MU-NLPC/Calc-aqua_rat huggingface dataset:
In a recent survey at a local deli, it was observed that 3 out of 5 customers bought a bagel and 5 out of 7 customers bought a coffee. Some customers bought both. If 8 customers are selected, what are the chances that at least 1 customer bought a coffee and a bagel?	Choose the correct choice from the following options
A) 27/343 B) 3/7 C) 27/125 D) 199/245 E) 9/125

Solution: Let us take 7*5= 
7*5 = 35
35 as the total number of customers. So  7*3= 
 7*3 = 21
21 customers bought a bagel and 5*5= 
5*5 = 25
25 customers bought a coffee.   chances that at least 1 customer bought a coffee and a bagel= 1 - chances that no customer bought a coffee and a bagel   chances that no customer bought a coffee and a bagel=24/35*23/34*22/33*21/32*20/31*19/30*18/29*17/28=46/245   chances that at least 1 customer bought a coffee and a bagel= 1 - 46/245 = 199/245   Answer 199/245.
Answer: D
|x+3| – |4-x| = |8+x| How many S solutions will this equation have? Pick one
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: |x| = x when x >= 0 (x is either positive or 0)   |x| = -x when x < 0 (note here that you can put the equal to sign here as well x <= 0 because if x = 0,   |0| = 0 = -0 (all are the same)   So the '=' sign can be put with x > 0 or with x < 0. We usually put it with 'x > 0' for consistency.0
Answer: A
The output of a factory was increased by 10% to keep up with rising demand. To handle the holiday rush, this new output was increased by 20%. By approximately what percent would the output now have to be decreased in order to restore the original output?  Pick one:  A) 20%  B) 24%  C) 30%  D) 32%  E) 79%

Solution: Let initial output is O then after 10% increase it will be 1.1O and after 20% increase on this new output the latest output will be 1.1O * 1.20 = 1.32O   Now we have to decrease the output by some percentage so that the new output is same as the starting output (O)   so, 1.32O * (1-x/100)   1.1  * 1.20= 
  1.1  * 1.20 = 1.32
1.32O   Now we have to decrease the output by some percentage so that the new output is same as the starting output (O)   so, 1.32O * (1-x/100)= O   => x = 24.24%   So, answer will be 24%
Answer: B
In a graduate physics course, 70 percent of the students are male and 30 percent of the students are married. If two-sevenths of the male students are married, what fraction of the male students is single?  Choose the correct choice from the following answers
A) 2/7  B) 1/3  C) 1/2  D) 2/3  E) 5/7

Solution: let assume there are 100 students of which 70 are male and 30 are females   if 30 are married then 70 will be single.   now its given that two-sevenths of the male students are married that means 2/7 of 70 = 20 males are married   if 30 is the total number of students who are married and out of that 20 are males then the remaining 10 will be females who are married.   total females = 70   married males = 20   then single males = 70-20= 
70-20 = 50
50   we need to find the fraction of male students who are single i.e single male students / total male student= 50/70 = 5/7 [5/7]
Answer: E
The cost of painting the whole surface area of a cube at the rate of 13 paise per Sq.cm is Rs. 343.98. Then the volume of the cube is	Choose the most appropriate option: A) 8500 cm3 B) 9000 cm3 C) 9250 cm3 D) 9261 cm3 E) None

Solution: Solution   Surface area	= (34398 / 13)= 
(34398 / 13) = 2_646
›2646cm3   ‹=›6a2= 2646   ‹=›a2= 441   ‹=›a = 21.   So,volume =(21x21x21)cm3= 9261cm3.   Answer 9261 cm3
Answer: D
A man sold 20 articles for $60 and gained 20%. How many articles should he sell for $50 to incur a loss 20%? Choose the correct choice from the following answers.
A) 25 B) 36 C) 40 D) 50 E) 48

Solution: Production cost per article: $60*(100%-20%) / 20 = $2.40   Required production costs for a loss of 20%: $50*(100% + 20%) = $60   Number of articles to be sold for $60 to incur a 20% loss: $60 / $2.40 = 25   Thus, solution 25 is correct.60 /  2.40= 
60 /  2.40 = 25
25   Thus, solution 25 is correct.
Answer: A
A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio:  Choose one:	A) 3:5	B) 2:1	C) 16:15	D) 4:5	E) None of these

