^2
C) 2390/60^2
D) 3586/60
E) 60^2/3590

Solution: Bill ran at an average of 1 mile/hour in march. So to run 1 mile he would take 1 hour = (60 * 60)= 
(60 * 60) = 3_600
3600 seconds.   If he increases his speed by 10 seconds, he will complete a mile in 3590 seconds. Converting in hours= 3590/(60 * 60) = 3590/(60^2)   3590/60^2NSWER: 3590/60^2
Answer: A
If positive integers x is even and y is odd, which of the following must be odd?	Choose the correct choice from the following choices
A) 2xy B) 3x+y-1 C) x+y D) x + y -1 E) 3(x + y) - 3

Solution: Let x = 2 and y = 1   2xy = 2*2*1= 
2*2*1 = 4
4   3x+y-1= 3*2 + 1 -1= 
3*2 + 1 -1 = 6
6   x+y= 2+1= 
2+1 = 3
3   x+y-1= 2+1-1= 
2+1-1 = 2
2   3(x+y) - 3= 6+3-3= 
6+3-3 = 6
6   Answer: x+y
Answer: C
A car crosses a 600 m long bridge in 5 minutes. Whatis the speed of car in km per hour? Choose the correct choice:
A) 7 km/hr	B) 7.2 km/hr	C) 8 km/hr	D) 8.2 km/hr	E) 8.3 km/hr

Solution: Speed = 600 m/sec.   5 x 60   = 2 m/sec.   Converting m/sec to km/hr (see important formulas section)   = 2 x 18 km/hr   5   = 7.2 km/hr   7.2 km/hr
Answer: B
Last year the price range (per kg) for 100 varieties of apples in wholesale market was $1,00. If the prices of each of the 100 varieties increased by 10 percent this year over what it was last year, what is the range of the wholesale prices of the 1000 varieties of apples this year? Options:  A) $ 50  B) $ 100  C) $ 110  D) $600  E) $300

Solution: let the lowest price be x.   Therefore, highest price is x +100.   Now price of each variety is increased by 10%.   Therefore the price will remain arranged in the same order as before.   or Lowest price = 1.1x and Highest = 1.1 * (x+100)   or Range = highest - lowest = 1.1 * (x+100) - 1.1x   = 110, Hence, $ 110
Answer: C
A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $3,500. If the price of the car in 1996 was $22,000, what is the car's price in 2002? Options:
A) $18,400
B) $19,500
C) $22,200
D) $20,400
E) $21,100

Solution: Price in 96 = 22000   Price decrease each year = 2.5/100*22000= 
2.5/100*22000 = 550
550   Price in 97= 22000 - 550   Price in 98 = 22000 - 2*550   Price in 99 = 22000 - 3*550   Price in 00 = 22000 - 4*550   Price in 01 = 22000 - 5*550   Price in 02 = 22000 - 6*550= 
22000 - 6*550 = 18_700
18700   Investment in the car= 3500   Net price of the car in 02 = 18700 + 3500= 
18700 + 3500 = 22_200
$22200   $22,200orrect Option: $22,200
Answer: C
A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10^4 -10^2)(0.0019)?	Pick:
A) 25 B) 20 C) 21 D) 18.81 E) 22

Solution: You get 10^2 (100-1) (.0019)   we know   19/10000= 
  19/10000 = 19/10_000 = around 0.0019
.0019   10^2 (99) * (19/10000)   10^2= 100 and 100^2 = 10000   Cancel out the 100 with the 10^2   Left with 99(19/100).   0.99*19= 
0.99*19 = 18.81
18.81   Answer : 18.81
Answer: D
Two assembly line inspectors, smithy and glen, inspect widgets as they come off the assembly line. If smithy inspects every fifth widget, starting with the fifth, and glen inspects every third, starting with the third, how many of the 98 widgets produced in the first hour of operation are not inspected by either inspector?	Choose the correct option
A) 50  B) 53  C) 55  D) 60  E) 65

