MU-NLPC/Calc-aqua_rat huggingface dataset:
A can do a piece of work in 6 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it? Choose the correct choice from the following answers.
A) 8.7 days B) 2.0 days C) 6.6 days D) 7.5 days E) 4.4 days

Solution: C = 1/2 - 1/6 - 1/5 =2/15   => 7.5 days   Answer: 7.5 days
Answer: D
Shekhar started a business investing Rs. 25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajeev joined him with an amount of Rs. 35,000. In 2001, Shekhar invested another additional amount of Rs. 10,000 and Jatin joined them with an amount of Rs. 35,000. What will be Rajeev's share in the profit of Rs. 1,50,000 earned at the end of 3 years from the start of the business in 1999 ?	Choose the most appropriate option.
A) 50000	B) 40000	C) 25000	D) 15200	E) 15000

Solution: Explanation:   Shekhar : Rajeev : Jatin   =(25000Ã—12+35000Ã—12+45000Ã—12) :(35000Ã—24) :(35000Ã—12)   =1260000:840000:420000=3:2:1.   Rajeev's share = Rs. (150000Ã—2/6) = Rs. 50000.   50000nswer IS 50000
Answer: A
The marks obtained by Polly and Sandy are in the ratio 3:5 and those obtained by Sandy and Willy are in the ratio of 5:2. The marks obtained by Polly and Willy are in the ratio of...?
Choose the correct choice from the following choices.
A) 2:1	B) 3:2	C) 4:3	D) 5:4	E) 6:5

Solution: Polly : Sandy = 3:5   Sandy : Willy = 5:2   Polly : Sandy : Willy = 3:5:2   Polly : Willy = 3:2   The answer is 3:2.
Answer: B
Two numbers are respectively 20% and 25% more than a third number. The percentage that is first of the second is?	Answers.
A) 80%	B) 85%	C) 96%	D) 125%	E) 150%

Solution: Explanation:   I II III   120 125 100   125----------120   100-----------? => 96%   ANSWER IS 96%
Answer: C
Rahul rented a power tool from a rental shop. The rent for the tool was $40 for the first hour and $20 for each additional hour. If Rahul paid a total of $160, excluding sales tax, to rent the tool, for how many hours did she rent it?	Choose the correct choice:
A) 1
B) 4
C) 9
D) 7
E) 3

Solution: 40 + 20n = 160   n = 6   Total time = n+1 hrs = 6+1= 
6+1 = 7
7 hrs   Answer : 7
Answer: D
In how many years, Rs. 150 will produce the same interest at 6% as Rs. 800 produce in 2 years at 4½% ? Choose the correct choice from the following choices.
A) 4 years B) 6 years C) 8 years D) 9 years E) 12 years

Solution: Explanation :   Let Simple Interest for Rs.150 at 6% for n years = Simple Interest for Rs.800 at 4½ % for 2 years   150×6×n/100=800×9/2×2/100   150×6×n=800×9/2×2   150×6×n=800×9   3×6×n=16×9   6×n=16×3   2×n=16   n=8 years   Answer : Option 8 years
Answer: C
A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going? Pick:
A) 7 sec
B) 6 sec
C) 1 sec
D) 7 sec
E) 9 sec

Solution: Speed of train relative to man = 60 + 6= 
60 + 6 = 66
66 km/hr.= 66 * 5/18 = 55/3 m/sec.   Time taken to pass the men = 110 * 3/55= 
110 * 3/55 = 6
6 sec.   Answer:6 sec
Answer: B
Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?	Choose the correct choice from the following choices:	A) 22	B) 12	C) 67	D) 20	E) 81

Solution: Relative speed = (42 + 30) * 5/18 = 4 * 5= 
4 * 5 = 20
20 mps.   Distance covered in passing each other= 120 + 280= 
120 + 280 = 400
400 m.   The time required= d/s = 400/20= 
400/20 = 20
20 sec.   Answer:20
Answer: D
When sold at a 40% discount, a sweater nets the merchant a 30% profit on the wholesale cost at which he initially purchased the item. By what % is the sweater marked up from wholesale at its normal retail price?  Choose the correct choice from the following answers:
A) 20% B) 40% C) 50% D) 53.85% E) 100%

