MU-NLPC/Calc-aqua_rat huggingface dataset:
How many seconds will a 600 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?	Choose the correct option.
A) 20
B) 30
C) 36
D) 50
E) 60

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18 = 50/3 m/sec.   Time taken to pass the man = 600 * 3/50= 
600 * 3/50 = 36
36 sec.   Answer: Option 36
Answer: C
Choose the missing terms out of the given alternatives.
AZ, BY, ?  Choices:
A) EF B) GH C) ED D) DW E) CX

Solution: E   CX   The first letter moves one step forward. The second letter moves one step backward.   Answer is CX
Answer: E
If X,Y is 25%,35% smaller than Z then how much percentage is Y greater than X?  Pick:  A) 13 1/2%  B) 13 1/4%  C) 13 1/3%  D) 12 1/2%  E) 14 1/2%

Solution: Explanation:   X = 75 %   Y = 65 %   Z = 100 %   X-Y/X * 100 = 10/75 * 100 = 13 1/3 % greater than X   Answer: Option 13 1/3%
Answer: C
A bike traveled 127 miles in 5 hours 11 minutes. What was the average speed of the bike in miles per hour?	Choose the correct option:
A) 24.50 miles / hour
B) 25.6 miles / hour
C) 25.9 miles / hour
D) 29.1 miles / hour
E) 30 miles / hour

Solution: We first convert the time of 5 hours 11 minutes in minutes   5 hours 11 minutes = 5* 60 + 11= 
5* 60 + 11 = 311
311 minutes   Average speed S is given by distance / time. Hence   S= 127 miles / 311 minutes = 0.408 mile / minute   = 24.50 miles / hour   correct answer 24.50 miles / hour
Answer: A
If m,s,and t are positive real numbers such that m(s+t) = 152, s(t+m) =162 , and t(m+s) = 170, then mst is Choose the correct choice from the following answers:
A) a) 672 B) b) 688 C) c) 704 D) d) 720 E) e) 750

Solution: ms+mt = 152 --------------------------------------1)   st+sm = 162---------------------------------------2)   mt+ts = 170---------------------------------------3)   Re-writing equation 3 as follows:   mt+ts = 162 + 8   mt+ts = st+sm + 8   mt = sm + 8 ............... (4)   Adding (1)(4)   2mt = 160   mt = 80   mst has to be multiple of 80, only 720 fits in   Answer = d) 720
Answer: D
Bert left the house with N dollars. He spent 1/4 of this at the hardware store, then $9 at the dry cleaners, and then half of what was left at the grocery store. When he got home, he had $15 left in his pocket. What was the value of N?  Choose the correct choice from the following choices
A) $36	B) $44	C) $52	D) $60	E) $68

Solution: started to test answer C   if he had 52, then he spent 13 at hardware store   now he was left with 39$   he spent 9 dollars on cleaning, thus he remained with 30$   he then spent 1/2 of 30, or 15, and was left with 15.   hence, the only option that can be right is $52.
Answer: C
A man has some hens and cows. If the number of heads be 48 and the number of feet equals 136, then the number of hens will be: Choose one.
A) 22  B) 23  C) 24  D) 26  E) 28

Solution: let hens be x and cows be y   now,   feet: x*2+y*4=136   heads: x*1+y*1=48   implies, 2x+4y=136 and x+y=48   solving these two equations, we get x=28 and y=20   Therefore, hens are 28.   ANSW28R:28
Answer: E
6+2=42
4+9=48
8+2=72
3+7=27
1+4=??
Solve it?
Choose the correct choice.
A) 9
B) 3
C) 42
D) 4
E) 16

