MU-NLPC/Calc-aqua_rat huggingface dataset:
130 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? Pick
A) 8 days	B) 6 days	C) 7 days	D) 9 days	E) 13 days

Solution: 1 women's 1 day work = 1/910   1 child's 1 day work = 1/140   (5 women + 10 children)'s 1 day work   = (5/910 + 10/140) = 1/13   5 women and 10 children will complete the work in 13 days.   Answer: 13 days
Answer: E
Five kilograms of oranges contained 90% of water. If the next day the concentration of water decreased by 10%, what was the new weight of the oranges, in kilograms?  Choose one:
A) 4.9
B) 4.8
C) 2.5
D) 2
E) 0.2

Solution: Five kilograms of oranges contained 90% of water. If the next day the concentration of water decreased by 10%, what was the new weight of the oranges, in kilograms?   (A) 4.9   (B) 4.8   (C) 2.5   (D) 2   (E) 0.2   If C is the answer, then the question means that the concentration of water the newt day became 80%.   Out of 5 kilograms 90%, or 4.5 kilograms was water and 0.5 kilograms was non-water.   The next day, after some water evaporated, oranges became 80% water and 20% of non-water, so the next day 0.5 kilograms of non-water composed 20% of oranges, which means that the new weight of the oranges was x*0.2=0.5 --> x=2.5 kilograms.   Answer: 2.5.
Answer: C
In a can, there is a mixture of milk and water in the ratio 3 : 7. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 4 : 7. Find the capacity of the can? Choose the correct answer.
A) 16.6  B) 44  C) 27  D) 50  E) 56

Solution: Let the capacity of the can be T litres.   Quantity of milk in the mixture before adding milk = 3/10 (T - 8)   After adding milk, quantity of milk in the mixture = 4/11 T.   4T/11 - 8 = 3/10(T - 8)   37T = 880- 264 => T = 16.6.   16.6nswer:16.6
Answer: A
Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.1740? Choose the correct choice from the following answers
A) Rs.1000  B) Rs.1550  C) Rs.1510  D) Rs.1500  E) None of these

Solution: Explanation:   1740 = P [1 + (5*16/5)/100]   P= 1500   Answer: Option Rs.1500
Answer: D
A camera lens filter kit containing 5 filters sells for $87.50. If the filters are purchased individually, 2 of them are priced at $16.45 each, 2 at $14.05 each, 1 at $19.50. The amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually?	Choose the correct choice from the following choices
A) 7%  B) 8%  C) 9%  D) 10%  E) 11%

Solution: Cost of kit = $87.50   If filters are purchased individually - $16.45*2 + $14.05*2 + $19.50 = $80.50   Amount saved = $87.50 - $80.50 = $7   Required %age 87.50 -  80.50= 
87.50 -  80.50 = 7
$7   Required %age= ($7/$87.50)*100 = 8%   So, the correct answer is 8%.( 7/ 87.50)*100= 
( 7/ 87.50)*100 = 8
8%   So, the correct answer is 8%.
Answer: B
An auto assembly plant performs six functions with each frame that arrives: add axles, add wheels to the axles, install the windshield to the frame, install the instrument panel, install the steering wheel, and install the interior seating. Once those six tasks are performed, each car goes to a separate building for finishing touches. If these tasks can be arranged along a linear assembly line in any order, except that the axles must be installed before the wheels can be added, how many ways can the assembly line be arranged? Options.
A) 120	B) 240	C) 360	D) 480	E) 720

Solution: there are 6C! ways to do the six tasks. Half will have wheels before axles and half will have axles before wheels. So we want 6360!/2 -> 720/2 = 360   ANS:360) 360
Answer: C
A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :  Choose the correct choice from the following
A) 8/15 B) 7/15 C) 2 D) 1/15 E) 1/10

Solution: A's 1 day's work =1/15   B's 1 day's work =1/20   (A + B)'s 1 day's work =(1/15+1/20)=7/60	.   (A + B)'s 4 day's work =(7/60 x 4)=7/15.   Therefore, Remaining work =(1 -7/15	)=8/15.   8/15nswer: Option 8/15
Answer: A
9 friends bought a shopping mall for 12 million dollars. If the all businessman have to pay the same amount and none of them have amount smaller than $1, how much money would they have to pay?
Pick one:
A) 11,999,997
B) 12,000,000
C) 12,000,002
D) 12,000,003
E) 12,000,004

