MU-NLPC/Calc-aqua_rat huggingface dataset:
X starts a business with Rs.45000. Y joins in the business after 5 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?  Choose the correct choice from the following:
A) 1:2
B) 2:1
C) 1:3
D) 3:1
E) 18:7

Solution: 18:7xplanation:   Ratio in which they should share the profit   = Ratio of the investments multiplied by the time period   =45000Ã—12:30000Ã—7   =45Ã—12:30Ã—7   =3Ã—12:2Ã—7   =18:7   Answer: Option 18:7
Answer: E
Each of the three people individually can complete a certain job in 4, 6, and 8 hours, respectively. What is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates?  Choose the correct option:
A) 3/8	B) 5/12	C) 7/24	D) 11/36	E) 13/48

Solution: The two slowest people work at rates of 1/6 and 1/8 of the job per hour.   The sum of these rates is 1/6 + 1/8 = 7/24 of the job per hour.   The answer is 7/24.
Answer: C
If x is an integer and y = 3x + 11, which of the following CANNOT be a divisor of y?	Choose the correct choice from the following choices:	A) 4	B) 5	C) 3	D) 7	E) 8

Solution: For any value of x, the expression 3x + 11 would never be divisible by 3,6,9...... onwards   So answer = 3 = 3
Answer: C
A volunteer organization is recruiting new members. In the fall they manage to increase their number by 6%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring? Select:  A) -16.16%  B) -15.15%  C) -14.14%  D) -13.13%  E) -12.12%

Solution: (100%+6%)*(100%-19%) = 1.06*.81 = 0.8586.   1-0.8586 = 14.14% lost = -14.14%   The Answer is -14.14%   The organization has lost 14.14% of its total volunteers from fall to spring.
Answer: C
A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 14% microphotonics; 25% home electronics; 15% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research?  Pick:  A) 8°  B) 10°  C) 18°  D) 33°  E) 52°

Solution: Here all percentage when summed we need to get 100% . As per data  14+25+15+29+8= 
 14+25+15+29+8 = 91
91%.   So remaining 9% is the balance for the astrophysics.   Since this is a circle all percentage must be equal to 360 degrees.   100% ---- 360 degrees   Then 9% will be 33 degrees..   IMO option 33°.
Answer: D
The Kiljaro Highway is marked with Milestones denoting the distance to the town of Kiljaro. Tommy left kiljaro and drove the highway, passing the 60 km milestone at 8:30. Some time afterwards, Tommy got a phone call asking him to return home, and he made a U-turn at the 160 km milestone. At 09:A0 Tommy passed the milestone marking 70 km to Kiljaro. The variable A represents the tens digit of the minutes in 09:A0. Assuming Tommy maintained the same constant speed during the entire drive, how many kilometers did Tommy travel in one minute? Choose the correct choice from the following answers:
A) 190/(30+10A)
B) 190/(30+60A)
C) 190/31A
D) 220/(30+10A)
E) 220/40A

Solution: Since we are dealing with the variables in the answer choices,the best possible method according to me would be substitution.   Substitute A with 3.meaning tommy would have travelled a distance of ((160-60) + (160-70)) in 60 minutes.   190 Kms in 60 minutes ==> 3.1km/hr.   Substitute A with 3 in the answer options.   Option 190/(30+10
Answer: A
A car travells the first 1/3 of certain distance with a speed of 7km/hr the next 1/2 distance witha a speed of 12 km/hr, and the last 1/4 distance with a speed of 16 km/hr. the average speed of the carfor the whole journey is?  Answers
A) 9.53km/hr
B) 56.89km/hr
C) 8.96km/hr
D) 7.96km/hr
E) 25.86km/hr

Solution: Let the whole distance travelled be x km   and the average speed of the car for he whole journey be y km/hr   then (x/3)/7+(x/2)/12+(x/4)/16=x/y   x/21+x/24+x/64=x/y   y=9.53km/hr   9.53km/hrnswer(9.53km/hr)
Answer: A
Mr. Suresh is on tour and he has 360 for his expenses. If he exceeds his tour by 4 days he must cut down daily expenses by 3. The number of days of Mr. Suresh’s tour programme is :  Options
A) 20 days
B) 24 days
C) 40 days
D) 42 days
E) None of these