Solution: x+y=x[y+(x-1)]=x^2+xy-x   6+2=6[2+(6-1)]=36+12-6= 
36+12-6 = 42
42   4+9=4[9+(4-1)]=16+36-4= 
16+36-4 = 48
48   8+2=8[2+(8-1)]=64+16-8= 
64+16-8 = 72
72   3+7=3[7+(3-1)]=9+21-3= 
9+21-3 = 27
27   1+4=1[4+(4-1)]=1+4-1= 
1+4-1 = 4
4   Answer :4
Answer: D
4/6 of the population of the country of Venezia lives in Montague Province, while the rest lives in Capulet Province. In the upcoming election, 80% of Montague residents support Romeo, while 70% of Capulet residents support Juliet; each resident of Venezia supports exactly one of these two candidates. Rounded if necessary to the nearest percent, the probability that a Juliet supporter chosen at random resides in Capulet is Choose the correct choice from the following answers.
A) 28%	B) 41%	C) 45%	D) 64%	E) 78%

Solution: Total population = 60 (assume).   4/6*60= 
4/6*60 = 40
40 people from Montague.   2/6*60= 
2/6*60 = 20
20 people from Capulet.   0.2*40= 
0.2*40 = 8
8 people from Montague support Juliet.   0.7*20= 
0.7*20 = 14
14 people from Capulet support Juliet.   The probability that a Juliet supporter chosen at random resides in Capulet is 14/(8+14)=~64.   Answer: 64%
Answer: D
find value for x from below equation? x + 1 = 2
Choose the correct choice from the following options: A) -5 B) 1 C) 4 D) 3 E) 2

Solution: 1. Subtract 1 from both sides:   x + 1 - 1 = 2 - 1   2. Simplify both sides:   x = 1   1
Answer: B
Among 400 people, 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of the people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam?
Select the correct option.
A) 20 B) 60 C) 80 D) 86 E) 120

Solution: 56%+44%-30%=70% who like either Strawberry, Apple, or both.   That means 100%-70% 56 +44 -30= 
56 +44 -30 = 70
70% who like either Strawberry, Apple, or both.   That means 100%-70% = 30% do not like either Apple of Strawberry jam.   30% is the most possible that like raspberry jam but do not like either strawberry or apple (assuming nobody in the group does not like any)   120  100 -70= 
  100 -70 = 30
30% do not like either Apple of Strawberry jam.   30% is the most possible that like raspberry jam but do not like either strawberry or apple (assuming nobody in the group does not like any)   120
Answer: E
Randy can rebuild an automobile engine in b hours. Alvin can rebuild the same engine in a hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Alvin will have to complete? Choose the most appropriate option:
A) ab/(a+b)  B) (b)/(a+b)  C) b/(b-a)  D) a/(a+b)  E) b/(a-b)

Solution: Randy can do the job in a hrs, Alvin can do the job in b hrs.   When they work together, you need to find the fraction of work that Randy doesn't need to do i.e. the fraction that will be done by Alvin.   Ratio of Randy's speed:Alvin's speed = b:a (since time taken by them is in the ratio a:b)   So Alvin does b/(a+b) of the work   Answer ((b)/(a+b)).
Answer: B
If x is an integer and 2.134 × 10^x is less than 21,000, what is the greatest possible value for x? Choose the most appropriate option.
A) 7	B) 6	C) 5	D) 4	E) 3

Solution: x is an integer and 2.134 × 10x is less than 21,000, what is the greatest possible value for x?   for 2.134 × 10x is less than 21,000 to remain true, the greatest number is 2,134, which makes x=3   E. 3
Answer: E
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good? Answers
A) 20/68
B) 20/63
C) 20/29
D) 20/20
E) 20/69

Solution: Required probability   = (⁵C₃ . ⁴C₁)/⁹C₄   = (10 * 4)/126 = 20/63   Answer:20/63
Answer: B
8900 ÷ 6 ÷ 4 = ? Choose the most appropriate option.
A) 349	B) 541.75	C) 224.37	D) 370.833	E) None of these

Solution: Explanation:   Given Exp. 8900 * 1/6 * 1/4   = 370.833   ANSWER: 370.833
Answer: D
On retirement, a person gets 1.53 lakhs of his provident fund which he invests in a scheme at 20% p.a. His monthly income from this scheme will be  Select the correct option:
A) 2,450	B) 2,500	C) 2,550	D) 2,600	E) None of these