Solution: In order to divide the sum in 9 parts, the amount must be divisible by 9   Divisibility rule of 9: The sum of the digits must be divisible by 9   Sum of digits of 12,000,000 = 12 and 9 is divisible by 9.   Hence, we need to remove 3 to this number for it to be divisible by 9   Correct Option: 11,999,997
Answer: A
A man can reach a certain place in 30 hours. If he reduces his speed by 1/15th, he goes 10 km less in that time. Find his speed.  Choices:
A) 4 1/2km/hr	B) 5 km/hr	C) 5 1/2km/hr	D) 6 km/hr	E) none

Solution: Sol.   Let the speed be x km/hr. Then,   30x-30*14/15x = 10   ⇔ 2x = 10   ⇔ x = 10/2= 
10/2 = 5
5 km/hr   Answer 5 km/hr
Answer: B
Nicky and Cristina are running a 200 meter race. Since Cristina is faster than Nicky, she gives him a 12 second head start. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?	Select:
A) 35 B) 30 C) 45 D) 40 E) 50

Solution: The distance traveled by both of them is the same at the time of overtaking.   3(t+12) = 5t   t=18.   Cristina will catch up Nicky in 18 seconds.   So in 18 seconds Cristina would cover = 18*5= 
18*5 = 90
90 meter.   Now Time taken my Nicky to cover 90 meter= 90/3= 
90/3 = 30
30 Seconds.   30
Answer: B
X Y
+Y X
________
The sum of the two digit numbers above is a three digit number PQ4, where each letter X, Y, P, and Q represents a different non zero digit. Which of the following can be the value of X?
I)	7
II)	8
III)	9 Choose one
A) I only	B) II only	C) III only	D) I , II and III	E) I and II only

Solution: it can be a combination of 6,8 or 7,7 or 5,9   I choose I , II and III as an answer.
Answer: D
Bag contain 10 back and 20 white balls, One ball is drawn at random. What is the probability that
ball is white  Select:  A) 1  B) 2/3  C) 1/3  D) 4/3  E) None of these

Solution: Explanation:   Total cases = 10 + 20= 
10 + 20 = 30
30   Favourable cases= 20   So probability = 20/30 = 2/3   Answer: 2/3
Answer: B
Pandi and Rani invested in a business. They earned some profit which they divided in the ratio of 3:2. If Pandi invested Rs.30, 000, the amount invested by Rani is: Choose the correct option.
A) Rs. 65,000 B) Rs. 20,000 C) Rs. 80,000 D) Rs. 90,000 E) Rs. 60,000

Solution: Invested by Rani = 30000/3*2= 
30000/3*2 = 20_000
20000   Answer : Rs. 20,000
Answer: B
In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students T in the class?
Choose the correct choice from the following choices:	A) A)10	B) B)12	C) C)15	D) D)20	E) E)25

Solution: the difference between the highest and lowest salaries is $100,000.   So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range.   Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k.   Mean = 20k more than median so in our example, mean salary = 70k   On the number line,   0........50k (median)........100k   Mean = 70k   So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get:   0....50k.....100k, 100k, 100k   But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get:   0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k   the median is not at 50k yet.   Add another 3 people at 50k and another 2 at 100k to get   0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k   Now the median is 50k and mean is 70k.   Total number of people is 15.   Answer (15)(70  + 20 )= 
(70  + 20 ) = 90
90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get:   0....50k.....100k, 100k, 100k   But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get:   0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k   the median is not at 50k yet.   Add another 3 people at 50k and another 2 at 100k to get   0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k   Now the median is 50k and mean is 70k.   Total number of people is 15.   Answer (15)
Answer: C
Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent should A pay?  Answers
A) 1/3 rd  B) 2/5 th  C) 2/3 rd  D) 1/5 th  E) 2/5 th

Solution: 3h = 5c   6c = 10s   1/3 rd = 21h*3 + 15c*2   = 63h + 30c   = 105c + 30c = 135c   B 105  + 30= 
105  + 30 = 135
135c   B= 15c*6 + 40s*7 1/2   = 90c + 300s   = 90c + 180c = 270c   1/3 rd:B 90  + 180= 
90  + 180 = 270
270c   1/3 rd:B= 135:270   27:52   1/3 rd = 27/79 = 1/3   1/3 rdNSWER:1/3 rd
Answer: A
If p - q = 2 and
p2+q2=26
, find the value of pq.
Choose the correct choice from the following choices.
A) 7
B) 8
C) 9
D) 11
E) 10

Solution: Explanation:   We know   2ab=(a2+b2)âˆ’(aâˆ’b)2   2pq=26âˆ’4=22   =>pq=11   Option 11
Answer: D
A cylinder of height h is 5/6 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?	Choose the correct choice from the following answers:
A) 25%
B) 50%
C) 60%
D) 72%
E) 100%