Solution: Widgets inspected by smithy: ((95-5)/5)+1=18+1= 
18+1 = 19
19   Widgets inspected by glen: ((96-3)/3)+1=31+1= 
31+1 = 32
32   Widgets inspected by both: ((90-15)+1=6   Total :   19+32 -6= 
  19+32 -6 = 45
45   hence, widgets not inspected: 98-45= 
98-45 = 53
53   Option 53
Answer: B
A booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 2400 . The emptying capacity of the tank is 10 per minute heigher than its filling capacity and the pump needs 8 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pump?	Choose the correct option:
A) 50 m^3/min  B) 90 m^3/min  C) 50 m^9/min  D) 59 m^3/min  E) 50 m^4/min

Solution: Explanation:   Let the filling capacity of the pump be x /min.   Then, emptying capacity of the pump=(x+10) /min.   so,   50 m^3/minnswer: 50 m^3/min) 50 m^3/min
Answer: A
The annual budget of a certain college is to be shown on a circle graph. If the size of each sector of the graph is to be proportional to the amount of the budget it represents, how many degrees of the circle should be used to represent an item that is 20 percent of the budget?
Choose the correct option:	A) 15 °	B) 36 °	C) 54 °	D) 72 °	E) 150 °

Solution: 100 percent = 360 degrees   20 percent = 360*20/100= 
360*20/100 = 72
72 degrees   Answer is 72 °.
Answer: D
Marts income is 50 percent more than Tims income and Tims income is 40 percent less than Juans income. What percentage of Juans income is Marts income	Choose the correct choice from the following options
A) 124% B) b) 120 % C) c) 96 % D) d) 90 % E) e) 64 %

Solution: M = (150/100)T   T = (60/100)J   => M = (90/100)J   Answer d) 90 %.
Answer: D
Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 60. He was allowed to drop his lowest score. After doing so, his average test score improved to 65. What is the lowest test score that was dropped? Choose the correct choice from the following choices
A) 20
B) 45
C) 55
D) 65
E) 80

Solution: The arithmetic mean of 4 equally weighted tests was 60. So what we can assume is that we have 4 test scores, each 60.   He dropped his lowest score and the avg went to 65. This means that the lowest score was not 60 and other three scores had given the lowest score 5 each to make it up to 60 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was  3 *5= 
 3 *5 = 15
15 less than 60.   So the lowest score= 60 - 15= 
60 - 15 = 45
45   Answer (45)
Answer: B
A batsman makes a score of 87 runs in the 17th inning and thus increases his avg by 3. Find his average after 17th inning.	Choose the correct answer:
A) 12
B) 39
C) 43
D) 52
E) 34

Solution: Let the average after 17th inning = x.   Then, average after 16th inning = (x - 3).   :. 16 (x - 3) + 87 = 17x or x = (87 - 48)= 
(87 - 48) = 39
39.   Ans: 39
Answer: B
Pipes A and B can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full? Choose the correct choice from the following choices
A) 16	B) 12	C) 14	D) 61	E) 51

Solution: 1/8 + 1/24   = 1/6   6 * 2= 
6 * 2 = 12
12   Answer:12
Answer: B
A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 6.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993 ?  Choose the correct answer.
A) 16.5%
B) 14%
C) 35%
D) 55%
E) 65%

Solution: The amount by which employment costs rose is equal to 0.035(salary costs + fringe benefit costs);   On the other hand the amount by which employment costs rose is equal to 0.03*salary costs + 0.065*fringe benefit costs;   So, 35(S+F) = 30S+65F --> S = 6F --> F/S = 1/6 --> F/(S+F) = 1/(1+6) = 1/7 = 0.14.   Answer: 14%.
Answer: B
Mr. Das decided to walk down the escalator of a mall. He found that if he walks down 26 steps, he requires 30seconds to reach the bottom. However, if he steps down 34 stair she would only require 18 seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom, find out the height of the stair way insteps?
Select the correct option.
A) 5	B) 6	C) 7	D) 8	E) 9

