MU-NLPC/Calc-aqua_rat huggingface dataset:
A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 40 paise per sq. metre	Choose the correct choice from the following options:
A) s340  B) s780  C) s880  D) s480  E) s980

Solution: area of the plot=110m*65m=7150sq.m   area of plot excluding gravel110 *65= 
110 *65 = 7_150
7150sq.m   area of plot excluding gravel=105m*60m=6300sq.m   area of gravel 105 *60= 
105 *60 = 6_300
6300sq.m   area of gravel=7150sq.m-6300sq.m =850sq.m   cost of building it = 850sq.m*40   = 34000p   in Rs =34000/100= 
34000/100 = 340
Rs340   s340NSWER:s340
Answer: A
A retailer sells 10 shirts. The first 3 he sells for $82,$100 and $90. If the retailer wishes to sell the 10 shirts for an overall average price of over $100, what must be the minimum average price of the remaining 7 shirts?
Select the correct option:	A) $100.00	B) $104.00	C) $110.00	D) $115.00	E) $119.00

Solution: First 3 shirts are sold for $82,$100 and $90=$272.   To get average price of $100,total sale should be 10*$100=$1000   So remaining 7 shirts to be sold for $1000-$27210* 100= 
10* 100 = 1_000
$1000   So remaining 7 shirts to be sold for $1000-$272=$728   Answer should be 728/71000- 272= 
1000- 272 = 728
$728   Answer should be   728/7= 
  728/7 = 104
$104.00 that is $104.00
Answer: B
Billy read 2 books. He read the first one in one week with 25 pages everyday. He read the second book in 12 days with 23 pages everyday. What is the total number of pages that Billy read? Choose the correct answer.
A) 670 pages
B) 442 pages
C) 451 pages
D) 553 pages
E) 344 pages

Solution: Pages read in the first book in one week which is 7 days with 25 pages everyday.   25* 7= 
25* 7 = 175
175 pages   Pages read in the second book in 12 days with 23 pages everyday.   23* 12= 
23* 12 = 276
276 pages   Total number of pages read     175 + 276= 
  175 + 276 = 451
451 pages   correct answer 451 pages
Answer: C
A contract is to be completed in 46 days sad 117 men were said to work 8 hours a day. After 33 days, (4/7) of the work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 9 hours a day?	Select:  A) 91  B) 87  C) 85  D) 81  E) None of them

Solution: Remaining work = (1-(4/7) =(3/7)   Remaining period = (46 - 33)= 
(46 - 33) = 13
13days   Let the total men working at it be x.   Less work, Less men	(Direct Proportion)   Less days, More men	(Indirect Proportion)   More Hours per Day, Less men	(Indirect Proportion)   Work (4/7): (3/7)   Days 13:33 } : : 117: x   Hrs/day 9 : 8   Therefore (4/7) x 13 x 9 x x=(3/7) x 33 x 8 x 117 or x=(3 x 33 x 8 x 117)/(4 x 13 x 9)=198   Additional men to be employed = (198 - 117)= 
(198 - 117) = 81
81.   Answer is 81.
Answer: D
The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
Select the correct option.
A) 20 years B) 21 years C) 18 years D) 29 years E) 30 years

Solution: 9 * 2= 
9 * 2 = 18
18 years   Answer:18 years
Answer: C
John throws a coin until a series of three consecutive heads or three consecutive tails appears. What is the probability that the game will end after the third throw?
Choose the correct choice from the following answers
A) 1/4  B) 2/16  C) 3/16  D) 7/16  E) 9/16

Solution: Let's consider the routes that would lead to ending the game on the fourth toss. In order to be a win at that point, tosses #2#3#4 would all have to be the same, either H or T, and in order for the game NOT to end on the third toss, the first toss would have to be different from the other four. Thus, the only two possible sequences are   T-T-T ----> P = (1/2)^3 = 1/8   H-H-H ----> P = (1/2)^3 = 1/8   Either one of these would satisfy the condition, so we could have one or the other. OR means add in probability.   1/8 + 1/8 = 2/8 = 1/4   1/4nswer(1/4).
Answer: A
To fill a tank, 200 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to four-fifths of its present ? Select the correct option
A) 50
B) 100
C) 150
D) 200
E) 250

