MU-NLPC/Calc-aqua_rat huggingface dataset:
A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 16 months?  Select the correct option.
A) 18:11
B) 16:11
C) 18:19
D) 18:121
E) 18:112

Solution: A invests Rs.8000 for 16 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.   A : 16:11   8000*16 : (8000*4) + (4000*14)   128000 : 88000   A:16:11 = 16:11.Answer:16:11
Answer: B
Worker A takes 10 hours to do a job. Worker B takes 12 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
Choose the correct choice from the following answers:
A) 40 days  B) 40/9 days  C) 60/11 days  D) 30/9 days  E) 60/9 days

Solution: A's one hour work = 1/10.   B's one hour work = 1/12.   (A+B)'s one hour work = 1/10+1/12 = 11/60.   Both A & B can finish the work in 60/11 days   60/11 days
Answer: C
The simple form of the ratio 4/2:2/5 is?
Choices.
A) 10:6
B) 5:1
C) 15:3
D) 25:3
E) 30:3

Solution: 4/2 : 2/5 = 20:4 = 5:1   ANSWER:5:1
Answer: B
What is the smallest no. which must be added to 8261955 so as to obtain a sum which is divisible by 11? Choose the correct choice from the following
A) 1  B) 2  C) 4  D) 6  E) 8

Solution: For divisibility by 11, the difference of sums of digits at even and odd places must be either zero or divisible by 11.   For 8261955, Difference =(8+6+9+5) -(2+1+5)=28-8= 
28-8 = 20
20.   The units digit is at odd place. So we add 2 to the number=> 8261955 +2= 
8261955 +2 = 8_261_957
8261957   Now , (8+6+9+7) -(2+1+5)=30-8= 
30-8 = 22
22=> 22 is a multiple of 11 and hence 8261957 is also divisible by 11   2
Answer: B
A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 700 m long?	Choose the correct answer:
A) 94sec
B) 90sec
C) 85sec
D) 80sec
E) 76sec

Solution: Speed = 240/24= 
240/24 = 10
10 m/sec.   Required time= (240 + 700)/10= 
(240 + 700)/10 = 94
94 sec.   94secnswer:94sec
Answer: A
There are 5 cars to be displayed in 5 parking spaces with all the cars facing the same direction. Of the 5 cars, 3 are red, 1 is blue and 1 is yellow. If the cars are identical except for color, how many different display arrangements of the 5 cars are possible?
Options:
A) 20 B) 25 C) 40 D) 60 E) 125

Solution: I think the above logic is correct except one thing:   # of arrangements is 5!3!=205!3!=20.   But a car can be arranged facing TWO directions (within one particular parking space), so we should multiply 20 by 2, 20∗2=4020∗2=40   Answer: 40.
Answer: C
If w is 40 percent less than e, e is 40 percent less than y, and z is 46 percent less than y, then z is greater than w by what percent of w?
Choices:
A) 4%  B) 18%  C) 36%  D) 40%  E) 50%

Solution: GIven w= 0.6e, e=0.6y, z=0.54y, substituting, w=2/3 Z----> z= 1.5w and thus z is 50% greater than w. 50% is the correct answer.
Answer: E
Which of the following is NOT the sum of the squares of two integers?  Choose the correct option
A) 36
B) 37
C) 65
D) 146
E) 147

Solution: List the numbers that are smaller than the given options - 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.   (A) 36 - 9+25. NO.   (B) 37 - 1+36. NO.   (C) 65 - 1+64. NO.   (D) 146 - 25+121. NO.   (E) - must be the answer.   ANSW147R:147
Answer: E
Which of the following cannot be the square of an integer  Pick one:
A) 275625
B) 385641
C) 227529
D) 261121
E) 426408

Solution: The square of an integer (n^2) can have only the following units digit:   0, if the units digit of n is 0;   1, if the units digit of n is 1 or 9;   4, if the units digit of n is 2 or 8.   5, if the units digit of n is 5;   6, if the units digit of n is 6 or 4;   9, if the units digit of n is 3 or 7.   As, you can see the square of an integer cannot have the units digit of 2, 3, 7, or 8.   Answer: 426408.
Answer: E
Two cubes of their volumes in the ratio 64 : 125. The ratio of their surface area is:
Choose the correct option:
A) 1.5:5
B) 2:5
C) 3:5
D) 1:5
E) 4:5

