MU-NLPC/Calc-aqua_rat huggingface dataset:
A certain company’s profit in 1996 was 15 percent greater than its profit in 1995, and its profit in 1997 was 35 percent greater than its profit in 1996. The company’s profit in 1997 was what percent greater than its profit in 1995? Choose one
A) 5% B) 18% C) 33% D) 35% E) 55.25%

Solution: Profit in 1995 - 100   Profit in 1996 - 115   %increae Profit in 1997 in comparison to 1995 = 15 + 115*35%= 55.25   Correct Option : 55.25%
Answer: E
A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.30 a.m.? Pick
A) 5
B) 6
C) 7
D) 8
E) 23

Solution: Relative speed = Speed of A + Speed of B (? they walk in opposite directions)   = 2 + 3= 
2 + 3 = 5
5 rounds per hour=> They cross each other 5 times in 1 hour and 2 times in 1/2 hour   Time duration from 8 am to 9.30 am = 1.5 hour   Hence they cross each other 7 times before 9.30 am   Answer is 7
Answer: C
In one hour, a boat goes 13 km/hr along the stream and 9 km/hr against the stream. The speed of the boat in still water (in km/hr) is:  Choose the most appropriate option:
A) 11 kmph  B) 13 kmph  C) 14 kmph  D) 15 kmph  E) 16 kmph

Solution: Explanation:   Let the speed downstream be a km/hr and the speed upstream be b km/hr, then   Speed in still water =1/2(a+b) km/hr   Rate of stream = 1/2(a−b) km/hr   Speed in still water = 1/2(13+9) kmph = 11 kmph.   11 kmphnswer: Option 11 kmph
Answer: A
If A and B get profits of Rs.6,000 and Rs.4,000 respectively at the end of year then ratio of their investments are	Choose the correct choice from the following choices:
A) 4:1	B) 1:4	C) 3:2	D) 2:3	E) 2:5

Solution: suppose a and b is ratio of investment. so a:b=6000+4000= 
6000+4000 = 10_000
10000   a/(a+b)*10000=6000   2a=3b   a/b=3/2   i.e 3:2   ANSWER:3:2
Answer: C
The area of a parallelogram is 162sq m and its altitude is twice the corresponding base. Then the length of the base is?  Choose the correct choice.
A) 8  B) 9  C) 7  D) 6  E) 5

Solution: 2x * x = 162 => x= 9   Answer: 9
Answer: B
A can run 224 metre in 28 seconds and B in 32 seconds. By what distance A beat B?  Pick
A) 38 metre B) 28 metre C) 23 metre D) 15 metre E) 28 metre

Solution: Clearly, A beats 28 metre by 4 seconds   Now find out how much 28 metre will run in these 4 seconds   Speed of 28 metre = Distance/Time taken by 28 metre=224/32=28/4= 
28/4 = 7
7 m/sDistance covered by 28 metre in 4 seconds= Speed × time =7×4=28 metre   i.e., A beat 28 metre by 28 metre   Answer is 28 metre
Answer: B
In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:	Choose the correct option.
A) 60 m
B) 40 m
C) 20 m
D) 10 m
E) 30 m

Solution: To reach the winning post A will have to cover a distance of (500 - 140)m, i.e., 360 m.   While A covers 3 m, B covers 4 m.   While A covers 360 m, B covers	4/3	x 360	m	= 480 m.   Thus, when A reaches the winning post, B covers 480 m and therefore remains 20 m behind.   A wins by 20 m. ANSWER:20 m
Answer: C
Difference of two numbers is 1660. If 7.5% of the number is 12.5% of the other number, find the number ?	Choose the correct option: A) 1660 B) 2500 C) 3250 D) 4150 E) 5250

Solution: Let the numbers be x and y. Then , 7.5 % of x =12.5% of y   X = 125*y/75 = 5*y/3.   Now, x-y =1660   5*y/3 –y =1660   2*y/3= 1660   y =[ (1660*3)/2= 
(1660*3)/2 = 2_490
2490.   One number= 2490, Second number =5*y/3 =4150.   Answer Option 4150) 4150.
Answer: D
A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work? Pick
A) 15 days	B) 25 days	C) 18 days	D) 20 days	E) 21 days