Solution: Let the capacity of 1 bucket = x.   Then, the capacity of tank = 200x.   New capacity of bucket = 4/5 x   Therefore, Required number of buckets = (200x)/(4x/5)   = (200x) x 5/4x   = 1000/4= 
1000/4 = 250
250   Answer is 250.
Answer: E
A photographer is to take group photographs of a class of students for the school magazine such that each photograph should have five students. If there are four girls and four boys in the class and each photograph must not have two girls or two boys standing together, how many different photographs can the photographer take?
Pick one
A) 80 B) 288 C) 44 D) 576 E) 288^2

Solution: Case-1: 3 Boys and 2 Girls are taken   Selection of 3 boys and 2 girls can be done in 4C3 * 4C2   Arrangement will look like B G B G B and Such arrangement of 5 individual can be done in desired manner in 3!*2! ways = 12 ways   No. of arrangement = 4C3 * 4C2 *3!*2! = 4*6*12= 
4*6*12 = 288
288   Case-2: 2 Boys and 3 Girls are taken   Selection of 2 boys and 3 girls can be done in 4C2 * 4C3   Arrangement will look like G B G B G and Such arrangement of 5 individual can be done in desired manner in 3!*2! ways= 12 ways   No. of arrangement = 4C2 * 4C3 *3!*2! = 4*6*12= 
4*6*12 = 288
288   Total Ways of Taking Photograph of 5 in desired manner= 288 + 288= 
288 + 288 = 576
576 ways   Answer: Option 576
Answer: D
Arabica coffee costs $0.6 per ounce while Robusta coffee costs $0.5 per ounce. If the blend of Arabica and Robusta costs $0.55 per ounce, what is the share of Arabica in this blend?	Choose the correct choice from the following answers
A) 20%
B) 24%
C) 30%
D) 50%
E) 40%

Solution: a= amount of arabica coffee   1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta   therefore:   .6a + .5(1-a) = .55   .6a + .5 - .3a = .55   a= .5   therefore: .5/1 ounce = 50%. Therefore, the answer should be 50%
Answer: D
A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze?  Choose the correct choice from the following answers.
A) 1217
B) 1219
C) 1210
D) 1212
E) 1312

Solution: π (232 – 122) = 1210   Answer:1210
Answer: C
A local bank that has 18 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 18 codes?
Choose the correct option.
A) 3  B) 4  C) 5  D) 6  E) 7

Solution: Pick any two integer.   Integers: 12   Code: 11, 12, 21, 22 = 4 Codes   Add one more integer: 3   13, 31, 33, 23, 32 = 5 Codes   Add one more integer: 4   44, 14, 41, 24, 42, 34, 43 = 7 Codes   Add one more integer: 5   55, 15, 51, 25, 52, 35, 53,54,45 = 9 Codes   Total = 25 Codes. Enough.   Answer: 5
Answer: C
Which of the following inequalities is equivalent to 40 + 6x > -3x - 11x + 20?	Select
A) x < 1
B) x < -1
C) x < 3
D) x < -3
E) x < 4

Solution: You can work with the inequality in the same way as you do when you have the equal to sign. You can take terms to the other side by flipping their sign, you can multiply/divide the inequality by the same term on both sides of the equation etc.   The only important thing to note is the following:   When you multiply/divide by a negative number, the sign of the inequality flips.   To illustrate,   40 + 6x > -3x - 11x + 20   40 + 20 > - 20x (Correct)   60 > - 20x (Correct)   -3 > x (Correct)   the correct option is x < -3
Answer: D
Find the average of the first 21 natural numbers?
Choose the correct choice from the following:
A) 8
B) 9
C) 10
D) 11
E) 12