Solution: Explanation:   For an income of Re. 1 in 9% stock at 96, investment = Rs. 96/9 = Rs.32/3   For an income Re. 1 in 12% stock at 120, investment = Rs. 120/12 = Rs. 10.   Ratio of investments =(32/3) : 10 = 32 : 30 = 16 : 15.   Answer: 16:15
Answer: C
A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?	Choose the correct choice from the following answers:	A) Rs. 45	B) Rs. 50	C) Rs. 55	D) Rs. 60	E) Rs. 65

Solution: Explanation:   A : B : C = (10 x 7) : (12 x 5) : (15 x 3) = 70 : 60 : 45 = 14 : 12 : 9.   C's rent = Rs.(175 x	9/35)= Rs. 45.   Rs. 45NSWER IS Rs. 45
Answer: A
A train 500 m long can cross an electric pole in 20 sec and then find the speed of the train?  Choices
A) 95 Kmph B) 90 Kmph C) 92 Kmph D) 95 Kmph E) 98 Kmph

Solution: Length = Speed * time   Speed = L/T   S = 500/20= 
500/20 = 25
25 M/Sec   Speed= 25*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 90 Kmph   ANSWER:90 Kmph
Answer: B
The smallest number when increased by " 1 " is exactly divisible by 6,9,15,35,45 is:
Choose the correct choice from the following
A) 631
B) 630
C) 359
D) 629
E) 600

Solution: LCM = 630   630 - 1= 
630 - 1 = 629
629   ANSWER:629
Answer: D
How many keystrokes are needed to type the numbers from 1 to 500?	Choose the correct choice from the following options:  A) 1156  B) 1392  C) 1480  D) 1562  E) 1788

Solution: There are 9 one-digit numbers from 1 to 9.   There are 90 two-digit numbers from 10 to 99.   There are 401 three-digit numbers from 100 to 500.   9 + 90(2) + 401(3) = 1392   The answer is 1392.
Answer: B
In a two-digit number, the digit in the unit's place is four times the digit in ten's place and the sum of the digits is equal to 10. What is the number?  Choose the correct option.
A) 82 B) 41 C) 14 D) 56 E) 28

Solution: Let the ten's digit be x. then, unit's digit = 4x   therefore x + 4x = 10 ==> 5x = 10 ==> x = 2   so ten's digit is 2 and unit's digit is 8, so the number is 28   so the correct answer is option 28) 28
Answer: E
The edge of a cube is 7a cm. Find its surface? Choose the correct answer.
A) 24a8	B) 24a4	C) 24a1	D) 24a2	E) 294a2

Solution: 6a2 = 6 * 7a * 7a = 294a2   Answer:294a26 * 7  * 7= 
6 * 7  * 7 = 294
294a2   Answer:294a2
Answer: E
A shop sells chocolates It is used to sell chocolates for Rs.2 each but there were no sales at that price.When it reduced the price all the chocolates sold out enabling the shopkeeper to realize Rs 164.90 from the chocolates alone If the new price was not less than half the original price quoted How many chocolates were sold?  Choose the correct choice from the following choices.
A) 1.9 B) 1.7 C) 1.2 D) 1.5 E) 1.6

Solution: 16490 = 2 × 5 × 17 × 97   Now now chocolate price should be greater than 1 and less than 2. So 2 x 5 x 17 = 170   So Total chocolates sold = 97 and New chocolate price = Rs.1.7   Answer:	1.7
Answer: B
A board 7ft. 9 inches long is divided into 3 equal parts . What is the length of each part? Select.
A) 31 inches  B) 32 inches  C) 33 inches  D) 34 inches  E) 35 inches

Solution: 7 ft 9 in is  84 + 9= 
 84 + 9 = 93
93 inches. so  93/3= 
 93/3 = 31
31 inches or 2 ft. 7 inch.   31 inchesNSWER:31 inches
Answer: A
Find the number of zeroes in the expression 15*32*25*22*40*75*98*112*125 Choose the correct choice from the following: A) 12 B) 9 C) 14 D) 7 E) 6