Solution: Explanation:   8/12 + 6/x = 1   X = Explanation:   8/12 + 6/x = 1   X = 18 days   Answer 18 days
Answer: C
Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is	Choose the most appropriate option.
A) 100 gallons
B) 110 gallons
C) 120 gallons
D) 130 gallons
E) 140 gallons

Solution: Work done by the waste pipe in 1 minute = 1/15-(1/20+1/24)   = -1/40[-ve means emptying]   so, volume of 1/40 part =3 gallons   volume of whole = 3*40= 
3*40 = 120
120 gallons   ANSWER:120 gallons
Answer: C
A company bought for its 8 offices 2 computers of brand N and 3 computers of brand M. In how many ways could computers be distributed among the offices if each office can have only 1 computer.
Choose the correct option:	A) 196	B) 210	C) 256	D) 292	E) 560

Solution: This problem has to do withcombinations. Here's the general idea: if you have a set of n elements, and you are going to choose r of them (r < n), then the number of combinations of size r one could choose from this total set of n is:   # of combinations = nCr = (n!)/[(r!)((n-r)!)]   where n! is the factorial symbol, which means the product of every integer from n down to 1. BTW, nCr is readn choose r.   In this problem, let's consider first the three computers of brand M. How many ways can three computer be distributed to seven offices?   # of combinations = 8C3 = 56   There are 56 different ways to distribute three computers to 8 offices. (The massive amount of cancelling that occurred there is very much typical of what happens in the nCr formula.)   One we have distributed those three M computers, we have to distribute 2 N computers to the remaining four offices. How many ways can two computer be distributed to four offices?   # of combinations = 5C2 = 10   For each of the 56 configurations of distributing the M computers, we have 10 ways of distributing the N computers to the remaining offices. Thus, the total number of configurations is 56 * 10= 
56 * 10 = 560
560. Answer choice= 560
Answer: E
A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?  Choose the correct choice from the following answers.
A) 39 B) 27 C) 40 D) 88 E) 21

Solution: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec   Total distance = 360+140= 
360+140 = 500
500 meter   Time= Distance/speed   = 500 * (2/25)= 
500 * (2/25) = 40
40 seconds   Answer: 40
Answer: C
Of the 800 employees of Company X, 70 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 40 percent ? Choose one:
A) 400	B) 160	C) 112	D) 80	E) 56

Solution: Original (Long-Term is 70%)   Total = 800   Long-Term = .7(800) = 560   New (Long-Term is 40%)   New Total = 800 - y   New Long-Term = 560 - y   560 - y = .4 (800 - y)   y = 400   400nswer: 400
Answer: A
20% of an 30% salt solution is replaced with water. From the resulting solution, again 20% is replaced with water. This step is repeated once more. What is the concentration of salt in the final solution obtained  Choices:
A) 19.58%
B) 15.36%
C) 20%
D) 9.72%
E) 11.64%

Solution: A quick answer: (30)(0.8)(0.8)(0.8)   Imagine you have 100 ml of 30% salt solution.   In step 1, 20% of the salt solution is replaced with water. This means 80% of the original salt quantity remains. Hence the resultant concentration is (30)(0.8)   This process is repeated for step 2 and three. Hence, we multiply 30 ml two more times with 0.8.   This gives the final concentration as 30x0.8x0.8x0.8 = 15.36%   Answer: 15.36%
Answer: B
The difference between the simple interest received from two different sources on 1500 for 3 years is 13.50. The difference between their rates of interest is:
Choose the correct answer.
A) 0.1%	B) 0.2%	C) 0.3%	D) 0.4%	E) None of these

Solution: (1500×R1×3/100)−(1500×R2×3100)=13.50   ⇒ 4500(R1 - R2) = 1350 ⇒ R1 - R2 = 1350⁄4500 = 0.3%   Answer 0.3%
Answer: C
A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?  Pick:
A) 392
B) 126
C) 26
D) 9
E) 8