Solution: Average of the first 'n' natural numbers = (n + 1)/2   We get  (21+ 1)/2= 
 (21+ 1)/2 = 11
11   ANSWER:11
Answer: D
For a finite sequence of non zero numbers, the number of variations in the sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -6?  Select.
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: The questions basically asks: how many pairs of consecutive terms are there in the sequence such that the product of these consecutive terms is negative.   1*(-3)=-3=negative;   -3*2=-6=negative;   5*(-6)=-30=negative.   So there are 3 pairs of consecutive terms.   Answer: 3.
Answer: C
10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How
many days will 5 women and 10 children take to complete the work?  Choices
A) 6 days  B) 7 days  C) 8 days  D) 9 days  E) None of these

Solution: Explanation:   1 woman's 1 day's work = 1/70   1 Child's 1 day's work = 1/140   5 Women and 10 children 1 day work =   (570+10140)=17   So 5 women and 10 children will finish the work in 7 days   Answer: 7 days
Answer: B
Peter traveled the entire 50 miles trip. If he did the first 12 miles of at a constant rate 36 miles per hour and the remaining trip of at a constant rate 48 miles per hour, what is the his average speed, in miles per hour?	Options:
A) 20mph B) 24mph C) 30mph D) 38mph E) 40mph

Solution: Average speed=sum of distance/sum of time. If he travelled the first 12 miles at 36 miles/hr, it would take 0.3 hr. For the remaining trip, if he went at 48 miles/1hr, it would take 1 hour. Then, the average speed is 50miles/(0.3+1)hrs=38miles/1hr.   Therefore, the answer is 38mph.
Answer: D
During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons. If Kim purchased 15 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount? Choose the correct choice:
A) 80%
B) 100%
C) 116.7%
D) 120%
E) 180%

Solution: Kim purchased 15 gallons of gas. She paid for   10 + 0.9*5= 
  10 + 0.9*5 = 14.5
14.5 gallons, so the overall discount she got was 0.5/15= 3.33%.   Isabella purchased 25 gallons of gas. She paid for   10 + 0.9*15= 
  10 + 0.9*15 = 23.5
23.5 gallons, so the overall discount she got was 1.5/25= 6%.   6 is 6/3.33*100 = 180% of 3.33.   Answer: 180%.
Answer: E
What is the least number of squares tiles required to pave the floor of a room 6 m 75 cm long and 4 m 5 cm broad?
Choose the correct option:
A) 15 B) 20 C) 40 D) 44 E) 54

Solution: Length of largest tile = H.C.F. of 675 cm and 405 cm = 135 cm.   Area of each tile = (135 x 135) cm2.   Required number of tiles =675 x 405/(135^2)= 15   15NSWER:15
Answer: A
Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 36 hours respectively. The ratio of their speeds is?	Choose the correct choice from the following options:
A) 3:6
B) 6:3
C) 4:9
D) 4:4
E) 4:2

Solution: Let us name the trains A and B.   Then, (A's speed) : (6:3's speed)   = âˆšb : âˆša = âˆš36 : âˆš9 = 6:3.Answer: 6:3
Answer: B
At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price? Choose one:
A) 62.5	B) 69.5	C) 62.3	D) 62.1	E) 62.4

Solution: CP = 47.50   SP = 47.50*(125/100)= 
47.50*(125/100) = 59.375
59.375   MP*(95/100)= 59.375   MP = 62.5   62.5nswer:62.5
Answer: A
The retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the 10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability that 3 of Sam’s 4 funds grew by at least 10% over last year?  Pick one:
A) 6C3 / 10C4	B) 6C3 * 4C1 / 10C4	C) 6C3 * 4C1 / 10P4	D) 6P3 * 4P1 / 10C4	E) 6P3 * 4P1 / 10P4