Solution: we should be careful about what are we measuring % on/what is the base..   let the Marked up price =100..   Selling price= 100-40%of 100=60..   profit= 30%..   therefore the wholesale purchase cost= x.... 1.3x=60   or x=46.15...   marked price was 100 so ...   so answer is 53.85%..   53.85%
Answer: D
A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 24,000 earned at the end of 2 years from the starting of the business?	Pick.
A) A)7500  B) B)7389  C) C)7200  D) D)7453  E) E)7637

Solution: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3   B's share = 24000 * 3/10 = Rs.7200.   Answer: 7200
Answer: C
How many 7-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example 1234321. Answers.
A) 100  B) 610  C) 729  D) 9000  E) 1000

Solution: Take the task of building palindromes and break it intostages.   Stage 1: Select the 7th digit   We can choose 1, 2, 3, 4, 5, 6, 7, 8, or 9   So, we can complete stage 1 in 9ways   Stage 2: Select the 6th digit   We can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9   So, we can complete stage 2 in10ways   Stage 3: Select the 5th digit   We can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9   So, we can complete stage 3 in10ways   Stage 4: Select the 5th digit   We can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9   So, we can complete stage 4 in10ways   IMPORTANT: At this point, the remaining digits are alreadylocked in.   Stage 5: Select the hundreds digit   This digit must be the SAME as the thousands digit (which we already chose in stage 2)   So, we can complete this stage in1way.   Stage 6: Select the tens digit   This digit must be the SAME as the thousands digit (which we already chose in stage 2)   So, we can complete this stage in1way.   Stage 7: Select the units digit   This digit must be the SAME as the ten-thousands digit (which we already chose in stage 1)   So, we can complete this stage in1way.   By theFundamental Counting Principle(FCP), we can complete all 5 stages (and thus build a 7-digit palindrome) in(9)(10)(10)(10)(1)(1)(1)ways (= 9000 ways)   Answer: 9000
Answer: D
P, Q, R enter into partnership and their capitals are in the proportion 1/3 : 1/4 : 1/5. P withdraws half his capital at the end od 4 months. Out of total annual profit of Rs. 8470/-, P’s share is:
Choose the most appropriate option
A) Rs. 2520/-  B) Rs. 2800/-  C) Rs. 3150/-  D) Rs. 4120/-  E) None of these

Solution: Explanation:   Ratio of capitals in the beginning = 1/3 : 1/4 : 1/5 = 20 : 15 :12   Suppose A, Rs. 2800/-, C invest Rs 20x, Rs 15x and Rs 12x Respectively   A : Rs. 2800/- : C = (20x * 4 + 10x * 8) : (15x * 12) : (12x * 12)   = 160x : 180x : 144x = 160 : 180 : 144 = 40 : 45 : 36   A’s Share = Rs(8470 * 40/125) = Rs 2800/-   Answer: Option Rs. 2800/-
Answer: B
A man can do a piece of work in 4 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ? Answers.
A) 12 days	B) 6 days	C) 5 days	D) 4 days	E) None of these

Solution: Explanation:   In this type of question, where we have one person work and together work done. Then we can easily   get the other person work just by subtracting them. 12 dayss   Son's one day work =   (1/3−1/4)=(4−3)/12=1/12   So son will do whole work in 12 days   12 daysnswer: 12 days
Answer: A
What is the difference between the compound interest on Rs.12000 at 22% p.a. for one year when compounded yearly and half yearly?
Choose one:  A) 399  B) 383  C) 120.2  D) 288.2  E) 145.2

Solution: When compounded annually, interest   = 12000[1 + 22/100]1 - 12000 = Rs.2640   When compounded semi-annually, interest   = 12000[1 + 11/100]2 - 12000 = Rs.2785.20.   Required difference = 2785.20 - 2640 = Rs.145.20   Answer: 145.2
Answer: E
A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in?
Choose the correct answer.
A) 3 hours B) 6 hours C) 7 hours D) 4 hours E) 8 hours