Solution: (3*5)*(2*2*2*2*2)*(5*5)*(2*11)*(2*2*2*2*5)*(5*5*3)*(2*7*7)*(2*2*2*2*7)*(5*5*5)   there are 9 (5*2) pairs which gives zero   so.no of zeros 9   ANSWER:9
Answer: B
The diagonals of a rhombus are 18 cm and 22 cm. Find its area?	Choose one:
A) 277
B) 266
C) 198
D) 288
E) 212

Solution: 1/2 * 18 * 22= 
1/2 * 18 * 22 = 198
198   Answer: 198
Answer: C
If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?
Pick:
A) 22 1/8 %
B) 22 3/2 %
C) 28 1/2 %
D) 22 1/2 %
E) 32 1/2 %

Solution: 9 = (1*40*R)/100   R = 22 1/2 %   Answer:22 1/2 %
Answer: D
A and B invests Rs.6000 and Rs.12000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?  Choose the correct choice from the following:
A) 32:99	B) 8:21	C) 32:45	D) 34:89	E) 35:21

Solution: A : 8:21   (6000*4)+(3000*8) : (12000*6)+(9000*6)   48000 : 126000   8 : 21   Answer:8:21
Answer: B
A train covers a distance of 10km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? Choose the correct answer.
A) m	B) m	C) m	D) m	E) m

Solution: Speed = (10/10 * 60) km/hr   = (60 * 5/18) m/sec = 50/3 m/sec.   Length of the train = 50/3 * 6= 
50/3 * 6 = 100
100 m.   Answer:m
Answer: C
The rental charge for a car is 34 cents for the first 1/4 mile driven and 6 cents for every 1/5 mile driven over the initial 1/4 mile. If a man paid $1.24 in rental charges, how many miles did he drive? Pick one:
A) 2.5
B) 3.0
C) 3.25
D) 3.75
E) 4.0

Solution: Total Rent = Rent for the first 0.25 mile + Rent After 0.25 mile   Rent for the first 0.25 mile = 34 cents   Rent After 0.25 mile = [6 cent/(1/5 mile)]*(x - 0.25) = 30(x-0.25)   Therefore, Total Rent = 35 + 30(x - 0.25)   124 = 34 + 30(x - 0.25)   90 = 30(x - 0.25)   3 = x - 0.25   x = 3 + 0.25= 
3 + 0.25 = 3.25
$3.25 3.25
Answer: C
A question paper consists of three sections 4,5 and 6 questions respectively. Attempting one question from each section is compulsory but a candidate need not attempt all the questions. In how many ways can a candidate attempt the questions?
Select the correct option.
A) 209  B) (4!-1)*(5!-1)*(6!-1)  C) 119  D) 29295  E) None

Solution: Solution:   At least 1 question from each section is compulsory, so from the 1st section the candidate can attempt 1 or 2 or 3 or 4 questions.   In each section each question can be dealt with in 2 ways, i.e. either he attempts it or leaves it.   So far 4 question there are 2 *2 *2 *2 ways to attempt. As he has to attempt at least 1 question, the total number of ways in which he can attempt questions from 1st section is 24−1.   Similarly for the 2nd section there are 25−1 ways in which he can attempt and for the 3rd section there are 26−1 ways.   The ways in which the attempts one or more questions in any section is independent of the number of ways in which he attempts one or more questions from the other sections.   Thus, total number of ways   Answer: Option 29295
Answer: D
10 women can complete a work in 9 days and 10 children take 12 days to complete the work. How many days will 6 women and 7 children take to complete the work?
Choose the correct choice:	A) 4	B) 5	C) 7	D) 8	E) 2

Solution: 1 women's 1 day work = 1/90   1 child's 1 day work = 1/120   (6 women + 7 children)'s 1 day work   = (6/90 + 7/120) = 1/8   6 women and 7 children will complete the work in 8 days.   8
Answer: D
Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 54. Find the third number? Choose the correct option:
A) A)37 B) B)85 C) C)48 D) D)43 E) E)54

Solution: Let the numbers be 5x, 6x, 7x.   Largest number = 7x.   Smallest number = 5x.   Third number = 6x.   7x + 5x = 6x + 54   6x = 54 => third number is 54.   Answer: Option 54
Answer: E
At the end of a business conference the nine people present all shake hands with each other once. How many handshakes will there be altogether ?
Select the correct option.
A) 20 B) 45 C) 36 D) 90 E) 95