Solution: Solution:   There are 8 students and the maximum capacity of the cars together is 9.   We may divide the 8 students as follows:   Case I:   5 students in the first car and 3 in the second.   Hence, 8 students are divided into groups of 5 and 3 in 8C3 = 56 ways.   Case II:   4 students in the first car and 4 in the second.   So, 8 students are divided into two groups of 4 and 4 in 8C4 = 78 ways.   Therefore, the total number of ways in which 8 students can travel is:   56 +70= 
56 +70 = 126
126   Answer: Option 126
Answer: B
While flying over the Pacific, an airplane makes a 25° turn to the right to avoid a storm. If, as a result, the airplane is traveling in a direction 9° east of north, in what direction was it originally flying?
Choose one
A) (a) 30° west of north	B) (b) 30° east of north	C) (c) 16° west of north	D) (d) 16° east of north	E) (e) 5° west of north

Solution: If after a turn of 25° you are 9°NEast, with a 16° turn you would be perfectly pointing at north. So you were, before the turn, 16° to the other side (West).   Answer (c) 16° west of north)
Answer: C
If a Poultry firm sells 15 of his chickens, his stock of feed will last for 4 more days than planned, but if he buys 20 more chickens, he will run out of feed 3 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?	Choices
A) 100 B) 90 C) 80 D) 70 E) 60

Solution: Let x = total feed required for the planned period   n= number of chicken   t = total time of the planned feed   x = nt   1) x = (n-15) * (t+4)   2) x = (n+20) * (t-3)   equating 12   (n-15) * (t+4) = (n+20) * (t-3)   7n = 35t   n =5t   x= n * n/5   substituting this value in 1   n * n/5 = (n-15) * (n/5+4)   5n = 300   n =60   60
Answer: E
John left home and drove at the rate of 45 mph for 2 hours. He stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination. How many miles did John drive?	Choose one.
A) 250 miles	B) 255 miles	C) 258 miles	D) 265 miles	E) 245 miles

Solution: 2*45= 
2*45 = 90
90;    3*55= 
 3*55 = 165
165;    90+165= 
 90+165 = 255
255 miles   ANSWER:255 miles
Answer: B
The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/8 of that total. What was the price of the basic computer? Choose the correct choice from the following choices:
A) 1500  B) 1600  C) 1750  D) 1900  E) 2125

Solution: Let the price of basic computer be C and the price of the printer be P: C+P=$2,500.   The price of the enhanced computer will be C+500 and total price for that computer and the printer will be 2,500+500=$3,000. Now, we are told that the price of the printer is 1/8 of that new total price: P=1/8*$3,000=$375.   Plug this value in the first equation: C+375=$2,500 --> C=$2,125.   Answer: 2125.
Answer: E
Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?	Choose one
A) 22
B) 77
C) 60
D) 88
E) 12

Solution: Let the speed of the slower train be x m/sec.   Then, speed of the train = 2x m/sec.   Relative speed = ( x + 2x) = 3x m/sec.   (100 + 100)/8 = 3x => x = 25/3.   So, speed of the faster train = 50/3 = 50/3 * 18/5= 
50/3 * 18/5 = 60
60 km/hr.   Answer:60
Answer: C
Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 40 percent ryegrass, what percent of the weight of this mixture is X ?  Choose one
A) 100%  B) 33.33 %  C) 40%  D) 50%  E) 66.66 %

Solution: ---------------->Ryegrass   X-------------->	40%   Y-------------->	25%   M(mixture)---->40%   0.4X + (M-X)0.25 = 0.4M   0.15X = 0.15M   X = 1M   X = 100% of M   100%
Answer: A
A 180 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
Options:  A) 176 kmph  B) 108 kmph  C) 176 kmph  D) 134 kmph  E) 161 kmph