Solution: The ratio of their surface area is   64 : 125   4 : 5   Answer is 4:5.
Answer: E
Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is ?  Choose the correct choice from the following answers:	A) 17/26	B) 17/29	C) 17/24	D) 17/20	E) 17/21

Solution: n(S) = 20   n(Even no) = 10 = n(E)   n(Prime no) = 8 = n(P)   P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20   Answer: 17/20
Answer: D
What is the banker's discount if the true discount on a bill of Rs.540 is Rs.90 ?
Choose the correct choice from the following answers:
A) Rs. 108  B) Rs. 120  C) Rs. 102  D) Rs. 106  E) None of these

Solution: Explanation :   Present Worth, PW = F - TD = 540 - 90 = Rs. 450   Simple Interest on the Present Worth = True Discount   Hence Simple Interest on 450 = 90 ------(Equation 1)   Simple Interest on the face value = Bankers Discount   => Simple Interest on 540 = Bankers Discount   From Equation 1, Simple Interest on 450 = 90   Hence, Simple Interest on 540 = 90/450×540=540/5 = Rs. 108   => Bankers Discount = Rs. 108 Rs. 108nswer : Option Rs. 108
Answer: A
In one year, the population, of a village increased by 10% and in the next year, it decreased by 10%. If at the end of 2nd year, the population was 7920, what was it in the beginning?  Choices:
A) 3337
B) 8000
C) 2788
D) 2999
E) 1121

Solution: x*110/100 * 90/100 = 7920   X*0.99=7920   X=7920/0.99= 
7920/0.99 = 8_000
> 8000   Answer: 8000
Answer: B
During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 80 miles per hour. In terms of x, what was Francine's average speed for the entire trip?
Choose the correct choice
A) (180-x)/2  B) 4800/x+60  C) (300-x)/5  D) 600/(115-x)  E) 12,000/(x+200)

Solution: total distance =100 ;total time = T   t1 = x/40 t2 = 100-x /80   T =t1+t2 = x/30 + 100-x/80 = (80x + 3000- 30x)/2400   = (50x+3000)/2400   = x +60 / 48   av speed = 100*48/x+60 = 4800/x+60   4800/x+60
Answer: B
The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years  Answers:
A) 7:8
B) 7:9
C) 3:8
D) 5:8
E) 6:8

Solution: Explanation:   Let P age and Q age is 6x years and 7x years.   Then 7x - 6x = 4 <=> x = 4   So required ratio will be (6x+4): (7x+4) => 28:32 => 7:8   7:8nswer: Option 7:8
Answer: A
Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:	Options:
A) 3 9 /17 hours  B) 1 13 /17 hours  C) 2 8 /11 hours  D) 4 1 /2 hours  E) None of these

Solution: Explanation:   Solution 1   Pipes A and B can fill the tank in 5 and 6 hours respectively. Therefore,   part filled by pipe A in 1 hour =1/5   part filled by pipe B in 1 hour =1/6   Pipe C can empty the tank in 12 hours. Therefore,   part emptied by pipe C in 1 hour =1/12   Net part filled by Pipes A,B,C together in 1 hour =1/5 +1/6+1/12 =17/60   i.e., the tank can be filled in 60/17=3 9/17 hours.   3 9 /17 hoursNSWER IS 3 9 /17 hours
Answer: A
Simple interest on a certain sum is 9.8 over 20 of the sum. Find the rate per cent and time, if both are equal.
Select the correct option:
A) 7% and 7 years
B) 6% and 6 years
C) 10% and 10 years
D) 12 % and 12 years
E) None of these

Solution: 9.8â„20 P = PÃ—RÃ—R/100   â‡’ R2 = 980â„20=49 â‡’ R = 7%   7% and 7 yearslso, time = 7 years   7% and 7 yearsnswer 7% and 7 years
Answer: A
An businessman earns an income of Re 2 on the first day of his business. On every subsequent day, he earns an income which is just double of that made on the previous day. On the 20th day of business, he earns an income of:  Choose the correct option.
A) 21	B) 22	C) 36	D) 20	E) 30

Solution: 2nd day he earns = 2(2 – 2)   3rd day he earns = 2(3 – 2)   On 20th day he earns 2(20 -2) = 36 rupees   ANSWER:36
Answer: C
Walking 6/7th of his usual speed, a man is 12 minutes too late. The usual time taken by him to cover that distance is :
Select
A) 1 hr 20 min	B) 1 hr 10 min	C) 1 hr 11 min	D) 1 hr 12 min	E) None