Solution: here when he step down 26 steps he has 30 seconds for remaining steps.   if he step down 34 stairs he has only 18 sec.   30-18= 
30-18 = 12
12   12 secs for 8 steps..   18 secs for 12 steps.   12+34= 
12+34 = 46
46   so ans is 46..   ANSWER:6
Answer: B
Find the fourth proportional to 2.4, 4.6 and 7.6?
Choose the correct option:
A) 14
B) 14.657
C) 15.56
D) 14.56
E) None of these

Solution: Explanation:   Formula = Fourth propotional = (b × c)/a   A = 2.4 , B = 4.6 and C = 7.6   (4.6 × 7.6)/2.4 = 14.56   Answer: Option 14.56
Answer: D
The sum of first five prime numbers is?
Choose the correct choice from the following answers:  A) 20  B) 25  C) 26  D) 28  E) 31

Solution: Required sum = (2 + 3 + 5 + 7 + 11)= 
(2 + 3 + 5 + 7 + 11) = 28
28.   Note: 1 is not a prime number.   28efinition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself   Option 28
Answer: D
The average (arithmetic mean) of all scores on a certain algebra test was 90. If the average of the 8 male students’ grades was 83, and the average of the female students’ grades was 92, how many female students took the test?	Choose the most appropriate option
A) 8 B) 9 C) 10 D) 21 E) 28

Solution: Total Marks of male = M   Total Marks of female = F   Number of males = 8   Number of females = f   Given: (M+F)/(8+f) = 90 -------------1   Also given, M/8 = 83 Thus M = 664 ---------2   Also, F/f = 92 thus F = 92 F - --------3   Put 2 and 3 in 1: we get   (664+92f)/(8+f) = 90   solving this we get f = 28   Ans: 28
Answer: E
If 6 cats can kill 6 rats in 6 minutes, how long will it take 100 cats to kill 100 rats?  Choose the most appropriate option:
A) 1 minutes
B) 2 minutes
C) 3 minutes
D) 4 minutes
E) 6 minutes

Solution: It will take 6 minutes for 100 cats to kill 100 rats.   1 cat can kill 1 rat in 6 minutes, so 100 cats can kill 100 rats in 6 minutes   Answer 6 minutes
Answer: E
Two identical machines have the ability to produce both nuts and bolts. However, it takes 1 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,400 nuts and 1,400 bolts?	Choose the correct answer:
A) 1,250 seconds
B) 1,500 seconds
C) 1,750 seconds
D) 2,100 seconds
E) 3,000 seconds

Solution: I used the Rate formula (R=\frac{1}{T})   Rate of 1st machine = Rate of making 1 bolt + Rate of making 1 nut = 1 + \frac{1}{2}   Rate of 1st machine = Rate of 2nd machine   After this I got lost.   Please can you help how to approach using algebra?   I wouldn't complicate:   1 machine needs 1,400*1 seconds to produce 1,400 bolts, so 2 need half of that, so 1,400/2 seconds.=700   1 machine needs 1,400*2 seconds to produce 1,400 nuts, so 2 need half of that, so 1,400*2/2 seconds.=1400   total = 2100 sec   2,100 seconds
Answer: D
L.C.M of two prime numbers x and y (x>y) is 161. The value of 3y-x is :  Pick
A) -2	B) -1	C) 1	D) 2	E) 0

Solution: Explanation:   H. C. F of two prime numbers is 1. Product of numbers = 1 x 161 = 161.   Let the numbers be a and b . Then , ab= 161.   Now, co-primes with product 161 are (1, 161) and (7, 23).   Since x and y are prime numbers and x >y , we have x=23 and y=7.   inline fn_jvn therefore 3y-x = (3 x 7)-23 = -2 . -2nswer: -2
Answer: A
A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 1 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?	Choose the correct choice from the following choices:
A) 0.5< t < 0.75  B) 1.75< t < 2.0  C) 6.0 < t < 6.5  D) 2.5 < t < 3.0  E) 3 < t < 3.5