Solution: Total funds = 10   >10% = 6   <10% = 4   Question: Prob to pick 4 funds (3>10% and 1> 10%)   Option 1: Pick 3 out of 6 = 6C3 = 20   Option 2: Pick 1 out of 4 = 4C1 = 4   Total # = 4C10 = 210   Probability = Option1∗Option2/Total   or "6C3 * 4C1 / 10C4"
Answer: B
A person buys an article at $200. At what price should he sell the article so as to make a profit of 10%? Choose the correct answer.
A) 240  B) 260  C) 220  D) 300  E) 360

Solution: 220   220   220ost price = $200   profit = 10% of 200 = $20   Selling price = 220ost price + Profit   = 200 + 20= 
200 + 20 = 220
220
Answer: C
Four of the following five parts numbered (a), (b), (c), (d) and (e) are exactly equal. The number of the part which is not equal to the other four parts is your answer.  Choose the correct choice from the following choices:	A) 2x2 – 3xy + y2	B) (2x + y)(x – y)	C) (x – y)2 + x(x – y)	D) (2x – y)2 – x(2x – y)	E) (2x – y)2 – 2x2 + xy

Solution: Other parts are equal to   2x2 + y2 – 3xy.   Answer (2x + y)(x – y)
Answer: B
A retailer buys a radio for Rs 225. His overhead expenses are Rs 30. He sellis the radio for Rs 300. The profit percent of the retailer is Choose the correct choice from the following answers:
A) 10%  B) 50%  C) 25%  D) 17.6%  E) None of these

Solution: Explanation:   cost price = (225 + 30)= 
(225 + 30) = 255
255 sell price= 300   gain = (45/255)*100 = 17.6%. Answer: 17.6%
Answer: D
what is the sum of the first 10 odd natural numbers Answers:
A) 300	B) 400	C) 500	D) 600	E) 100

Solution: sum of first n odd natural nuber is = n^2   so sum of the first 10 odd natural numbers=(10)^2=100   ans 100   ANSW100R:100
Answer: E
Albert borrowed a total of $ 6000 from Brian and Charlie. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1400 as total interest. What is the interest paid to Brian at the end of three years?	Options:
A) 825
B) 790
C) 795
D) 785
E) 770

Solution: Let x be the amount borrowed form Brian. So amount borrowed form Charlie = 6000-x.   1400 = 21/100x + 27/100(6000-x)   =>x = 22000/6.   Interest paid = 3*7/100*22000/6= 
3*7/100*22000/6 = 770
770.   770
Answer: E
A train speeds past a pole in 15 seconds and a platform 100 meter long in 25 seconds. What is length of the train ? Select:
A) 140 meter B) 145 meter C) 150 meter D) 155 meter E) 160 meter

Solution: Explanation:   Let the length of the train is x meter and Speed of the train is y meter/second   Then x/y = 15 [because distance/speed = time]   => y = 15/x   x+100/25 =x/15   x=150 meters   So length of the train is 150 meters   ANSWER IS 150 meter
Answer: C
A starts business with Rs.3500 and after 10 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is Bâ€™s contribution in the Capital ?  Answers.
A) 24887 B) 20778 C) 23788 D) 31500 E) 2811

Solution: Explanation:   A invested Rs.3500 for 12 months.   Let B joined with investment x. And he invested for 12 - 10= 
12 - 10 = 2
2 months.   So there profit ratio= (3500 Ã— 12) : (2x) = 2 : 3   â‡’ x = 31500   Answer: 31500
Answer: D
A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 6 employees to 2 different offices? Options:
A) 64 B) 65 C) 44 D) 43 E) 56

Solution: Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 2*2*2*2*2*2=2^6=64.   64nswer: 64.
Answer: A
The average age of M boys is ‘b’ years and of ‘n’ girls ‘c’ years. The average age of all together is?  Choose the correct choice
A) (mb + nc)/ (m + m) years  B) (mb + nc)/ (n + n) years  C) (mb + nc)/ (m + n) years  D) (mb + nn)/ (m + n) years  E) (mn + nc)/ (m + n) years