Solution: Let Suresh undertakes a tour of x days.   Then, expenses for each day = 360⁄x   now, 360/x+4=360/x−3   or 360(1/x−1/x+4)=33   or x2 + 4x - 480 = 0 or x = – 24 or x = 20   Since, x ≠ -24 we have x = 20   20 daysnswer 20 days
Answer: A
A bat is bought for Rs.400 and sold at a gain of 20% find its selling price
Choose the correct answer:
A) Rs.400/-
B) Rs.420/-
C) Rs.440/-
D) Rs.460/-
E) Rs.480/-

Solution: 100 % ------> 400 (100 * 4 = 400)   120 % ------> 480 (120 * 4 = 480)   Selling price = Rs.480/-   Rs.480/-
Answer: E
If a stationery store owner buys 50% more identically-priced calendars than she usually purchases, she will be given a 20% discount off the standard price. Her total cost would then be 120 times the dollar value of the standard price of one calendar. How many calendars does she usually purchase? Answers.
A) 40 B) 80 C) 100 D) 120 E) 140

Solution: Let the Price is x per item   and the final number of items she bought is y items   So to buy y items , the cost will be .8x (80% of original price , since there is a 20% discount on it)   120*x = y*0.8*x   Solving we get y =150   now to get the discount she bought 50% more than what she usually buys   So the number of items she usually buys is 50% less than 150   i.e. original number of items she usually buys is = 150*(100/150)= 
150*(100/150) = 100
100   Hence Answer is (100)
Answer: C
A woman has three blouses of different colors, five skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear?
Choose the correct choice from the following choices:
A) 8 B) 12 C) 28 D) 17 E) 18

Solution: total ways = 3*5*2=30..   now its better to find the ways in which the pink blouse and green skirt are together and subtract from total to get the answer..   the ways in which the pink blouse and green skirt are together=1*1*2=2..   total ways =30-2=28..   ANSWER:28
Answer: C
A combustion reaction forms carbon dioxide. A carbon dioxide molecule contains one carbon and two oxygen atoms. If, over a period of 12 minutes, a combustion reaction creates 12,000 molecules of carbon dioxide then approximately how many more atoms of oxygen than carbon are created on average per minute? Choose the correct answer:
A) 20  B) 60  C) 600  D) 1,000  E) 1,200

Solution: Solution:   12,000 carbon dioxide molecules are created over a period of 12 minutes. Therefore 12,000/12 = 1,000 carbon dioxide molecules are created on average per minute   Each carbon dioxide molecule contains one carbon atom and two oxygen atoms. So 1,000 carbon dioxide molecules contain 1 × 1,000 = 1,000 carbon atoms and 2 × 1,000 = 2,000 oxygen atoms. The difference is 2,000 – 1,000 = 1,000.   The correct answer is 1,000.
Answer: D
In a dice game, a player wins if he rolls the same number on his second roll as he rolls on his first. If Jason rolls a total of 4 on the first roll, what is the probability that he wins on his next roll? In this game, each roll is made with 2, fair, six-sided dice.  Choose the correct choice from the following choices
A) 1/6  B) 1/9  C) 1/12  D) 1/15  E) 1/18

Solution: There are 3 ways to roll a 4: 1 and 3, 3 and 1, and 2 and 2.   There are  6*6= 
 6*6 = 36
36 ways to roll two dice.   Thus the probability of rolling a 4 is 3/36= 1/12   1/12
Answer: C
A group consists of 4 men, 6 women and 4 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?
Choose the correct choice from the following answers.
A) 400
B) 480
C) 287
D) 278
E) 281

Solution: Explanation:   Two men, three women and one child can be selected in â´Câ‚‚ * â¶Câ‚ƒ * âµCâ‚ ways   = (4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 4= 
(4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 4 = 480
480 ways.   Answer:480
Answer: B
A positive number when decreased by 4 is equal to 21 times the reciprocal of the number. The number is:	Choose the most appropriate option.
A) 2 B) 5 C) 9 D) 7 E) 6

Solution: Let the number be x   x-4=21/x   x^2 - 4x -21=0   (x-7)(x+3)=0   x=7   correct answer 7
Answer: D
If P(A) = 1/5 and P (B) = 2/5, find P (A n B) if A and B are independent events.  Pick:
A) 7/25 B) 3/25 C) 8/25 D) 2/25 E) 3/17