Solution: S = 180/6 * 18/5= 
180/6 * 18/5 = 108
108 kmph   Answer: 108 kmph
Answer: B
If @ is a binary operation defined as the difference between an integer n and the product of n and 5, then what is the largest positive integer n such that the outcome of the binary operation of n is less than 18?  Pick:
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: @(n) = 5n - n   We need to find the largest positive integer such that 5n - n < 18.   Then 4n < 18 and n < 4.5   The largest possible integer is n = 4.   The answer is 4.
Answer: D
In a urban village of india named "owlna" , 75% people have refrigerator , 90% people have television , 85% people got computers and 75% got Air-conditionor. how many people(minimum) got all these luxury.	Options:	A) 23%	B) 17%	C) 11%	D) 10%	E) 25%

Solution: 25%   10%   100 - [ (100-75)+(100-90)+(100-85) +(100-75)]   =100-(25+10+15+25)   =100-75
Answer: E
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 15 sec. What is the length of the fast train?  Select:
A) 83 7/6 m B) 83 7/4 m C) 83 7/2 m D) 83 1/3 m E) 83 7/7 m

Solution: Relative speed = (40 - 20)= 
(40 - 20) = 20
20 km/hr.= 20 * 5/ 18 = 50/9 m/sec.   Length of faster train = 50/9 * 15 = 750/9 = 83 1/3 m.Answer:83 1/3 m
Answer: D
A corporation double its annual bonus to 100 of its employees. What percent of the employees’ new bonus is the increase?  Pick one:
A) 50%
B) 12%
C) 8%
D) 6%
E) 5%

Solution: Let the annual bonus be X.   A corporation double its annual bonus.   So new bonus = 2X.   Increase = 2X-X =X   The increase is what percent of the employees’ new bonus   = (X/2X)*100   = 50%   Hence 50%.
Answer: A
i row from a to b against the current in 8 hrs and from b to a in 2 hrs if speed of river is 9 m/sec.what is the speed of boat in still water.  Choose the correct choice:
A) 10 m/sec
B) 15 m/sec
C) 25 m/sec
D) 18 m/sec
E) 20 m/sec

Solution: If x m/sec is my speed in still water , then   (x+9)*2*3600= (x-9)*8*3600   6x=90   x= 15 m/sec   ANSWER:15 m/sec
Answer: B
Danny is sitting on a rectangular box. The area of the front face of the box is half the area of the top face, and the area of the top face is 1.5 times the area of the side face. If the volume of the box is 5184, what is the area of the side face of the box? Pick one
A) 123  B) 167  C) 178  D) 199  E) 288

Solution: Lets suppose length= l, breadth= b, depth= d   Front face area= l*w = 1/2 w*d (l=1/2 d or d=2l)   top face area= w*d   side face area= w*d = 1.5 d*l (w=1.5l)   Volume = l*w*d= 5184   l*1.5l*2l= 5184   l=12   Side face area= l*d= l*2l= 12*2*12= 
12*2*12 = 288
288   288 is the answer
Answer: E
Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.72000 after completion of one year. What will be Jose's share of profit? Choose the correct choice from the following choices:
A) 20000
B) 10000
C) 25000
D) 34000
E) 40000

Solution: SoL = ~s- So Anju’s share = [5/9] x 72000 = 40000   40000
Answer: E
476 ** 0 is divisible by both 3 and 11. The non-zero digits in the hundred's and ten's places are respectively: Choose the correct answer: A) 7 and 4 B) 7 and 5 C) 8 and 5 D) 6 and 4 E) 5 and 8

Solution: Let the given number be 476 xy 0.   Then (4 + 7 + 6 + x + y + 0) = (17 + x + y) must be divisible by 3.   And, (0 + x + 7) - (y + 6 + 4) = (x - y -3) must be either 0 or 11.   x - y - 3 = 0 y = x - 3   (17 + x + y) = (17 + x + x - 3) = (2x + 14)   x= 2 or x = 8.   x = 8 and y = 5.   ANSWER 8 and 5
Answer: C
A man is 30 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?  Pick
A) 23 years	B) 28 years	C) 21 years	D) 20 years	E) 19 years