Solution: number of handshakes = 9362= 9*8/2= 
9*8/2 = 36
36   ANSWER:36
Answer: C
Sum of the squares of three numbers is 351 and the sum of their products taken two at a time is 245. Find the sum?
Select the correct option:
A) 20  B) 22  C) 25  D) 26  E) 29

Solution: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 351 + 2* 245   a + b + c = √841 = 29   29
Answer: E
What is the are of an equilateral triangle of side 16 cm?  Choose the correct answer:
A) 64√6 cm2	B) 64√3 cm2	C) 64√9 cm2	D) 34√3 cm2	E) 24√3 cm2

Solution: Area of an equilateral triangle = √3/4 S2   If S = 16, Area of triangle = √3/4 * 16 * 16   = 64√3 cm2;   Answer: 34√3 cm2
Answer: D
Each of the following equations W has at least one solution EXCEPT Choose the most appropriate option.
A) W=–2^n = (–2)^-n	B) 2^-n = (–2)^n	C) 2^n = (–2)^-n	D) (–2)^n = –2^n	E) (–2)^-n = –2^-n

Solution: While it is possible to reason out which of these choices must not work, we may not have time or the confidence to do so. However, this problem has variable in its answer choice, and relatively simple math. Therefore, an easy alternative is picking numbers.   Since we're dealing with exponents, we want to keep things as easy as possible. Hence, we'll start with the easiest exponent possible: n = 1. A, B, and C are not solved (x^-n = 1/(x^n), so we're comparing integers to fractions), but choices D and E both end up valid, eliminating them from contention.   In the process of doing this, however, we've uncovered a major clue to our next step: A, B, and C, all compared integers to fractions, and the only integer equal to it's reciprocal is 1, which is equal to 1/1. This, in turn, tells us the we need to pick n = 0. Remember, for all non-zero x, x^0 = 1.   If we plug n = 0 into choices B and C, we end up with 1 = 1 both times. Choice A, however, results in the false 1 = -1. Thus, we conclude that the first choice has no valid solutions, and is therefore the correct answer.
Answer: A
If the population of a certain country increases at the rate of one person every 40 seconds, by how many persons does the population increase in 1 hour? Choose the most appropriate option.
A) 90
B) 120
C) 150
D) 180
E) 160

Solution: 90nswer = 1.5 * 60= 
1.5 * 60 = 90
90   90nswer is 90
Answer: A
A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
Select the correct option:	A) 288	B) 180	C) 288	D) 277	E) 265

Solution: Length of the train be ‘X’   X + 120/15 = X + 180/18   6X + 720 = 5X + 900   X = 180m .Answer: 180
Answer: B
Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm? Choose the correct choice from the following options.
A) 272 sq.cm B) 267 sq.cm C) 286 sq.cm D) 251 sq.cm E) 600 sq.cm

Solution: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.   BE2 + AE2 = AB2   252 = 152 + AE2 AE   = √(625 - 225)= 
(625 - 225) = 400
√400= 20,   AC = 20 + 20= 
20 + 20 = 40
40 cm.   Area of a rhombus= 1/2 * d1d2   = 1/2 * 40 * 30= 
1/2 * 40 * 30 = 600
600 sq.cm.   Answer:600 sq.cm
Answer: E
How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length? Select the correct option:
A) 12.8 sec  B) 12.1 sec  C) 12.2 sec  D) 12.6 sec  E) 11.1 sec

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec   Total distance covered= 110 + 132= 
110 + 132 = 242
242 m.   Required time= 242/20= 
242/20 = 121/10 = around 12.1
12.1 sec.   Answer: 12.1 sec
Answer: B
The consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 60 kmph its consumption is 1 litre per hour. if each litre costs $60 and other expenses per hous is $ 60, then what would be the minimum expenditure required to cover a distance of 600 Km?  Choose the correct choice from the following options.
A) 120
B) 1250
C) 1200
D) 1100
E) 1150