Solution: P (A n B) = P(A) . P(B)   P (A n B) = 1/5 . 2/5   P (A n B) = 2/25.   2/25
Answer: D
A man invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. If the rate of dividend be 12%, his annual income is:  Choose the correct choice from the following options.
A) 233
B) 648
C) 366
D) 266
E) 991

Solution: Explanation:   Number of shares = = 540.   Face value = Rs. (540 x 10) = Rs. 5400.   Annual income = = Rs. 648.   Answer: 648) 648
Answer: B
The average of four consecutive even numbers is 27. Find the largest of these numbers.
Choose the correct choice
A) 28  B) 30  C) 32  D) 34  E) 36

Solution: Given:   Consider the consecutive even numbers as : x, (x + 2), (x + 4) and (x+ 6)   Average =	Sum of Quantities/Number of Quantities   =	[x + (x + 2) + (x + 4) + (x + 6)] /4=	(4x + 12) /4	= 27   Simplifying we get, x = 24   Therefore,   Largest number = (x + 6) = (24 + 6)= 
(24 + 6) = 30
30   Smallest number= 24   ANSWER IS 30
Answer: B
A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?	Answers.
A) 86  B) 67  C) 30  D) 15  E) 17

Solution: US = 25   DS = 35   M = (35 + 25)/2= 
(35 + 25)/2 = 30
30   Answer: 30
Answer: C
The length and breadth of a rectangle is increased by 10% and 25% respectively. What is the increase in the area?
Choose the correct answer:
A) 37.2%	B) 37.5%	C) 57.5%	D) 37.4%	E) 27.2%

Solution: 100 * 100= 
100 * 100 = 10_000
10000   110 * 125= 
110 * 125 = 13_750
13750   -----------   3750   10000 ------ 3750   100 ------- ?=> 37.5%   27. The side of a rhombus is 2   Answer: 37.5%
Answer: B
Find the least number which when divided by 26, 36 and 46 leaves the remainders 12, 22 and 32 respectively.
Pick one
A) 10570	B) 10750	C) 17050	D) 10075	E) 10085

Solution: Explanation:   The difference between any divisor and the corresponding remainder is 14,   L.C.M of 26,36,46 -14   = 10764-14= 
10764-14 = 10_750
10750   Answer: Option 10750
Answer: B
When 6 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads? Pick one
A) 1
B) 3
C) 16
D) 31
E) 30

Solution: Total outcome is 2^6 = 64   Favourable cases = H_ _ _ _ H   The second, third, fourth and fifth places can be occupied by either H or T   There are 2^4 =16 ways that can be done.   Hence, the correct option is 16
Answer: C
In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (4,-3), (4, 7), (10, 4), (10,-7)?  Select the correct option:	A) 51	B) 54	C) 57	D) 60	E) 63

Solution: By graphing the points, we can see that this figure is a trapezoid. A trapezoid is any quadrilateral that has one set of parallel sides, and the formula for the area of a trapezoid is:   Area = (1/2) × (Base 1 + Base 2) × (Height), where the bases are the parallel sides.   We can now determine the area of the quadrilateral:   Area = 1/2 × (10 + 11) × 6 = 63.   The answer is 63.
Answer: E
Six years ago Ram was P times as old as Shyam was. If Ram is now 17 years old, how old is Shyam now in terms of P ?
Choose the correct choice from the following options:
A) 11/P + 6
B) P/11 +6
C) 17 - P/6
D) 17/P
E) 11.5P

Solution: let's call Shyam's age six years ago is x   so six years ago Ram was: 17-6= 
17-6 = 11
11 years old   and six years ago Ram was P times as old as Shyam was=> 11/x = P   => x = 11/P   => Now Shyam's age will be : x+6 = 11/P+6   => the answer is 11/P + 6
Answer: A
A professional janitor can clean a certain high school in (4+4) hours, working at a constant rate. A student sentenced to detention can clean that same high school in 20 hours, also working at a constant rate. If the student is paid $7 total per hour and the janitor is paid $21 per hour, how much more would it cost the school to pay the janitor to do the job himself than it would to pay the student and the janitor to do the job together?
Pick one.
A) -$56 B) -$6 C) $0 D) $6 E) $8