Solution: Basically we can disregard the radius is 25% information, as we are only asked about the height of the original and the new cylinder.   This is becausethe new cylinder is 3/5 fullmeans the same as that it's height is 3/5.   Original cylinder 5/6   New cylinder 3/5   So 3/5/5/6 = 3/5 *6/5= 
3/5 *6/5 = 18/25 = around 0.72
0.72 or 72%.   Answer 72%
Answer: D
In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/6. For a group of 200 newborn members of the population, approximately how many would be expected to survive the first 3 months of life? Choose the correct option
A) 116
B) 146
C) 152
D) 162
E) 170

Solution: The probability of survival for each of the first 3 months of life is 1-1/6= 5/6, so of 200 newborn 200*5/6*5/6*5/6=~116 is expected to survive.   116nswer: 116.
Answer: A
A train passes a station platform in 34 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Choose the correct option:
A) 200  B) 210  C) 240  D) 250  E) 260

Solution: Speed = [54 * 5/18] m/sec = 15 m/sec.   Length of the train = (15 * 20)= 
(15 * 20) = 300
300 m.   Let the length of the platform be x meters.   Then, x + 300 / 34= 15   x + 300 = 510   x = 210 m.   Answer: Option 210
Answer: B
What is the solution of the equations x - y = 0.1 and 1(x + y)-1 = 2 ?	Choose one
A) x = 0.3, y = -0.2
B) x = 1, y = 0.1
C) x = 2, y = 1.1
D) x = 1.2, y = 0.3
E) None

Solution: x = 0.3, y = -0.2nswer   x - y = 0.1 ...(i)   and 1(x + y)-1=2   ⇒ 1/ (x + y) = 2   ⇒ 2(x + y) =1   ⇒ x + y = 1/2 ...(ii)   On solving Eqs.(i) and (ii),we get   x = 0.3   and y = -0.2   Correct Option: x = 0.3, y = -0.2
Answer: A
Anthony and Michael sit on the six member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent Q of all the possible subcommittees that include Michael also include Anthony?  Select:
A) 20%  B) 30%  C) 40%  D) 50%  E) 60%

Solution: The answer is C. Let's look at a committee where Mike belongs (he's person # 1) on that committee. When we choose person #2, there is a 1/5 probability that it's going to be Anthony (then it doesn't matter who the third person is), and 4/5 probability that it's going to be someone else (then person #3 is going to be Anthony with probability 1/4). Total probability Q= 1/5+4/5*1/4 = 2/5.40%
Answer: C
78 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,075 bacteria each. How many bacteria are there approximately?	Choices:
A) 10^7
B) 10^8
C) 10^9
D) 10^10
E) 10^11

Solution: 78 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,075 bacteria each. How many bacteria are there approximately?   A. 10^7   B. 10^8   C. 10^9   D. 10^10   E. 10^11   -> Due to approximately, 78=80, 48=50, 25,075=25,000 are derived, which makes (78)(48)(25,075)=(80)(50)(25,000)=10^8. The answer is 10^8.
Answer: B
A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18900. A's share is? Options
A) 6300 B) 2765 C) 6000 D) 1298 E) 1261

Solution: x* 12 : 2x* 6: 3x* 4   1:1:1   1/3 * 18900= 
1/3 * 18900 = 6_300
6300   6300nswer:6300
Answer: A
What is the 4 digit no. in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is 3 times the second?
Select the correct option
A) 1123  B) 1234  C) 1349  D) 1455  E) 1567

Solution: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.   First + second = third => we can eliminate 3 & 9 since  3 + 9= 
 3 + 9 = 12
12.   Last is 3 times the second=> we can eliminate option 2 & 6 since  3 * 6= 
 3 * 6 = 18
18.   Hence the number is 1349   1349
Answer: C
$2,000 is deposited in a savings account that pays 4% annual interest compounded semiannually. To the nearest dollar, how much is in the account at the end of the year?	Choose the correct choice from the following options.
A) $2125.15  B) $2083.12  C) $2184.22  D) $2150.84  E) $2080.80

Solution: this is the case of semi-annual compoundingso, multiply time period by 2 and divide rate by 2   So,   new time=2periods and new rate=4/2= 
4/2 = 2
2%   Now,   CA=2000(1+2/100)^2=$2080.80   Hence answer is $2080.80
Answer: E
Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?  Choices
A) 287  B) 369  C) 125  D) 279  E) 361