Solution: B   6 hours   Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.   Then, (1/x + 2/x + 3/x) = 1/2   6/x = 1/2 => x = 12   So, 6 hours takes 6 hours to finish the work.
Answer: B
A can run 224 meter in 28 seconds and B in 32 seconds. By what distance A beat B?	Select the correct option:
A) 28 meter  B) 24 meter  C) 34 meter  D) 32 meter  E) 38 meter

Solution: Clearly, 28 meter beats B by 4 seconds   Now find out how much B will run in these 4 seconds   Speed of B = Distance/Time taken by B=224/32=28/4= 
28/4 = 7
7 m/s   Distance covered by B in 4 seconds= Speed × time =7×4=28 meter   28 meter beat B by 28 meter   28 meterNSWER:28 meter
Answer: A
A 10-by-8 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?
Pick
A) The volume of the cylinder with height 10 is 80/pi cubic inches greater than the volume of the cylinder with height 6. B) The volume of the cylinder with height 8 is 80/pi cubic inches greater than the volume of the cylinder with height 10. C) The volume of the cylinder with height 10 is 80pi cubic inches greater than the volume of the cylinder with height 6. D) The volume of the cylinder with height 8 is 80pi cubic inches greater than the volume of the cylinder with height 10. E) The volume of the cylinder with height 8 is 240/pi cubic inches greater than the volume of the cylinder with height 10.

Solution: Pretty straightforward. Plug in the values to compute the volume of the cylinder. Keep in mind 8 and 10 are the circumference of the base and not the radius. The volume of the cylinder with height 8 is 80/pi cubic inches greater than the volume of the cylinder with height 10. is the right answer.
Answer: B
Which of the following MUST yield an integer when divided by 3? Choose the correct choice.
A) The sum of three consecutive positive integers.
B) The square of a prime number.
C) The sum of two odd integers.
D) The product of three consecutive odd numbers.
E) The difference between a multiple of 8 and a multiple of 3.

Solution: For option A: Let the numbers be (x-1), (x), (x+1), .   Now, (x-1) + (x) + (x+1) = 3(x). Hence A is true. No need to check other answers since there can only be one correct answer.   So, The sum of three consecutive positive integers.ns(The sum of three consecutive positive integers.).
Answer: A
The greatest number by which the product of three consecutive multiplies of 3 is always divisible is Choose the most appropriate option:
A) 54  B) 81  C) 162  D) 243  E) None

Solution: Sol.   Required number = Product of first three multiplies of 3   = (3 × 6 × 9) = 162.   Answer 162
Answer: C
Two spherical balls lie on the ground touching. If one of the balls has a radius of 10 cm, and the point of contact is 12 cm above the ground, what is the radius of the other ball?
Select the correct option.
A) 2 cm
B) 5/2 cm
C) 5 cm
D) 15/2 cm
E) none of the these

Solution: similar triangle properties..   2/r+10 = 10/r-10   giving r = 15/2.   Answer: 15/2 cm
Answer: D
Dames school has 2000 boys and 5000 girls. What is the percentage increase from boys to total attendance and girls to total attendance?
Choose the most appropriate option:
A) A) 40%
B) B) 10%
C) C) .4%
D) D) 50%
E) E) 12%

Solution: Ratio of boys to total attendance (2/7)   Ratio of girls to total attendance (5/7)   percentage increase is (difference/initial quantity)*100   (2/7)/(5/7 )* 100= 
(2/7)/(5/7 )* 100 = 40
40%   Correct answer is 40%
Answer: A
Shreyas bought an article and sold it for 125% of its cost price. What was the cost price of the article, if Shreyas sold it for Rs.30750/-?	Choose one:
A) Rs.24600 B) Rs.25640 C) Rs.24250/- D) Rs.23200 E) None of these

Solution: Explanation:   125% of CP = Rs.30750   :. CP = Rs.30750x100/125 = Rs.24600.   Rs.24600nswer: Option Rs.24600
Answer: A
Y can do a work in 2/3 the time it takes X. Z can do the same work in ¾ the time it takes Y.When all three are typing at the same time what fraction of their total work does Y do  Choose the correct choice from the following choices
A) 1/3 B) 4/13 C) 9/23 D) 8/29 E) 10/29