Solution: A professional janitor can clean a certain high school in (4+4) or 8 hours   So (applying rule #1), the janitor can clean 1/8 of the school in ONE HOUR   A student sentenced to detention can clean that same high school in 20 hours   So (applying rule #1), the student can clean 1/20 of the school in ONE HOUR   So, COMBINED, the student and janitor can clean (1/8 + 1/20) of the school in ONE HOUR   1/8 + 1/20 = 5/40 + 2/40 = 7/40   So, in ONE HOUR they can clean 7/40 of the school.   Applying rule #2, it will takethem40/7 hoursto clean the ENTIRE school.   The janitor earns $21/hour and the student earns $7/hour, so their combined rate is$28/hour.   Theircombined wages= (pay rate)(time) = ($28/hour)(40/7 hours) =$160   Working ALON$8, the janitor takes 8 hours and earns $21/hour   So, working alone, the janitor's earnings = (pay rate)(time) = ($21/hour)(8 hours) =$168   $168-$160= $8, so the answer is $8 168- 160= 
 168- 160 = 8
$8, so the answer is $8
Answer: E
The present age of a father is 3 years more than three times the age of his son.Three years hence,father as age will be 12 years more than twice the age of the son.Find the present age of the father.  Choose the correct choice from the following choices
A) 88
B) 39
C) 33
D) 44
E) 55

Solution: Explanation:   Let the present age be 'x' years. Then father's present age is 3x+3 years. Three years hence (3x+3)+3=2(x+3)+12 x=12 Hence father's present age = 3x+3 =[ (3 x 12) + 3] = 39 years.   Answer: 39
Answer: B
If x is the interest on y and y is the interest on z, the rate and time is the same on both the cases. What is the relation between x, y and z?	Choose the correct answer:
A) 9810
B) 1002
C) 2799
D) 1000
E) 2729

Solution: (x*5*1)/100 + [(2500 - x)*6*1]/100   = 140   X = 1000   Answer:1000
Answer: D
A rower can row upstream at 7 km/hr and downstream at 14 km/hr. What is the rower's rate in still water?
Choose the correct choice from the following options:
A) 9.5 km/hr
B) 10.0 km/hr
C) 10.5 km/hr
D) 11.0 km/hr
E) 11.5 km/hr

Solution: The rate in still water is 1/2 * (14 + 7)= 
1/2 * (14 + 7) = 21/2 = around 10.5
10.5 km/hr   The answer is 10.5 km/hr.
Answer: C
How many even number in the range between 10 to 160 inclusive are not divisible by 3	Options
A) 15  B) 30  C) 51  D) 63  E) 76

Solution: We have to find the number of terms that are divisible by 2 but not by 6( as the question asks for the even numbers only which are not divisible by 3)   For 2,   10,12,14...160   using AP formula, we can say 160 = 10 + (n-1) *2   or n=76.   For 6,   12,18,...156   using AP formula, we can say 156 = 12 + (n-1) *6   or n=25.   Hence, only divisible by 2 but not 3 =76-25= 
76-25 = 51
51. hence, Answer 51
Answer: C
Edward's home have 3 taps,One tap, working alone at its maximum constant rate, can fill a certain sink in 270 seconds.A second tap working alone at its maximum constant rate, can fill a certain sink in 274 seconds. A third tap, working alone at its maximum constant rate, can fill the same sink in 276 seconds. If all taps work together at their respective maximum constant rates, the time it will take to fill the sink is closest to	Answers:	A) 91 seconds	B) 102 seconds	C) 177 seconds	D) 200 seconds	E) 270 seconds

Solution: Tap 1 : 270 secs   Tap 2 : 274 secs   Tap 3:276 secs   Considering the average of these 3 taps : 273.33 secs.   So 1 tap can fill the tank in 273.33 secs, so 3 taps can fill the tank in 273.33/3= 
273.33/3 = 91.11
91.11 secs.   Closest answer is 91 seconds.
Answer: A
The average age of a family of 6 members is 26 years.If the age of the youngest member is 10 years,what was the average age of the family at the birth of the youngest member?  Choose the correct option:
A) 15  B) 18  C) 16  D) 12  E) 19