Solution: Sol.   New speed = 6/7 of usual speed.   New time = 7/6 of usual time   ∴ [7/6 of usual time] - (usual time) = 1/5 hr.   ⇒ 1/6 of usual time = 1/5 hr ⇒ usual time = 6/5 hr = 1 hr 12 min.   Answer 1 hr 12 min
Answer: D
Raju age after 25 years will be 5 times his age 5 years back, What is the present age of Raju
Answers:
A) 28
B) 17
C) 10.21
D) 77
E) 12.5

Solution: Clearly,   x+25 = 5(x-5)   <=> 4x = 50 => x = 12.5   Answer:12.5
Answer: E
What is the least integer that is a sum of four different prime numbers each greater than 10?  Choose one.
A) 60
B) 62
C) 64
D) 66
E) 68

Solution: The sum of the four smallest primes greater than 10 is  11+13+17+19= 
 11+13+17+19 = 60
60.   The answer is 60.
Answer: A
At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 55 other employees of Company K, how many employees does Company K have?	Choose the correct choice from the following
A) 160	B) 180	C) 190	D) 200	E) 220

Solution: Let the total number of employees in the company be x   % of secretaries = 15%   % of salespeople = 60%   % of of employees other than secretaries and salespeople = 100 - 75= 
100 - 75 = 25
25%   But this number is given as 55   so 25% of x= 55   x = 220   Therefore there a total of 220 employees in the company K   Correct answer - 220
Answer: E
If you divide 7^93 by 5, which remainder do you get?	Choose the most appropriate option.
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: The units digit of 7^1 is 7.   The units digit of 7^2 is 9.   The units digit of 7^3 is 3.   The units digit of 7^4 is 1.   The units digit of 7^5 is 7.   etc...   The units digit of 7^n repeats in blocks of 4: {7, 9, 3, 1}   The remainder of 93/4 is 1.   So the units digit of 7^93 is 7.   The remainder of 7^93 / 5 is 2.   The answer is 2.
Answer: C
An athlete runs 200 meters race in 18sec. His speed is?  Choose the correct choice from the following
A) 20km/hr  B) 15km/hr  C) 30km/hr  D) 25km/hr  E) 40km/hr

Solution: speed = 200/18 = 100/9 m/sec   = 100/9 * 18/5 km/hr = 40km/hr   Answer is 40km/hr
Answer: E
The number of roots common between the two equations x3+3x2+4x+5=0x3+3x2+4x+5=0 and x3+2x2+7x+3=0x3+2x2+7x+3=0 is	Select the correct option:
A) 22
B) 27
C) 13
D) 88
E) 21

Solution: Here f(x) = x3+3x2+4x+5=0x3+3x2+4x+5=0 and g(x) = x3+2x2+7x+3=0x3+2x2+7x+3=0   To find the common roots we have to solve the equation f(x) - g(x) = 0   i.e. (x3+3x2+4x+5)(x3+3x2+4x+5) - (x3+2x2+7x+3)=0(x3+2x2+7x+3)=0   x2−3x+2=0x2−3x+2=0   x = 2, x = 1   These are the points of intersection f(x) and g(x). Whether these points are also the common root will have to be checked by putting these vales in f(x) = 0 and g(x) = 0.   For x = 2;   f(2) = g(2) = 43 ≠≠ 0. Hence 2 is not a common root but only a point of intersection.   For x = 1;   f(1) = g(1) = 13 ≠≠ 0. Again 1 is not a common root but a point of intersection. Hence, we find that the two equations do not have any common root between them.   Answer:13
Answer: C
If a quality control check is made inspecting a sample of 2 light bulbs from a box of 8 lighbulbs, how many different samples can be chosen?
Choose the correct choice from the following choices: A) 6 B) 28 C) 36 D) 66 E) 72

Solution: Try using the formula for combinations:   n!/r!(n-r)!   8!/2!(8-2)!   8!/2!*6!    8*7/2*1= 
 8*7/2*1 = 28
28   28
Answer: B
A boy want to make a cuboid of dimension 5m, 6m, 7m from small cubes of .04 m3. Later he realized he can make same cuboid by making it hollow. Then it takes some cubes less. What is the no. of these cubes?  Select:
A) 2150  B) 2250  C) 2350  D) 2850  E) 3250