Solution: Let present age of the son =x years   Then, present age the man =(x+30) years   Given that, in 2 years, man's age will be twice the age of his son   â‡’(x+30)+2=2(x+2)   â‡’x=28   ANSWER:28 years
Answer: B
After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?  Select the correct option:
A) 1200
B) 2899
C) 1200
D) 2781
E) 2782

Solution: 1200P* (76/100) = 912   1200P1200 * (76/100)= 
1200 * (76/100) = 912
912   1200P= 12 * 100= 
12 * 100 = 1_200
> 1200P= 1200   Answer:1200
Answer: C
A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?	Choose one:
A) 3630
B) 9232
C) 8828
D) 2387
E) 2813

Solution: 6300:4200:10500   3:2:5   3/10 * 12100= 
3/10 * 12100 = 3_630
3630   3630nswer: 3630
Answer: A
A tourist does not have to pay tax on the first $600 of goods he purchases in Country B, but does have to pay a 12 percent tax on the portion of the total value that is in excess of $600. What tax must be paid by a tourist if he buys goods with a total value of $1720?
Choose the most appropriate option:
A) $54.00 B) $64.80 C) $90.00 D) $100.80 E) $134.40

Solution: Correct Answer: E   The tourist must pay tax on $1720 - $600 = $1120. Thus, the amount of tax he has to pay is 0.12 ($1120) 1720 -  600= 
1720 -  600 = 1_120
$1120. Thus, the amount of tax he has to pay is 0.12 ($1120)= $134.40. The correct answer is $134.40.
Answer: E
At a certain supplier, a machine of type A costs $25,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?  Choose the correct choice from the following answers: A) $0 B) $11,200 C) $12,000 D) $12,800 E) $13,200

Solution: Total Cost of 2 Machines of Type $0   = 20% of (Cost of 2 machine $0) + remainder + 40 % remainder   = 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000)   = 66000   Total Cost of 1 Machine of Type B   = 20% of (Cost of 1 machine B) + remainder + 40 % remainder   = 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000)   = 66000   Diff = 66000 - 66000= 
66000 - 66000 = 0
0   Hence, $0.
Answer: A
In a box, there are 3 grey, 5 brown and 2 yellow pencils. One pen is picked up randomly. What is the probability that it is neither brown nor yellow? Pick one:
A) 2/5
B) 3/5
C) 3/10
D) 3/4
E) 3/11

Solution: Explanation :   Neither brown nor yellow means the pencils drawn is grey.   Total number of outcomes = (3+5+2)= 
(3+5+2) = 10
10.   Number of Favourable outcomes= 3 = Number of grey pencils.   Hence, Probability of the event = 3/10 = 3/10.   Answer : 3/10
Answer: C
A sum of money invested at C.I. amounts to Rs. 800 in 3 years to Rs. 840 in 4 years. The rate of interest per annum is? Choose the correct choice from the following:
A) 6%
B) 2%
C) 5%
D) 9%
E) 1%

Solution: S.I. on Rs. 800 for 1 year   = (840 - 800) = Rs. 40 Rate   = (100 * 40)/(800 * 1)= 
(100 * 40)/(800 * 1) = 5
5%   Answer:5%
Answer: C
Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?	Choose the correct choice from the following:	A) 450	B) 754	C) 456	D) 123	E) 729

Solution: The first ring can be worn in any of the 3 fingers (3 ways).   Similarly each of the remaining 5 rings also can be worn in 3 ways.   Hence total number of ways   =3×3×3×3×3×3=36=729   Ans: 729
Answer: E
In 10 years, A will be twice as old as B was 10 years ago. If A is now 8 years older than B the present age of B is	Choose the correct answer.
A) 37	B) 38	C) 39	D) 40	E) 41

Solution: let present age of A be a and 38 be b   a+10 = 2*(b-10)   => 2b-a = 30 ......(i)   a = b+8   =>2b-b-8 = 30   b=38   so the present age of b is 38 years   ANSWER:38
Answer: B
If 1 persons can do 1 times of a particular work in 1 day, then, 7 persons can do 7 times of that work in
?  Choose the correct choice from the following answers
A) 3 days  B) 1 day  C) 9 days  D) 11 days  E) 15 days