Solution: D=2, and R=1   circumference thus is 2pi miles   we know that she walked 1mph   knowing the formula rt=D, we can deduce that t= D/r   D is 2pi miles and r is 1mph   t = 2pi/1   pi can be rewritten as 22/7   2*22/7 = 44/7 and multiply this by 1/1 = 44/7. This is greater than 6, but less than 6.5, therefore, 6<t<6.5. Answer choice 6.0 < t < 6.5.
Answer: C
In how many ways can 4 men and 3 women can arrange with a condition that each men should not sit together and they must be in the order of their age.  Choose the correct choice from the following answers.
A) 210	B) 5040	C) 120	D) 110	E) none of these

Solution: 4 men can take 4 position which can be done in 4!   and women can be sit in 3! ways so 4!*3!   ANSWnone of theseR:none of these
Answer: E
If an object travels at nine feet per second, how many feet does it travel in one hour?
Select the correct option
A) 30 B) 300 C) 720 D) 1800 E) 32400

Solution: Speed = 9 feet per second.   1 Hour= 60X60 Seconds = 3600 Seconds.   Total no of feet traveled in 1 hour = 3600X9 = 32400   Answer 32400
Answer: E
A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?	Select the correct option
A) 5 minutes B) 6 minutes C) 8 minutes D) 9 minutes E) 10 minutes

Solution: Let's say the distance between the buses is d. We want to determine Interval=\frac{d}{b}, where b is the speed of bus.   Let the speed of cyclist be c.   Every 12 minutes a bus overtakes cyclist: \frac{d}{b-c}=12, d=12b-12c;   Every 4 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=4, d=4b+4c;   d=12b-12c=4b+4c, --> b=2c, --> d=12b-6b=6b.   Interval12 -6= 
12 -6 = 6
6b.   Interval=\frac{d}{b}=\frac{6b}{b}=6   Answer: 6 minutes (6 minutes).
Answer: B
P software has coding line 5% more than N, N software has coding line 1/3 more than M. M software has 90 lines of coding. find P lines. Choose the most appropriate option.
A) 106	B) 107	C) 126	D) 109	E) 110

Solution: M s/w has 90 line of code   N s/w has = 90+90*1/3= 
90+90*1/3 = 120
120 line of code   P s/w 5% more N' code 120+6= 
120+6 = 126
126   ANSWER:126
Answer: C
In a locality, the prevailing price of a 700 square feet property last year was US Dollar 1000. The owner made some additions and the 900 square feet property is now fetching a price of US Dollar 1500. By approximately what percent did the ratio of price to size increase from the previous year's price?	Choose the correct choice.
A) 12  B) 14  C) 17  D) 21  E) 19

Solution: Initial price/area ratio = 1000/700 = 9000/6300   Revised mileage/weight ratio = 1500/900 = 10500/6300   Answer: 17
Answer: C
On dividing 271 by a number, the quotient is 9 and the remainder is 1. Find the divisor?
Choose the correct choice from the following answers:
A) A)12
B) B)15
C) C)16
D) D)17
E) E)30

Solution: d = (D-R)/Q   = (271 - 1)/9   = 270/9= 
270/9 = 30
30   30)
Answer: E
If 5 machines can produce 20 units in 10 hours, how long would it take 10 to produce 80 units?  Answers
A) 63  B) 20  C) 42  D) 65  E) 84

Solution: 5 machines would produce 80 units in 40 hours. Increasing the amount of machines by 2 would mean dividing 40 hours by 2.   40/2= 
40/2 = 20
20   Answer : 20
Answer: B
There is a square with sides of 9. What is the area of the biggest circle that can be cut out of this square?
Choose the correct choice from the following choices.
A) 72.83 B) 63.62 C) 81 D) 254.47 E) 100

Solution: Area of a circle = area=Ï€r^2   Square is 9 wide, so circle's diameter would be 9, and radius would be 4.5   area=Ï€4.5^2 which is approximately 63.62   Answer is 63.62
Answer: B
There are 8 stations between Vijayawada and Chennai. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?  Options:
A) 100 B) 90 C) 190 D) 110 E) 105

Solution: The total number of stations = 10   From 10 stations we have to choose any two stations and the direction of travel (i.e.,Vijayawada to Chennai is different from Chennai to Vijayawada) in 10P2 ways.   10P2= 10 * 9= 
10 * 9 = 90
90   ANSWER: 90
Answer: B
In how many ways can the letters of the English alphabets be arranged so that there are seven letters between the letters A and B, and no letter is repeated?	Pick one.
A) 24P7*2*18! B) 24P7*2*20! C) 18*24! D) 36*24! E) 36*25!