Solution: given the ratio of the time of y and x is 2/3 : 1   therefore the ratio of speed of the x and y becomes 2 : 3.   similarly the ratio of the speed of the z and y given as 4 : 3   therefore the speed of the y and z becomes 3 : 4.   now , comparing the ratio of the x,y and z   it becomes 2: 3 :: 3 : 4   hence the y is doing 3/9 hence it is doing 1/3 work.   1/3NSWER:1/3
Answer: A
In how many ways, a committee of 8 members can be selected from 10 men and 8 ladies, consisting of 5 men and 3 ladies? Choose one:
A) 15000 B) 14567 C) 14112 D) 13445 E) 14431

Solution: (5 men out 10) and (3 ladies out of 8) are to be chosen   Required number of ways = 10141125*8141123 = 14112   Answer is 14112
Answer: C
One hour after Adrienne started walking the 60 miles from X to Y, Harold started walking from X to Y as well. Adrienne walks 3 miles per hour and Harold walks 1 mile per hour faster than Adrienne. How far from X will Harold be when he catches up to Adrienne?
Options:
A) 8 miles  B) 12 miles  C) 10 miles  D) 11 miles  E) 14 miles

Solution: First, determine how far Adrienne has walked in the one hour. She has walked three miles which means she is three miles ahead of Harold when he sets off. Harold walks at four miles/hour which means that every hour, Harold will get one mile closer to Adrienne. If he gets one mile closer every hour, it will take him three hours to catch up to her which means he travels 3hours * 4 miles/hour = 12 miles and she travels 4 hours * 3 miles/hour = 12 miles. He will be 12 miles from X when he catches up to her.   A slightly different way to solve...   We don't know how long they will walk before they catch up to one another but we do know that A walks for one hour more than J. J = T and A = T+1. We are looking for the distance at which they meet up which means the distance will be the same. D=r*t so,   r*t (Harold ) = r*t (adrienne)   r*(t) = r*(t+1)   4t = 3t+3   t=3   d=r*t   d=4*3= 
4*3 = 12
12   12 miles) 12 miles
Answer: B
A box contains 3 blue marbles, 4 red, 6 green marbles and 1 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?  Select the correct option
A) 1/364  B) 2/455  C) 1/91  D) 4/455  E) None of these

Solution: Given that there are three blue marbles, four red marbles, six green marbles and one yellow marbles.   Probability that all the three marbles picked at random are blue = 3C₃/14C₃ = (1 * 3 * 2 * 1)/(14 * 13 * 12) = 1/364   1/364NSWER:1/364
Answer: A
If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/8, then what is the value of abc/def ?  Select the correct option:  A) 27/4  B) 27/8  C) 3/4  D) 3/16  E) 1/4

Solution: Say a = 2. Then:   a/b = 1/3 --> b = 6;   b/c = 2 --> c = 3;   c/d = 1/2 --> d = 6;   d/e = 3 --> e = 2;   e/f = 1/8 --> f = 16.   abc/def = (2*6*3)/(6*2*16) = 3/16.   Answer: 3/16.
Answer: D
Salesperson A's compensation for any week is $300 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of B's total sales for that week. For what amount of total weekly sales would both salespeople earn the same compensation?
Choose the correct choice from the following options.
A) $21,000
B) $18,000
C) $12,000
D) $8000
E) $4000

Solution: 300+0.06(x-1000) = 0.08x   0.02x = 240   x = $12,000   The answer is $12,000.
Answer: C
A, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 9 days respectively. They worked together for five days and then C completed the remaining work all alone. If $720 was the net sum to be paid for the entire work, what was the average daily wage of B? Pick:
A) $144
B) $80
C) $60
D) $54
E) $48

Solution: The correct answer is $80.
Answer: B
Exactly 20% of the reporters for a certain wire service cover local politics in Country X. If 20% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics? Choose the correct choice from the following answers:
A) 20%  B) 42%  C) 44%  D) 75%  E) 84%