Solution: Present age of total members = 6 X 26 = 156   10 yrs back their ages were = 6 x 10 = 60   Ages at the birth of youngest member = 156 - 60= 
156 - 60 = 96
96   Therefore, avg age at the birth of youngest member= 96/6= 
96/6 = 16
16.   ANSWER:16
Answer: C
What amount does Kiran get if he invests Rs. 16000 at 15% p.a. simple interest for four years? Choose the correct choice from the following answers: A) 29893 B) 27773 C) 25600 D) 28800 E) 29883

Solution: Simple interest = (16000 * 4 * 15)/100 = Rs. 9600   Amount = P + I = 16000 + 9600 = Rs. 25600   Answer: 25600
Answer: C
The average of five numbers id 27. If one number is excluded, the average becomes 25. What is the excluded number?	Choose the correct option: A) 30 B) 40 C) 32.5 D) 35 E) 37

Solution: Explanation:   Sum of 5 numbers = 5 × 27   Sum of 4 numbers after excluding one number = 4 × 25   Excluded number   = 5 × 27 - 4 × 25   = 135 - 100= 
135 - 100 = 35
35   Answer: Option 35
Answer: D
A envelop weight 9.2 gm,if 800 of these envelop are sent with an advertisement mail. How much wieght? Choose the correct choice from the following answers.
A) 6.6kg
B) 6.8kg
C) 6.7kg
D) 6.9kg
E) 7.36kg

Solution: 800*9.2   7360.0gm   7.36kg   ANSW7.36kgR:7.36kg
Answer: E
A rectangular mat has an area of 120 sq.metres and perimeter of 46 m. The length of its diagonal is:  Choose the correct choice from the following choices.
A) 19m
B) 17m
C) 15m
D) 16m
E) 20m

Solution: rectangular area = l × b = 120 and perimeter = 2(l+b) = 46   l+b = 23   (l-b)power2 - 4lb = (23)power2 - 4 × 120 = (529-480)= 
(529-480) = 49
49= l-b = 7   l+b = 23, l-b = 7, we get l = 15, b = 8   Diagonal = √152+82   √ 225+64= 
 225+64 = 289
> √289= 17m   Answer is 17m.
Answer: B
If x and y are different integers and x^2 = xy, which of the following must be true ?
I. x = y
II. y = 0
III. x = 0	Select:  A) I only  B) II only  C) III only  D) I and III only  E) I, II, and III

Solution: Answer choice A is correct.   The question gives you x^2=xy   you can simplify that as x^2-xy=0   x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer.   Answer III only
Answer: C
If (2 to the x) - (2 to the (x-2)) = 3 (2 to the 10), what is the value of x? Answers.
A) 9  B) 11  C) 13  D) 12  E) 17

Solution: (2 to the power x) - (2 to the power (x-2)) = 3 (2 to the power 10)   2^x - 2^(x-2) = 3. 2^10   Hence x = 12.   Answer is 12
Answer: D
The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 10 percent, and on day 3, it is discounted an additional 25 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
Choose the correct choice from the following:
A) 28%	B) 67.5%	C) 64.8%	D) 70%	E) 72%

Solution: original price = 100   day 1 discount = 10%,price = 100-10= 
100-10 = 90
90   day 2 discount= 10%,price = 90-9= 
90-9 = 81
81   day 3 discount= 25%,price = 81-20.25= 
81-20.25 = 60.75
60.75   which is 60.75/90 *100 of the sale price on day 1= ~67.5%   Answer 67.5%
Answer: B
A can do a work in 6 days. B can do the same work in 8 days. Both A&B together will finish the work and they got $1000 from that work. Find their shares?	Choose the correct option:
A) 600,400
B) 600,800
C) 300,700
D) 800,200
E) 550,450

Solution: Ratio of their works A:600,800 = 6:8   Ratio of their wages A:600,800 = 3:4   A's share = (3/5)1000 = 600   600,800's share = (4/5)1000 = 800   correct option is 600,800
Answer: B
John read the quarter of the time that Tom read. Tom read only two-fifth of the time that Sasha read. Sasha read twice as long as Mike. If Mike read 5 hours, how long did John read?	Pick
A) 1 hour	B) 2 hour	C) 3 hour	D) 4 hour	E) 5 hour