Solution: 60 kmph consumption is 1 lt/hr   so 600 km will take 10 hrs and the consumption is 10 lt for entire distance.   1 lt costs $60   so 10 lt costs $600   extra expenses for 1 hr - $60   10 hrs - $600   total expense - $600 + $600 = $1200   Answer : 1200
Answer: C
From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. What is the probability of having 0 woman in committee ? Choose the correct choice:
A) 7/36  B) 9/144  C) 1/36  D) 1/18  E) 5/18

Solution: We may have (3 men and 2 women) = (71/363 x 61/362) = 525   or (4 men and 1 woman) = (71/364 x 61/361) = 210   or (5 men only) = (71/365) = 21   Required ways = 756   Probability of having 0 woman in committee = 21 / 756 =1/36   ans - 1/36
Answer: C
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good.? Answers:
A) 20/69	B) 20/63	C) 20/65	D) 20/61	E) 20/62

Solution: Required probability = (10 * 4)/126 = 20/63.Answer: 20/63
Answer: B
A train passes a station platform in 32 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?  Select the correct option:  A) 228  B) 240  C) 887  D) 166  E) 180

Solution: Speed = 54 * 5/18= 
54 * 5/18 = 15
15 m/sec.   Length of the train= 15 * 20= 
15 * 20 = 300
300 m.   Let the length of the platform be x m . Then,   (x + 300)/32= 15 => x = 180 m.   Answer: 180
Answer: E
If |w|=−w, which of the following must be true? Choose the correct choice from the following options:
A) x≥0
B) w≤0
C) x2>x
D) x3<0
E) 2x<x

Solution: |w| =-w means absolute value of w is equal to negative of w. Since absolute value cannot be negative hence negative of w should result in a non negative number. It means w is a non positive number i.e. w<0. Answer is w≤0
Answer: B
Two numbers are less than third number by 30% and 37% respectively. How much percent is the second number less than by the first  Choose the correct choice from the following options:
A) 8%  B) 9%  C) 10%  D) 11%  E) 12%

Solution: Explanation:   Let the third number is x.   then first number = (100-30)= 
(100-30) = 70
70% of x= 7x/10   Second number is (63x/100)   Difference = 7x/10 - 63x/100 = 7x/10   So required percentage is, difference is what percent of first number   => (7x/100 * 10/7x * 100 )% = 10%Explanation:   Let the third number is x.   then first number (7 /100 * 10/7  * 100 )= 
(7 /100 * 10/7  * 100 ) = 10
10%Explanation:   Let the third number is x.   then first number= (100-30)= 
(100-30) = 70
70% of x= 7x/10   Second number is (63x/100)   Difference = 7x/10 - 63x/100 = 7x/10   So required percentage is, difference is what percent of first number   => (7x/100 * 10/7x * 100 )% = 10%   Option 10%(7 /100 * 10/7  * 100 )= 
(7 /100 * 10/7  * 100 ) = 10
10%   Option 10%
Answer: C
How many numbers from 39 to 79 are exactly divisible by 11?	Pick one.
A) 5	B) 7	C) 4	D) 11	E) 12

Solution: 39/11 = 1 and 79/11 = 7 ==> 7 - 3= 
7 - 3 = 4
4 Numbers   Answer : 4
Answer: C
It is found that the volume of a cube is numerically equal to its surface area. Then the measure of its edge in meters is:  Answers
A) 4
B) 6
C) 8
D) 9
E) cannot be determined

Solution: if edge of cube = a   volume of cube = a^3   surface area = 6(a^2)   then   a^3 = 6(a^2)   a = 6   ANSWER:6
Answer: B
if there are 30 cans out of them one is poisned if a person tastes very little he will die within 14 hours so if there are mice to test and 24 hours to test, how many mices are required to find the poisned can?  Choose the correct option: A) 3 B) 2 C) 6 D) 1 E) 7

Solution: as we know only one can is poisoned so try mice every can n notice the time   for ex suppose for ist can time was 12:05 then after 5 min test for can 2 means 12:10..n if 1st can contain poision then according to time it can be cleared..   ANSWER:1
Answer: D
How long does a train 165 meters long running at the rate of 72 kmph take to cross a bridge 660 meters in length?	Pick:
A) 28
B) 41.25
C) 55
D) 18
E) 12