Solution: (mb + nc) / (m+ n)   Answer:(mb + nc)/ (m + n) years
Answer: C
From the sale of sleeping bags, a retailer made a gross profit of 17% of the wholesale cost. If each sleeping bag was sold for $28, what was the wholesale cost per bag?	Choose the correct option:  A) 3.0  B) 3.36  C) 23.93  D) 25.0  E) 31.36

Solution: Cost price * 1.17 = Selling price --> Cost price * 1.17= $28 --> Cost price = $23.93.   Answer: 23.93.
Answer: C
Ronika deposited Rs.7000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much ?	Choose the correct choice from the following choices
A) 9850  B) 9500  C) 9620  D) 9760  E) 9100

Solution: Explanation:   As the interest rate increases by 2%   => (7000x3x2)/100 = 420   9200   --------   9620   ANSWER IS 9620
Answer: C
A train speeds past a pole in 50 seconds and a platform 500 m long in 100 seconds. Its length is:
Choose the correct choice from the following choices:	A) 550 m.	B) 300 m.	C) 600 m.	D) 400 m.	E) 500 m.

Solution: Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 50 => y = x/50   x + 500 / 100 = x / 50   x = 500 m.   Answer: Option 500 m.
Answer: E
Raman,Lakshmi and Muthu enter into partnership. Raman invests some money at the beginning, Lakshmi invests double the amount after 6 months, and Muthu invests thrice the amount after 8 months. If the annual gain be Rs.36000. Lakshmi's share is?	Pick one:	A) 12000	B) 14000	C) 8000	D) 5000	E) 3000

Solution: x* 12 : 2x* 6: 3x* 4   1:1:1   1/3 * 36000= 
1/3 * 36000 = 12_000
12000   12000nswer: 12000
Answer: A
A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is? Pick one:
A) 25 B) 28 C) 20 D) 21 E) 18

Solution: M = 15   S = 5   DS = 15 + 5= 
15 + 5 = 20
20   Answer:20
Answer: C
A man can do a piece of work in 8days, but with the help of his son, he can finish it in 3days. In what time can the son do it alone? Choose the correct choice from the following answers: A) 5 B) 5 1/2 C) 4 4/5 D) 6 E) 9 1/2

Solution: Son's 1day work = 1/3 - 1/8 = 5/24   Son alone can do the work in 24/5days = 4 4/5 days   Answer is 4 4/5
Answer: C
If f > x > y > z on the number line, y is halfway between x and z, and x is halfway between w and z, then (y - x)/(y - f) = Choose the correct choice from the following answers.
A) 1/4  B) 1/3  C) 1/2  D) 3/4  E) 1

Solution: Let y-z=t ---> since y is halfway between x and z and x>y we have x-y=t. Moreover x-z=(x-y)+(y-z)=2t. Similarly since x is halfway between w and z, we have f-x=2t. So y-x=-t, y-f=-3t. ---> (y - x)/(y - f) = 1/3.   The answer is (1/3).
Answer: B
A father is now three times as old as his son. Five years back, he was four times as old as his son. The age of the son (in years) is Choices
A) 12
B) 15
C) 18
D) 20
E) 22

Solution: Explanation:   Let son's age be x years. Then, father's age = (3x) years.   Five years ago, father's age = (3x - 5) years and son's age = (x - 5) years.   So, 3x - 5 = 4 (x - 5) 3x - 5 = 4x - 20 x = 15.   Answer: 15
Answer: B
Two trains each 260 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively. In what time will they cross each other completely? Choose the most appropriate option:
A) 15 sec  B) 19 sec  C) 12.48 sec  D) 10 sec  E) 11 sec