Solution: Let S.I. = x   = 1.53×10(5)×20/100   = 2,500   Answer 2,500
Answer: B
Three runners Q, B and C run a race, with runner A finishing 12m ahead of runner B and 18m ahead of runner C, while runner B finishes 8m ahead of runner C. Each runner travels entire distance at a constant speed. What was the length of the race?  Choose the correct choice from the following choices:	A) 36m	B) 48m	C) 60m	D) 72m	E) 84m

Solution: Let distance of race be x mtrs. Then when Q finishes x m , B has run (x- 12)mtrs and C has run x-18 mtrs. so at this point B is 6 m ahead of C. Now to finish race b needs to run another 12 m, so he runs another 12 m. when B finishes race he is 8 m ahead of C. so last 12 m B has run, C has run 10 m.   as speeds are constant, we have equation,   x-12/ x-18 = 12/10 > x = 48.   Answer 48m
Answer: B
In racing over a given distance d at uniform speed, A can beat B by 10 meters, B can beat C by 4 meters, and A can beat C by 12 meters. What is the distance d in meters?  Choose the correct choice from the following choices
A) 16 B) 20 C) 30 D) 40 E) 50

Solution: When A is at the finish line, B is 10 meters back, and C is 12 meters back.   When B runs another 10 meters to the finish line, C is 4 meters back.   So B gains 2 meters every 10 meters covered.   To gain a final difference of 4 meters, B runs a total of 20 meters.   The answer is 20.
Answer: B
A sum was put at simple interest at a certain rate for 10 years . Had it been put at 5% higher rate , it would have fetched Rs.200 more. What was the Sum?
Choose one
A) s.550	B) s.1000	C) s.600	D) s.200	E) s.400

Solution: At 5% more rate, the increase in S.I for 10 years = Rs.200 (given)   So, at 5% more rate, the increase in SI for 1 year = 200/10 = Rs.20/-   i.e. Rs.20 is 5% of the invested sum   So, 1% of the invested sum = 20/5   Therefore, the invested sum = 20 × 100/5 = Rs.400 Answer: s.400
Answer: E
If a=2/3b , b=2/3c, and c=2/3d what part of d is b/	Select.
A) 8/27  B) 4/9  C) 2/3  D) 7/8  E) 4/3

Solution: now put c=2/3d in b=2/3c   so b=2/3*2/3d   b=4/9d   ANSWER:4/9
Answer: B
I. j; k; m; n; p
II. j - 10; m; m; m; p + 15
III. j + 2; k + 1; m; n - 1; p - 2
If j, k, m, n, and p are consecutive positive integers such that j < k < m < n < p, the data sets I, II, and III above are ordered from greatest standard deviation D to least standard deviation in which of the following?	Choose the correct choice from the following options:
A) I, III, II
B) II, I, III
C) II, III, I
D) III, I, II
E) III, II, I

Solution: Range of 1st Set = (p-j)   Range of 2nd Set = P+15 - j +10 = (p-j) +25   Range of 3rd Set = P -2 - j - 2 = (p-j) - 4   R2 > R1 > R3 ==> SD2 > SD1 > SD3   Since,D= Higher the Range -> More Dispersion in the Set -> More Standard Deviation.II, I, III
Answer: B
The ages of 2 persons differ by 32 years. If 9 years ago the elder one be 5 times as old as the younger one, find the present age of elder person. Choose the correct choice from the following answers:	A) 30	B) 42.5	C) 45	D) 49	E) 47.9

Solution: age of the younger person = x   age of the elder person = x+32   5(x-9) = x+32-9   x= 17   age of elder person =17+32= 
17+32 = 49
49   Answer is 49
Answer: D
Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/7 rooms in 4/3 hours. How many hours would it take Albert to paint 3n rooms by himself? Select the correct option
A) 7
B) 21
C) 11
D) D.13
E) 15