Solution: That is, 1 person can do one time of the work in 1 day.   Therefore, 7 persons can do 7 times work in the same 1 day itself.   Option '1 day'
Answer: B
The speed of a train is 94 kmph. What is the distance covered by it in 12 minutes?  Select the correct option
A) 15 kmph
B) 11 kmph
C) 88 kmph
D) 19 kmph
E) 12 kmph

Solution: 94 * 12/60= 
94 * 12/60 = 94/5 = around 18.8
18.8 kmph   Answer:19 kmph
Answer: D
5, 9, 17, 29, 45, ?  Choices.
A) 65
B) 56
C) 74
D) 57
E) 32

Solution: The pattern is + 4, + 8, + 12, + 16, ....   65nswer : 65.
Answer: A
What is the two-digit number? I. The difference between the two-digit number and the number formed by interchanging the digits is 27. II. The difference between the two digits is 3. III. The digit at unit's place is less than that at ten's place by 3.  Choose the correct choice from the following choices:
A) I and II  B) II and III only  C) all  D) Even with all I, II and III, answer cannot be give.  E) I and either II or III

Solution: Let the tens and units digit be x and y respectively.   I. (10x + y) - (10y + x) x - y = 3.   II. x - y = 3.   III. x - y = 3.   Thus, even all the given three statements together do not give the answer.   Correct answer is (Even with all I, II and III, answer cannot be give.).
Answer: D
During a two-week period, the price of an ounce of silver increased by 10 percent by the end of the first week and then decreased by 10 percent of this new price by the end of the second week. If the price of silver was x dollars per ounce at the beginning of the two-week period, what was the price, in dollars per ounce, by the end of the period? Options.
A) 0.97x
B) 0.98x
C) 0.99x
D) x
E) 1.01x

Solution: The price at the end is 0.9(1.1x)=0.99x   The answer is 0.99x.
Answer: C
In a game, one player throws two fair, six-sided die at the same time. If the player receives at least a one or five on either die, that player wins. What is the probability that a player wins after playing the game once?	Choose the correct choice from the following options:
A) 1/3  B) 4/9  C) 3/4  D) 2/3  E) 5/9

Solution: We're looking for the number of outcomes that include AT LEAST a 1 or a 5.   #getting a one in 1st die = {(1,1), (1,2), ...(1,6) }= 6   #getting a one in 2nd die {(2,1), (3,1), ...(6,1) } = 4 [exclude 1,1 and 5,1] since it will be counted twice   #getting a five in 1st die {(5,1), (5,2), ...(5,6) }= 6   #getting a five in 1st die {(2,5), (3,5), ...(6,5) } = 4 [exclude 1,5 and 5,5] since it will be counted twice   Total possibilities = 20   Probability of rolling at least a 1 or a 5 on two dice: 20/36 = 5/9   5/9
Answer: E
By selling an article at Rs.600, a profit of 60% is made. Find its cost price?	Choose the correct answer:
A) 228 B) 267 C) 375 D) 480 E) 811

Solution: SP = 600   375P = (SP)*[100/(100+P)]   = 600 * [100/(100+60)]   = 600 * [100/160] = Rs.375   Answer: 375
Answer: C
The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of the correct time. How much a day does the clock gain or lose?  Choose the correct answer.
A) (10 + 10/143 )min
B) (10 + 10/843 )min
C) (10 + 19/143 )min
D) (90 + 10/143 )min
E) (10 + 10/193 )min

Solution: In a correct clock, the minute hand gains 55 min. spaces over the hour hand in 60 minutes.   To be together again, the minute hand must gain 60 minutes over the hour hand.   55 minutes are gained in 60 min.   60 min. are gained in [(60/55) * 60] min = min.   But they are together after 65 min.   Therefore, gain in 65 minutes = = min.   Gain in 24 hours = = 1440/143 min.   Therefore, the clock gains (10 + 10/143 )minutes in 24 hours.   (10 + 10/143 )minnswer: (10 + 10/143 )min) (10 + 10/143 )min
Answer: A