Solution: Mike read 5 hours. Sasha read twice as long as Mike. Hence Sasha read:   2 ? 5 = 10 hours   Tom read two-fifths of the time that Sasha read. Hence Tom read:   (2 / 5) ? 10 = 4 hours   John read the quarter of the time that Tom read. Hence John read:   (1 / 4) ? 4 = 1 hour   correct answer 1 hour
Answer: A
A circular ground whose diameter is 34 metres, has a 2 metre-broad garden around it. What is the area of the garden in square metres?
Answers: A) 226.3 B) 226.2 C) 228.2 D) 227 E) 226

Solution: Req. area = Ï€[(19)2 â€“ (17)2]   = 22â„7 Ã— (36 Ã— 2)[since a2 - b2 = (a + b)(a - b)]   = (22 Ã— 36Ã— 2)/7 = 226.3sq m   226.3nswer 226.3
Answer: A
What is the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9m 2 cm broad? Choose the correct choice from the following:
A) 724
B) 804
C) 814
D) 844
E) None

Solution: Solution   Length of largest tile = H.C.F. of 1517cm & 902cm = 41cm.   Area of each tile = (41 x 41)cm2   ∴ Required number of tiles	= [1517x902/41x41]   = 814.   Answer 814
Answer: C
In May Mrs Lee's earnings were 30 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?  Choices
A) 34
B) 67
C) 85
D) 25
E) 38

Solution: Lets say the Family Income is 100   In May, lee earned 30Family income is 70   In june, Lee earned 20% more than May, so it is (30+20*30/100 = 36)   Family Income is same 70   In June Lee's Income percent is 36*100/106 ~ 34   34ns is 34
Answer: A
The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 25hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor?  Options:
A) 400 km
B) 500 km
C) 331.2 km
D) 550 km
E) 600 km

Solution: Sol. Average speed of a tractor = 23 km / h   The speed of a bus in an hour = 23 × 2 = 46 km   The speed of a car in an hour = 9/5 * 46= 
9/5 * 46 = 414/5 = around 82.8
82.8 km   So, the distance covered by car in 4 h is   82.8 × 4= 331.2 km   Ans.(331.2 km)
Answer: C
The distance between stations A and B is 148 km. An express train left station A towards station B with the speed of 80 km/hr. At the same time, a freight train left station B towards station A with the speed of 36 km/hr. They met at station C at 12 pm, and by that time the express train stopped at at intermediate station for 10 min and the freight train stopped for 5 min. Find:
a) The distance between stations C and B.
b) The time when the freight train left station B.
Choose the correct choice from the following
A) 12.17  B) 10.35  C) 29.28  D) 12.32  E) 12.22

Solution: a) Let x be the distance between stations B and C. Then the distance from station C to station A is (148−x)(148−x) km. By the time of the meeting at station C, the express train travelled for 148−x80+1060148−x80+1060 hours and the freight train travelled for x36+560x36+560 hours. The trains left at the same time, so: 148−x80+16=x36+112148−x80+16=x36+112. The common denominator for 6, 12, 36, 80 is 720. Then   9(148−x)+120=20x+609(148−x)+120=20x+60   1332−9x+120=20x+601332−9x+120=20x+60   29x=139229x=1392   x=48x=48. Therefore the distance between stations B and C is 48 km.   b) By the time of the meeting at station C the freight train rode for 4836+5604836+560 hours, i.e. 11 hour and 2525 min.   Therefore it left station B at 12−(1+2560)=10+356012−(1+2560)=10+3560 hours, i.e. at 10:35 am.   Answer:10.35
Answer: B
Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?  Choose the correct choice:
A) Rs.1261	B) Rs.1440	C) Rs.1185	D) Rs.1346	E) Rs.1446

Solution: Rs.1261 = 8000(21/20)3   = 9261   = 8000   ---------   1261   Rs.1261NSWER:Rs.1261
Answer: A
Mary’s annual income is $15,000 and John’s annual income is $18,000. By how much must Mary’s annual income increase so that it constitutes 80% of Mary and John’s combined income? Select:
A) $3,000
B) $4,000
C) $7,000
D) $11,000
E) $57,000

Solution: Let Mary's income increase by x, then the equation will be   15,000 + x= (80/100)* (15,000 + x + 18000 )   15,000 + x = (4/5) * (33,000 + x)   75,000 + 5x = 4x + 132,000   x = 57,000   x = 57,000   So, Answer will be $57,000
Answer: E