Solution: first we can arrange 7 letter b/w in 24p7 way   then 24P7*2*18! and B can be arrenge in *2 way so total is 24p7*2   no consider this 9 letter as 1 number so remainin number can be arrange in   (26-9+1)!   so ans = 24p7*2*18!   24P7*2*18!NSWER:24P7*2*18!
Answer: A
Which of the following CANNOT be a product of two distinct positive integers X and Y?	Choose the correct option
A) X	B) Y	C) 3Y + 2X	D) Y - X	E) YX

Solution: In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with   take X = 1 and Y = 2 and work with the options   XY = 2   A) X take X =2, Y = 1   B) Y take X = 1 Y = 2   C) 3Y + 2X Seems tricky, lets see other options and then come back to it.   D) Y - X take Y = 1 and X = 2 --> Y - X = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them?   E) YX Always true   You don't even have to worry what C is !   ans Y - X
Answer: D
How many cubes of 10cm edge can be put in a cubical box of 1m edge Choices
A) 10	B) 100	C) 1000	D) 10000	E) None of these

Solution: Explanation:   number of cubes=(100 x 100 x 100)/(10 x 10 x 10)=1000   Answer: 1000
Answer: C
In what time a sum of money double itself at 5% per annum simple interest?	Choose the correct choice:
A) 33 1/8%
B) 20%
C) 83 1/3%
D) 33 4/3%
E) 73 1/3%

Solution: P = (P*5*R)/100   R = 20%   Answer:20%
Answer: B
3 years before age of A was double than age of B.after 7 years the sum of their ages will 83.calculate the age of A.	Options:  A) 24  B) 21  C) 40  D) 45  E) 42

Solution: Let 3 years before age of B=x year and age of A=2x year   present age of B=(x+3) and present age of A=(2x+3)   after 7 years age of B=(x+10) year and age of A=(2x+10) year   (x+10)+(2x+10)=83,3x=63,x=21.   present age of A=(2x+3)=45 years   answer 45
Answer: D
A started a business with 4500 and another person B joined after some period with 3000. Determine this period after B joined the business if the profit at the end of the year is divided in the ratio 2 : 1	Select: A) After 3 months B) After 4 months C) After 6 months D) After 2 1⁄2 months E) None of these

Solution: Let B joined after x months.   Then, 4500 × 12 : 3000 (12 – x) = 2 : 1   Ratio of their investments   4500×12/3000(12−x)=2/1 ⇒ x = 3   After 3 monthsnswer After 3 months
Answer: A
A total of 525 players participated in a single tennis knock out tournament. What is the total number of matches played in the tournament? (Knockout means if a player loses, he is out of the tournament). No match ends in a tie.	Choose the correct choice:
A) 511 B) 512 C) 256 D) 524 E) 1023

Solution: There are 525 players, only 1 person wins, 524 players lose. in order to lose, you must have lost a game.   524 games.   Ans- 524
Answer: D
A retail item is offered at a discount of x percent (where x > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of x, would result in the same final price?	Choose the correct option
A) x+5/1.05
B) x/1.05 +5
C) 1.05x-5
D) x-5/1.05
E) 1.05(x – 5)

Solution: Let y be the price of the item.   Final price after discount and sales tax = y * (1 - x/100) * 1.05   Let z be the percent discount which would result in the same final price.   Then,   y * (1 - x/100) * 1.05 = y * (1 - z/100)   => 1.05 - 1.05x/100 = 1 - z/100   => z/100 = 1.05x/100 - .05   => z = 1.05x - 5   Hence ,option 1.05x-5 is correct.
Answer: C