Solution: You are correct. People who cover local politics are a subset of people who cover politics.   20% of reporters who cover politics do not cover local politics so 80% DO cover local politics.   Reporters covering local politics= 80% of reporters covering politics= 20% ofall reporters   Reporters covering politics/All Reporters = 20/80 = 1/4   Reporters not covering politics/All Reporters = 3/4 = 75%=75%
Answer: D
Set W consists of all even integers between 2 and 100, inclusive. Set X is derived by reducing each term in set W by 50, set Y is derived by multiplying each term in set W by 1.5, and set Z is derived by dividing each term in set W by -4. Which of the following represents the ranking of the three sets in descending order of standard deviation?	Answers:
A) X, Y, Z B) X, Z, Y C) Y, Z, X D) Y, X, Z E) Z, Y, X

Solution: Set W - {2, 4, ..., 100};   Set X - {-48, -46, ..., 50};   Set Y - {3, 6, ..., 150};   Set Z - {-2/4, -4/4, ..., -100/4} = {-1/2, -1, -3/2, ..., -25}.   If we add or subtract a constant to each term in a set the SD will not change, so sets W and X will have the same SD.   If we increase or decrease each term in a set by the same percent (multiply by a constant) the SD will increase or decrease by the same percent, so set Y will have 1.5 times greater SD than set W and set Z will have 4 times less SD than set W (note SD can not be negative so SD of Z wil be SD of W divided by 4 not by -4).   So, the ranking of SD's in descending order is: Y, W=X, Z.   Answer: Y, X, Z.
Answer: D
Sonika deposited Rs.4500 which amounted to Rs.8400 after 2 years at simple interest. Had the interest been 4% more. She would get how much? Choose the correct answer:
A) 9680 B) 8790 C) 8760 D) 9020 E) 5000

Solution: (4500*2*4)/100= 
(4500*2*4)/100 = 360
360   8400   --------   8760   Answer: 8760
Answer: C
How many of the factors of 280 are divisible by 2?  Choose the correct choice from the following:
A) 4
B) 8
C) 10
D) 12
E) 16

Solution: 280 = 2^3*5*7   The total number of factors is (1+3)(1+1)(1+1) = 16   The odd factors are 1, 5, 7, and 35.   The number of even factors is 16-4= 
16-4 = 12
12   The answer is 12.
Answer: D
The average (arithmetic mean) of eight numbers is 43.2. If the sum of half of these numbers is 156.4, what is the average of the other half?	Choose the correct choice from the following answers.
A) 47.3
B) 51.5
C) 55.8
D) 59.2
E) 63.7

Solution: The average of this half is 156.4/4= 
156.4/4 = 39.1
39.1   This is 4.1 below the overall average, thus the average of the other half of the numbers must be 4.1 above the overall age, that is 43.2+4.1= 
43.2+4.1 = 47.3
47.3   The answer is 47.3.
Answer: A
The very opening sentence of the passage speaks about the ‘semantic conspiracy’ which means linguistic intrigue; a trickery usage of language. Choose the correct answer:
A) 11  B) 21  C) 112  D) 112  E) 1111

Solution: Answer:1111
Answer: E
A mother bought three dress for her triplets daughters(one for each) and put the dresses in the dark. One by one the girls come and pick a dress.
What is the probability that no girl will choose her own dress?  Options.
A) 1/2	B) 3/4	C) 2/3	D) 1/3	E) 2/4

Solution: Assuming D1 is the dress for Sister1, D2 is the dress for Sister2 and D3 is the dress for Sister3.   Therefore the total number of cases are illustrated below.   Sister1 Sister2 Sister3   D1 D2 D3   D1 D3 D2   D2 D1 D3   D2 D3 D1 ..... (1)   D3 D1 D2 .... (2)   D3 D2 D1   In both steps (1) & (2), no one gets the correct Dress.   Therefore probability that no sister gets the correct dress is 2/6 = 1/3   correct answer is 1/3)1/3
Answer: D
A stock trader originally bought 100 shares of stock from a company at a total cost of m dollars. If each share was sold at 50% above the original cost per share of stock, then interns of m for how many dollars was each share sold? Pick:
A) a) 3m/300
B) b) m/300
C) c) m/200
D) d) m/300 + 50
E) e) 350/m