Solution: volume of cuboid=5*6*7= 
5*6*7 = 210
210m3   volume of inner cuboid=(5-1)*(6-1)*(7-1)= 
(5-1)*(6-1)*(7-1) = 120
120m3   therefore,volume of hollow cuboid=210-120= 
210-120 = 90
90 m3   no of cubes required=90/.04= 
90/.04 = 2_250
2250 cubes   ANSWER:2250
Answer: B
If X,Y is 20%,25% greater than Z then how much percentage is X smaller than Y?
Choose the correct option:  A) 2  B) 4  C) 6  D) 7  E) 1

Solution: X=120%   Y=125%   Z=100%   X-Y/Y*100 = 5/125*100   ==>4%   ANSWER 4
Answer: B
A data set with a mean of 60 has a standard deviation of 8.7. Which of the following is the smallest number that falls within one standard deviation of the mean?	Pick one:
A) 51
B) 56
C) 59
D) 63.5
E) 65

Solution: One standard deviation of the mean is from{mean}-{deviation}=60-8.7= 
60-8.7 = 51.3
51.3 to{mean}+{deviation}=60+8.7=68.7. The smallest number within this range from the options is 51.   Answer: A.   Hope this helps.
Answer: A
Anne traveled from City A to City B in 4 hours, and her speed was between 20 miles per hour and 40 miles per hour. John traveled from City A to City B along the same route in 2 hours, and his speed was between 45 miles per hour and 60 miles per hour. Which of the following could be the distance, in miles, from City A to City B? Choose the correct option.
A) 95
B) 115
C) 125
D) 160
E) 180

Solution: In four hours Anne must travel 4 times her speed   so Anne's possible distances =   4(20 -40) or 80-160 miles   in two hours John travels 2 times his speed or   2(45-60) or 90-120 miles   the statement is only true if both distances are possible,   so you can tell its between or equal to   90-120   115 is the answer.
Answer: B
At the time of marriage, a man was 6 years elder to his wife. 14 years after their marriage, his age is 8/7 times the age of his wife. What was wife's age at the time of marriage ? Choose one answer.  Choose the correct choice from the following answers:  A) 36 years  B) 30 years  C) 28 years  D) 14 years  E) 26 years

Solution: let wifes age= x   husband age = x+6   now after 14 years of mrg x+14 wifes age   x+6+14 husbands age   8/7(x+14)=x+6+14   after solving x=28   ANSWER:28 years
Answer: C
g(a) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(y) is divisible by 4^11, what is the smallest possible value for a?
Select: A) 22 B) 24 C) 28 D) 32 E) 44

Solution: g(a)=4^11=2^22. So we have to find a product with atleast 22 2's in it.   in option 1 22 the total no of 2's = [22/2] + [22/4] +[22/8] +[22/16] = 11+5+2+1= 
11+5+2+1 = 19
19   in option 2 24 the total no of 2's= [24/2] + [24/4] +[24/8] +[24/16] = 12+6+3+1= 
12+6+3+1 = 22
22 . Hence 24
Answer: B
A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He
gains 14% on the whole. The Quantity sold at 18% profit is
Choose the correct option.
A) 300 B) 400 C) 600 D) 500 E) None of these

Solution: Explanation :   By the rule of alligation,we have   Profit% by selling 1st part Profit% by selling 2nd part   8 18   Net % profit   14   18-14= 
18-14 = 4
4 14-8=6   => Quantity of part1 : Quantity of part2 = 4 : 6 = 2 : 3   Total quantity is given as 1000Kg   So Quantity of part2 (Quantity sold at 18% profit) = 1000×35=600Kg   Answer : Option 600
Answer: C
A train 960 m long passed a pole in 24 sec. How long will it take to pass a platform 800 m long? Choose the correct choice:
A) 40	B) 44	C) 48	D) 52	E) 56

Solution: Speed = 960/24= 
960/24 = 40
40 m/sec.   Required time= (960 + 800)/40= 
(960 + 800)/40 = 44
44 sec.   Answer:44
Answer: B
All the students of class are told to sit in circle shape. Here the boy at the 6 th position is exactly opposite to 16 th boy. Total number of boys in the class?  Pick one:
A) 10	B) 15	C) 20	D) 25	E) 30

Solution: As half the circle shape consist of 16-6= 
16-6 = 10
10 boys,   So total number of boys in full circle=2*10= 
2*10 = 20
20   ANSWER:20
Answer: C
The speed of a boat in upstream is 75 kmph and the speed of the boat downstream is 115 kmph. Find the speed of the boat in still water and the speed of the stream?
Choose one
A) 20 kmph  B) 76 kmph  C) 12 kmph  D) 97 kmph  E) 15 kmph