Solution: T = (660 + 165)/72 * 18/5= 
(660 + 165)/72 * 18/5 = 165/4 = around 41.25
41.25   Answer: 41.25
Answer: B
A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 15%. What was its profit on the items sold in February?
Choose one:
A) 27.5%	B) 30%	C) 35%	D) 37.5%	E) 40%

Solution: 27.5%ssume the total price = 100x   Price after 20% markup = 120x   Price after 25%further markup = 1.25*120= 
1.25*120 = 150
150x   Price after the discount= 0.85*150= 
0.85*150 = 127.5
127.5x   Hence total profit= 27.5%   Option 27.5%
Answer: A
If books bought at prices ranging from Rs. 98 to Rs. 195 are sold at prices ranging from Rs. 120 to Rs 215, what is the greatest possible profit that might be made in selling 13 books ?
Select.
A) Rs. 1650 B) Rs. 3000 C) Rs. 1521 D) Rs. 1400 E) Rs. 1560

Solution: The greatest profit is possible only if the cost price of the books are minimum and selling prices are maximum.   Let lowest cost price of the 13 books = 98*13 = Rs. 1,274   Maximum selling price of 13 books = 215 *13 = Rs. 2,795   So, maximum profit = 2795 - 1274 = Rs. 1,521   ANSWER : OPTION Rs. 1521
Answer: C
Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 60kmph, find the rate at which the train B runs.
Choose the correct choice from the following options:
A) 40	B) 90	C) 120	D) 80	E) 100

Solution: If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:   Sa/Sb = √(b/a)   i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.   Sa/Sb = √(4/9) = 2/3   This gives us that the ratio of the speed of A : speed of B as 2:3.   Since speed of A is 60 kmph, speed of 90 must be 60*(3/2)= 
60*(3/2) = 90
90 kmph   Answer 90
Answer: B
I bought three toys for my triplet boys (one for each). I placed the toys in the dark store. One by one each boy went to the store and pick the toy. What is the probability that no boy will choose his own toy? Choose the correct choice from the following choices
A) 1/3  B) 2/3  C) 3/3  D) 4/3  E) 5/3

Solution: Solution:   1/3   Assuming T1 is the Toy for brother1, T2 is the toy for brother2 and T3 is the toy for brother3.   Following are the possible cases for toys distribution:   Boy1 Boy2 Boy3   T1 T2 T3   T1 T3 T2   T2 T1 T3   T2 T3 T1 .... (A)   T3 T1 T2 .... (B)   T3 T2 T1   In both steps (A) & (B), no one gets the correct toy.   Therefore probability that none brother can get the own toy is 2/6 = 1/3   1/3nswer 1/3
Answer: A
A man, a woman and a boy can complete a job in 3 days, 4 days and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4th of a day? Choose the most appropriate option
A) 10 B) 41 C) 31 D) 21 E) 22

Solution: Explanation:   1 man’s 1 day’s work = 1/3, ¼ day’s work = 1/3 × ¼ = 1/12   1 woman’s 1 day’s work = ¼, ¼ day’s work = ¼ × ¼ = 1/16   1 boy’s 1 day’s work = 1/12, ¼ day’s work = 1/12 × ¼ = 1/48   Let ‘x’ be the No. of boys required.   Then, (1 man + 1 woman + x boy)’s ¼ day’s work 1/12 + 1/16 + x/48 = 1   = (4 + 3 + x)/48 = 1   i.e. 7 + x= 48 and x = 41.   Answer: Option 41
Answer: B
At present, the ratio between the ages of Amit and Dhiraj is 5 : 4. After 6 years, Amit’s age will be 26 years. What is the age of Dhiraj at present?  Choose the correct choice from the following choices:
A) 16	B) 77	C) 566	D) 197	E) 161

Solution: Explanation:   Let the present ages of Amit and Dhiraj be 5x years and 4x years respectively. Then,   5x + 6 = 26   5x = 20   x = 4   Dhiraj’s age = 4x = 16 years   16NSWER: 16
Answer: A
A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
Choose one:
A) 9:6 B) 9:8 C) 9:1 D) 9:9 E) 9:5

Solution: (3*6 + 6*6): (4*12)   54:48 => 9:8.Answer:9:8
Answer: B