Solution: Explanation:   D = 260 m + 260 m = 520 m   RS = 80 + 70= 
80 + 70 = 150
150 * 5/18= 125/3   T = 520 * 3/125= 
520 * 3/125 = 312/25 = around 12.48
12.48 sec   Answer: Option 12.48 sec
Answer: C
We have boxes colored either red or blue. In each blue box there is a fixed number of blueberries. In each red box there is a fixed number of strawberries. If we dispose of one blue box for one additional red box, the total number of berries would increase by 12, and the difference between the total number of strawberries and the total number of blueberries would increase by 76. Each blue box contains how many blueberries? Choose the most appropriate option:  A) 26  B) 28  C) 30  D) 32  E) 34

Solution: Let x be the number of blueberries in each blue box.   Then there are x+12 strawberries in each red box.   x+(x+12)=76   x = 32   The answer is 32.
Answer: D
The average salary of workers in an industry is Rs.200 the average salary of technicians being Rs.400 and that of non-technicians being Rs.125. What is the total number of workers? Select the correct option:
A) 277 B) 665 C) 287 D) 208 E) 268

Solution: 8 * 84= 
8 * 84 = 672
672 – 7= 665   Answer:665
Answer: B
What is the normal price of an article sold at $108 after two successive discounts of 10% and 20%?
Select the correct option
A) $130	B) $140	C) $150	D) $160	E) $170

Solution: 0.8*0.9*cost price = $108   cost price = $150   The answer is $150.
Answer: C
A batsman makes a score of 87 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?
Pick one:
A) 25 B) 31 C) 27 D) 29 E) 39

Solution: Let the average after 17 innings = x   Total runs scored in 17 innings = 17x   Average after 16 innings = (x-3)   Total runs scored in 16 innings = 16(x-3)   Total runs scored in 16 innings + 87 = Total runs scored in 17 innings   => 16(x-3) + 87 = 17x   => 16x - 48 + 87 = 17x   => x = 39   Answer is 39.
Answer: E
How many seconds will a 450 metre long train take to cross a man running with a speed of 6 km/hr in the direction of the moving train if the speed of the train is 60 km/hr?
Choose the correct choice from the following:
A) 25 B) 30 C) 40 D) 45 E) 60

Solution: Explanation :   Speed of train relatively to man = ( 60 - 6)km/hr   = 54 km /hr   = (54 x 5 / 18)m/sec   = 15 m/sec   Time taken to pass the man = (450 / 15)= 
(450 / 15) = 30
30 sec.   Answer : 30
Answer: B
A bakery orders a shipment of apples and uses them all to make 150 apple pies. On slow days it takes 6 hours to sell all 150 apple pies. On busy days they sell 200 pies in 6 hours. Calculate how many hours one shipment of apples will last on a busy day.  Choose the correct choice from the following choices.
A) 6.2  B) 5  C) 4.5  D) 4.2  E) 3.8

Solution: First set up a ratio with all the relevant values and also the unknown variable:   150*6 = 200*x   Now solve by multiplying 150 by 6 and then dividing that product by 200:    150*6= 
 150*6 = 900
900   900/200= x   x = 4.5 hours   Answer: 4.5
Answer: C
If 13 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day can do it in how many days? Options:	A) 78 days.	B) 143 days.	C) 149 days.	D) 148 days.	E) 67 days.

Solution: B   143 days.   From the above formula i.e (m1*t1/w1) = (m2*t2/w2)   so (13*6*88/1) = (6*8*d/1)   on solving, d = 143 days.
Answer: B
A’s speed is 22/19 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?	Choose the most appropriate option.
A) 1/22 B) 1/19 C) 3/19 D) 2/19 E) 3/22

Solution: We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time.   This is what the beginning of the race will look like:   (Start) A_________B______________________________   If A covers 22 meters, B covers 19 meters in that time. So if the race is 22 meters long, when A reaches the finish line, B would be 3 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 3 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 22 meters) would be the same as the time required by B (to cover 19 meters) to reach the finish line.   So B should get a head start of 3/22th of the race.   Answer (3/22)
Answer: E