Solution: 3x * 2x = 3750 => x = 25   2(75 + 50) = 250 m   250 * 1/2   = Rs.125   Answer:125
Answer: C
In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?	Choose the correct choice from the following answers:	A) 2.5 sec	B) 2.6 sec	C) 2.7 sec	D) 2.8 sec	E) 2.9 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 100/40= 
100/40 = 5/2 = around 2.5
2.5 sec.   2.5 secnswer: Option 2.5 sec
Answer: A
What is the probability of flipping a fair coin four times and the coin landing on heads on exactly two flips?	Select the correct option
A) 1/6
B) 3/4
C) 1/3
D) 2/5
E) 3/8

Solution: Probability = (Favorable combination)/(Total combination)   Favorable combination = (HHTT, HTHT, HTTH,THHT,THTH,TTHH) ==> 6   Total combination = 16 (2^4)   Probability = (6)/(16) = 3/8   (3/8)
Answer: E
A bus trip of 360 miles would have taken 1 hour less if the average speed V for the trip had been greater by 5 miles per hour. What was the average speed V, in miles per hour, for the trip?	Choose the correct choice from the following options:	A) 35	B) 40	C) 45	D) 50	E) 55

Solution: The time is the distance/speed. The time difference is 1 hour.   360/V - 360/(V+5) = 1   360(V+5) - 360V = (V)(V+5)   1800 = (V)(V+5)   40*45 = (V)(V+5)   V = 40 mph   The answer is 40.
Answer: B
By selling 10 pencils for a rupee a man loses 15%. How many for a rupee should he sell in order to gain 15%?	Choose the correct choice from the following choices.
A) 8.39  B) 6.39  C) 7.39  D) 9.39  E) 2.39

Solution: 85% --- 10115% --- ?85/115 * 10 = 7.39Answer: 7.39
Answer: C
4,6,8,10,12,.... Answers: A) 58 B) 14 C) 61 D) 62 E) 63

Solution: 2*2= 
2*2 = 4
4   3*2= 
3*2 = 6
6   4*2= 
4*2 = 8
8   5*2= 
5*2 = 10
10   6*2= 
6*2 = 12
12   7*2= 
7*2 = 14
14   ANSWER:14
Answer: B
Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.6. If VP Adams approves the proposal, then the probability that vice-president Baker will approve the proposal is 0.2. If VP Adams doesn’t approve the proposal, then the probability that vice-president Baker will approve the proposal is 0.3. What is the probability that at least one of the two VPs, approves Johnson’s proposal?	Choose the correct choice from the following answers
A) 0.36 B) 0.24 C) 0.28 D) 0.48 E) 0.72

Solution: (1at approves * second rejects ) + (1st rejects * 2nd approves ) + (both approves )   =0.6*0.2+0.4*0.3+0.6*0.2   = 0.12+0.12+0.12= 
0.12+0.12+0.12 = 0.36
0.36   0.36
Answer: A
JOHN and Antony can finish the work 36 days if they work together. They worked together for 24 days and then Antony left. JOHN finished the remaining work in another 24 days. In how many days JOHN alone can finish the work?
Choose the correct option.
A) 30 days  B) 72 days  C) 70 days  D) 80 days  E) 90 days

Solution: Amount of work done by JOHN and Antony in 1 day = 1/36   Amount of work done by JOHN and Antony in 24 days = 24 Ã— (1/36) = 2/3   Remaining work â€“ 1 â€“ 2/3 = 1/3   JOHN completes 1/3 work in 24 days   Amount of work JOHN can do in 1 day = (1/3)/24 = 1/72   => JOHN can complete the work in 72 days   Answer : 72 days
Answer: B
A cycle is bought for Rs.750 and sold for Rs.1080, find the gain percent?	Choose the correct choice from the following choices.
A) 22  B) 44  C) 99  D) 88  E) 11

Solution: 750 ---- 180   100 ---- ? => 44%   Answer:44
Answer: B
The sum of first four prime numbers is?  Choose the correct choice from the following choices
A) 17
B) 23
C) 24
D) 28
E) 30

Solution: Required sum = (2 + 3 + 5 + 7)= 
(2 + 3 + 5 + 7) = 17
17.   Note: 1 is not a prime number.   Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.   17
Answer: A
If x is equal to the sum of the integers from 50 to 60, inclusive, and y is the number of EVEN integers from 50 to 60, inclusive, what is the value of x+y ? Answers.
A) 171
B) 281
C) 391
D) 491
E) 611