Solution: Speed of the boat in still water   = (75+115)/2   = 90 kmph. Speed of the stream   = (115-75)/2= 
(115-75)/2 = 20
20 kmph.   20 kmphnswer:20 kmph
Answer: A
Data sufficiency question:
There are six people. Each cast one vote in favor of other five. Who won the elections?
i) 4 older cast their vote in favor of the oldest candidate
ii) 2 younger cast their vote to the second oldest	Choose the correct option:  A) 287  B) 27  C) 199  D) 17  E) 191

Solution: xplanation:   Total possible votes are 6. Of which 4 votes went to the oldest person. So he must have won the election. Statement 1 is sufficient.   Answer:17
Answer: D
A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?	Choose the correct answer:
A) 187  B) 200  C) 827  D) 289  E) 270

Solution: The number of ways to select two men and three women   = ⁵C₂ * ⁶C₃   = (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)= 
(5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2) = 200
200   Answer:200
Answer: B
What is the smallest positive integer x such that 864x is the cube of a positive integer Options
A) 6  B) 12  C) 9  D) 5  E) 2

Solution: Given 864x is a perfect cube   so we will take 1728= 12*12*12   864x = 1728   x =1728/864= 
1728/864 = 2
2   correct option is 2
Answer: E
The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 12 units?
Pick one.
A) 140 B) 99 C) 88 D) 72 E) 168

Solution: Given that the area of the square = 1225 sq.units   => Side of square = √1225 = 35 units   The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35= 
2/5 * 35 = 14
14 units   Given that breadth= 12 units   Area of the rectangle = lb = 14 * 12= 
14 * 12 = 168
168 sq.units   Answer: 168
Answer: E
A is twice as good a work man as B and together they finish a piece of work in 24 days.The number of days taken by A alone to finish the work is :	Choices:
A) 28 days.  B) 16 days.  C) 12 days.  D) 24 days.  E) 36 days.

Solution: Solution   (A’s 1 day’s work): (B’s 1 day’s work)= 2 : 1.   (A + B)'s 1 day’s work = 1/24   Divide 1/14 in the ratio 2 : 1.   ∴ A’s 1 day’s work = (1/24 x2/3)= 1/36   Hence,A alone can finish the work in 36 days.   Answer 36 days.
Answer: E
For a particular American football game, the probability of a team's quarterback throwing a completed pass on each throw is 3/10. What is the least number of times that the quarterback should throw the ball that will increase the probability of getting a completed pass at least once to more than 50%.	Choose one
A) 10
B) 5
C) 2
D) 3
E) 1

Solution: Rule of Subtraction: P(A) = 1 - P(A')   Rule of Multiplication: P(A ∩ B) = P(A) P(B)   The probability that the quarterback throws a completed pass at least once in 2 throws is 1- (7/10)^2 = 1 - 49/100 = 51/100 > 50%   Answer: 2
Answer: C
If x and y are multiples of 2 then which are all the multiples of 2
1) x*y
2) x^y
3) x+y
4) x-y
5) x/y	Select
A) 1,3	B) 1,2,4,5	C) 1,2,5	D) 1,2,3,4	E) all of these

Solution: x*y,x^y,x+y, x-Y are even numbers   ANSWER:1,2,3,4
Answer: D
A father was as old as his son's present at the time of your birth. If the father's age is 38 years now, the son's age 5years back was?
Choose the correct choice from the following choices:
A) 10 years B) 12 years C) 14 years D) 16 years E) 18 years

Solution: Let the son's present age be x years. Then, (38 - x) = x   2x = 38.   x = 19.   Son's age 5 years back (19 - 5)= 
(19 - 5) = 14
14 years.   14 years
Answer: C
what is the sum of the first 30 odd natural numbers Options
A) 300
B) 400
C) 900
D) 600
E) 700

Solution: sum of first n odd natural nuber is = n^2   so sum of the first 30 odd natural numbers=(30)^2=900   ans 900   ANSWER:900
Answer: C
How many times digit 10 is used while writing numbers from 100 to 1000? Choose the correct choice from the following answers
A) 100
B) 90
C) 85
D) 110
E) 120