Solution: Let Cost of 100 shares be $ 1000   So, Cost of 1 shares be $ 10 =>m/100   Selling price per share = (100+50)/100 * m/100   Or, Selling price per share = 3/2 * m/100 => 3m/200   Hence answer will be (a) 3m/300)
Answer: A
If A and B are two prime numbers bigger than 2, which of the following can't be true?
(1) A + B is an even number.
(2) A x B is also a prime number.
(3) A- B is also a odd number.
Choose the correct choice from the following choices:
A) 1 only. B) 2 only. C) 3 only. D) 1 and 3 only. E) 2 and 3. Only

Solution: (1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true   (2) A x B is also a prime number. : Beats the property of primes, so false   (3) A^B is also a prime number. : Beats the property of primes, so false   Ans 2 and 3. Only
Answer: E
The average of first 10 natural numbers is? Choose the correct choice:
A) 5.2
B) 5.5
C) 5.3
D) 5.9
E) 5.1

Solution: Sum of 10 natural no. = 110/2= 
110/2 = 55
55   Average= 55/10= 
55/10 = 11/2 = around 5.5
5.5   Answer:5.5
Answer: B
The difference between the compound interest and simple interest on a certain sum of money at 5% per annum for 2 years is 45. Then the original sum is?	Answers:
A) 17000  B) 12000  C) 19000  D) 14000  E) 18000

Solution: For 2 years = (100(power 2)D)/R(power 2)   = (100(power 2) × 45)/(5 × 5) = (10000 × 45)/25 = Rs.18000/-   Answer is 18000.
Answer: E
A reduction of 30% in the price of oil enables a house wife to obtain 9 kgs more for Rs.1800, what is the reduced price for kg?	Choose one
A) Rs.55  B) Rs.60  C) Rs.65  D) Rs.70  E) Rs.75

Solution: Explanation:   1800*(30/100)= 
1800*(30/100) = 540
540 ---- 9   ? ---- 1=> Rs.60   Answer: Rs.60
Answer: B
The speed at which a man can row a boat in still water is 15 km/hr. If he rows downstream, where the speed of current is 3 km/hr, how many seconds will he take to cover 110 meters?
Pick
A) 18	B) 20	C) 22	D) 24	E) 28

Solution: The speed of the boat downstream = 15 + 3= 
15 + 3 = 18
18 km/hr   18 km/hr * 5/18= 5 m/s   The time taken to cover 110 meters = 110/5= 
110/5 = 22
22 seconds.   The answer is 20.
Answer: B
The sum of three consecutive numbers is 102. The greatest among these three number is:  Select the correct option.
A) 26
B) 35
C) 29
D) 30
E) 31

Solution: Let the numbers be x, x + 1 and x + 2   Then,   x + (x + 1) + (x + 2) = 102   3x = 102   x = 33   Greatest number, (x + 2) = 35.   ANSWER:35
Answer: B
If an item that originally sold for z dollars was marked up by x percent and then discounted by y percent, which of the following expressions G represents the final price of the item?  Choose the correct answer:	A) G=(10,000z + 100z(x – y) – xyz)/10,000	B) G=(10,000z + 100z(y – x) – xyz)/10,000	C) G=(100z(x – y) – xyz)/10000	D) (100z(y – x) – xyz)/10000	E) 10000 /(x – y)

Solution: -G=(10,000z + 100z(x – y) – xyz)/10,000-   z=Original Price   x= MU   y=MD   New price with MU:   z(x/100+1)   New price with MD:   z[(x/100+1)(-y/100+1)]   Solvingâ€¦   =z[((x+100)/100)((-y+100)/100)]   =z(x100-xy+10000-100y)/10000   =(zx100-xyz+10000z-100yz)/10000 --> similar to G=(10,000z + 100z(x – y) – xyz)/10,000
Answer: A
A bag contains 5 red and 3 green balls. Another bag contains 4 red and 6 green balls. If one ball is drawn from each bag. Find the probability that one ball is red and one is green. Choose the most appropriate option: A) 19/20 B) 17/20 C) 21/40 D) 8/10 E) 9/40

Solution: Let A be the event that ball selected from the first bag is red and ball selected from second bag is green.   Let B be the event that ball selected from the first bag is green and ball selected from second bag is red.   P(A) = (5/8) x (6/10) = 3/8.   P(B) = (3/8) x (4/10) = 3/20.   Hence, the required probability is P(A) + P(B) which is nothing but 21/40.   ANSWER:21/40
Answer: C