Solution: sum s= n/2{2a+(n-1)d} = 11/2{2*50+ (11-1)*1} =11*55= 
11*55 = 605
605=X   number of even number =( 60-50)/2 +1= 
( 60-50)/2 +1 = 6
6= Y   X+Y = 605+6= 
605+6 = 611
611   611
Answer: E
3 men and 8 women complete a task in same time as 6 men and 2 women do. How much fraction of work will be finished in same time if 5 men and 2 women will do that task.
Choices
A) 6/7 B) 3/10 C) 3/18 D) 3/16 E) 3/11

Solution: 3 m + 8 w = 6 m + 2 w   3 m = 6 w   1 m = 2 w   Therefore 3 m + 8 w = 14 w   5 m +2 w =12 w   6/7nswer is 12/14 =6/7   6/7nswer: 6/7
Answer: A
Micheal and Adam can do together a piece of work in 20 days. After they have worked together for 14 days Micheal stops and Adam completes the remaining work in 10 days. In how many days Micheal complete the work separately.
Choose the correct choice from the following answers
A) 50 days B) 100 days C) 120 days D) 110 days E) 90 days

Solution: Rate of both = 1/20   Together they do = 1/20*14 = 7/10   Left work = 1 - 7/10 = 3/10   Adam completes 3/10 work in 10 day   so he took 10*10/3 = 100/3 days to complete the left work alone.   Thus the rate of adam is 3/100   Rate of Micheal = 1/20 - 3/100 = 1/50   Thus micheal takes 50 days to complete the whole work.   ans. 50 days
Answer: A
There were two candidates in an election. Winner candidate received 62% of votes and won the election by 360 votes. Find the number of votes casted to the winning candidate?
Choose the correct option: A) 456 B) 744 C) 930 D) 1200 E) 1400

Solution: W = 62% L = 38%   62% - 38% = 24%   24% -------- 360   62% -------- ?  62  - 38= 
 62  - 38 = 24
24%   24% -------- 360   62% -------- ?=> 930   ANSWER:930
Answer: C
Alfred buys an old bike for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the bike for Rs. 5800, his gain percent is?	Options:
A) 5 5/11%  B) 5%  C) 5/7%  D) 6%  E) 6/11%

Solution: Cost Price (C.P.) = Rs. (4700 + 800) = Rs. 5500.   Selling Price (S.P.) = Rs. 5800.   Gain = (S.P.) - (C.P.) = Rs.(5800 - 5500) = Rs. 300.   Gain % = 300	x 100	%	= 5	5	%   5500	11   5 5/11%)
Answer: A
Diane find 2 and a half cans of paint are just enough to paint one third of her room. How many more cans of paint will she need to finish her room and paint a second room of the same size?
Choose the correct answer:
A) 5
B) 7 and a half
C) 10
D) 12 and a half
E) 15

Solution: We know that 2.5 cans = 25/10 is used to paint 1/3 of a room. We need to find how much paint we'll need in order to paint the rest of the room (1-1/3=2/3) and 1 room more, hence 2/3+1=5/3   25/10 : 1/3 = x : 5/3   (25/10)*(5/3) = (1/3)*x   25/6=x/3   6*x=25*3= 
25*3 = 75
75/6= 
75/6 = 25/2 = around 12.5
12.5   ANSWER:12 and a half
Answer: D
Two cars, Car1 and Car2 move towards each other from Q and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach Q starting from Y? Choose the correct choice from the following choices:
A) 15.5 sec
B) 8.4 sec
C) 33.6 sec
D) 31.11 sec
E) 16.8 sec

Solution: Q--------------------------------------|----------------------------Y   Car A(20mps)------------------------->P<---------------Car B(15mps)   Let 2 cars meet each other at point P in t seconds.   Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance QY= 35t.   From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further.   so, 15t/20 = 10   So t=40/3 sec and total distance = (35*40)/3   Hence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx.   Answer 31.11 sec
Answer: D
If, in a baseball game, a single picher can decide to throw either a 100mph fastball or 60 mph knuckleball on any pitch, how much less time, in seconds, does the batter have from when the ball is released as a fastball than when the ball is released as a knuckle ball? (Assume where the batter's point of contact is exactly 60ft away from the pitcher's release point. 5280 ft = 1 mile.) Pick one
A) 6/22s
B) 7/22s
C) 8/22s
D) 9/22s
E) 15/22s

Solution: One conversion to know is = 1 mile = 5280 ft   Time taken for fastball = (60 / (100 * 5280)) * 60 * 60 = 9/22   Time taken for knuckle ball = (60 / (60 * 5280)) * 60 * 60 = 15/22   Qn is the difference between the time taken by the two balls => 15/22 - 9/22 = 6/22   Option 6/22s
Answer: A