Solution: in 100 to 300 there are 20 ten's   in 300 to 500 there are 20 ten's   in 500 to 700 there are 20 ten's   in 700 t0 900 there are 20 ten's   in 900 to 1000 there are 10 ten's   so total is 90 ten's   CORRECT OPTION :90
Answer: B
Workers at a campaign office have 3000 fliers to send out. If they send out 1/5 of them in the morning and 1/4 of the remaining ones out during the afternoon, how many are left for the next day? Choose the correct choice from the following answers:
A) 1800
B) 800
C) 1100
D) 1200
E) 1900

Solution: (1/5)*3000= 
(1/5)*3000 = 600
600   Remaining= 3000-600= 
3000-600 = 2_400
2400   (1/4) of remaining= (1/4)*2400= 
(1/4)*2400 = 600
600   Remaining now= 2400-600= 
2400-600 = 1_800
1800   1800nswer: Option 1800
Answer: A
Arun went for a movie nine days ago. He goes to watch movies only on Thursdays. What day of the week is today?
Choose one:
A) Wednesday
B) Saturday
C) Friday
D) Sunday
E) Monday

Solution: Explanation:   Clearly it can be understood from the question that 9 days ago was a Thursday   Number of odd days in 9 days = 2 (As 9-7= 
9-7 = 2
2, reduced perfect multiple of 7 from total days)   Hence today= (Thursday + 2 odd days) = Saturday   Answer: Option Saturday
Answer: B
By selling 12 toffees for a rupee, a man loses 20%. How many for a rupee should be sell to get a gain of 20%?  Choose the correct choice from the following answers:
A) 7	B) 8	C) 9	D) 6	E) 4

Solution: Let S.P. of 12 toffees be Rs. x.   Then, 80:1 = 120:x or x = 120/180 = 3/2   For Rs. 3/2, toffees sold = 12.   For Re. 1, toffees sold = 12 * 2/3= 
12 * 2/3 = 8
8   Answer: 8
Answer: B
When working alone, painter W can paint a room in 2 hours, and working alone, painter X can paint the same room in f hours. When the two painters work together and independently, they can paint the room in 3/4 of an hour. What is the value of f?	Pick one
A) 3/4	B) 1[1/5]	C) 1[2/5]	D) 1[3/4]	E) 2

Solution: Rate*Time=Work   Let Painter W's rate be W and Painter X's rate be X   R*T = Work   W * 2 = 1 (If the work done is same throughout the question then the work done can be taken as 1) => W = 1/2   X * f = 1 => X = 1/f   When they both work together then their rates get added up   Combined Rate = (W+X)   R*T = Work   (W+X) * 3/4 = 1   => W+X = 4/3   => 1/2 + 1/f = 4/3   => 1/f = (8-3)/6 = 5/6   => f = 6/5 = 1[1/5]   Answer 1[1/5]
Answer: B
If 2 tables and 3 chairs cost Rs, 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost ?
Choose the correct answer:
A) 2377
B) 1000
C) 2778
D) 766
E) 18811

Solution: Let the cost of a table and that of a chair be Rs. x and Rs, y respectively.   Then, 2x + 3y = 3500 ...(i)   and 3x + 2y = 4000 .....(ii)   solving (i) and (ii) we get x = 1000, y = 500   Answer: 1000) 1000
Answer: B
A type A machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type A machines and 3 type B machines working together and independently to complete the job?  Pick.
A) 1/5 B) 29/35 C) 5/6 D) 35/29 E) 35/12

Solution: A needs 5 hours to complete the job   2A need 5/2 hours to complete the job,   similarly 3B need 7/3 hours to complete the job   Lets consider 2A and 3B as single entity (X, Y)   so   1/X + 1/Y = 1/Z Z is the time to complete the job if working together.   1/(2/5) + 1/(7/3) =1/Z   2/5 + 3/7 =1/Z   29/35 = 1/Z   Z = 35/29   so if 2A and 3 B working together, they would need 35/29 hours to complete the job.   ANSWER:35/29
Answer: D
A boat ma goes 2km against the current of the stream in 1 hr and goes 1 km along the current in 10 min. how long will it take to go 5 km in stationary water  Choose the most appropriate option: A) 40 min B) 1hr C) 1hr 15 min D) 1hr 30 min E) 4 hr

Solution: rate down stream=(1/10*60)km/hr=6km/hr   rate up stream=2km/hr   speed still water =1/2(6+2)=4km/hr   required time =(5/4)=1 1/4=1hr 15 min   Answer(1hr 15 min)
Answer: C