Solution: rate of bob to paint n rooms is n/T(bob)   rate of Albert to paint n rooms is n/T(albert).   albert paints the room 1 hour slower than bob, so T (albert) = T(bob) -1   Together they paint the 3n/5 rooms in 4/3 hours. Rate is equal to work over time   Therefore   n/x + n/x-1 = (3n/5)/(4/3) =   n/x + n/x-1 = 9n/20. Fastest way for me is to think how would make the denominator 20. 4*5 = 20 and it fits x and x-1 or you can solve the quadratic   4n/20 + 5n/20 = 9n/20. Therefore you know it takes Albert 5 hours to paint n room, since Albert's rate is n/5.   7*3 = 3n   21 = 3n.   Answer is 21
Answer: B
We had $840 left after spending 30% of the money that we took for shopping. How much money did we start with? Choose the correct choice from the following.
A) $1000	B) $1050	C) $1100	D) $1150	E) $1200

Solution: Let x be the amount of money we started with.   0.7x = 840   x = 1200   The answer is $1200.
Answer: E
In a certain supermarket, a triangular display of cans is arranged in 10 rows, numbered 1 through 10 from top to bottom. Each successively numbered row contains 3 more cans than the row immediately above it. If there are fewer than 150 cans in the entire display, how many cans are in the seventh row? Choose the correct choice from the following answers:
A) 13	B) 15	C) 17	D) 19	E) 21

Solution: Let x be the number of cans in row 1.   The total number of cans is x + (x+3) + ... + (x+27) =   10x + 3(1+2+...+9) =   10x + 3(9)(10)/2 =   10x + 135   Since the total is less than 150, x must equal 1.   The number of cans in the 7th row is 1 + 3(6) = 19   The answer is 19.
Answer: D
Average of 13 results is 65. If the average of first six results is 61 and average of last six results is 59 Then find the seventh result? Choose the correct choice from the following choices:
A) 118
B) 120
C) 125
D) 130
E) 134

Solution: 125   Option '125'
Answer: C
Four bells ring at an interval of 4, 8, 6, 10 minutes. If they toll together at 2:00 A.M, when will they toll together again?	Choose the correct option
A) 4 am B) 5 am C) 6 am D) 7 am E) 8 am

Solution: l.c.m of 4,8,6,10 is 120 min i.e 2 hours   so ans is 2 am + 2=4 am   4 amNSWER:4 am
Answer: A
The no. of gift pack bought by Dexter is 1 more than the price, in rupees, of each gift pack. The amount of Rs.380 which Dexter had, fell short of the required amount. What is theamount by which he might have fallen short.  Pick one:
A) 38	B) 40	C) 45	D) 48	E) 49

Solution: Let the price of gift pack be 'aa'   Then number of packs bought =a+1=a+1   Hence total cost is a(a+1)a(a+1)   It is given that 380<a(a+1)380<a(a+1)   If a=19a=19, the total cost =19×20=380=19×20=380   Dexter would not have fallen short, If:   a=20a=20, a(a+1)=420a(a+1)=420   So he would have fallen short by Rs 40.   This is the minimum amount by which he may have fallen short.   40)
Answer: B
A reduction of 20% in the price of salt enables a lady to obtain 4 kgs more for Rs.100, find the original price per kg? Options:
A) 6.16	B) 6.21	C) 6.25	D) 2.4	E) 2.7

Solution: 100*(20/100)= 
100*(20/100) = 20
20 --- 4   ? --- 1=> Rs.5   100 --- 80   ? --- 5 => Rs.6.25   Answer: 6.25
Answer: C
A rectangular window is twice as long as it is wide. If its perimeter is 12 feet, then what are its dimensions in feet? Choose the correct choice:	A) 2 by 4	B) 5/3 by 10/3	C) 2.5 by 5	D) 3 by 6	E) 10/3 by 20/3

Solution: Let x be the width of the window. Then the length is 2x.   x+2x+x+2x = 12   6x = 12   x = 2   The width is 2 and the length is 4.   The answer is 2 by 4.
Answer: A
99^n is such a number begin with 8, least value of n?
Choose the correct choice from the following options:
A) 11  B) 10  C) 9  D) 8  E) n does not exist

Solution: 99^1=9801   99^2=971299   99^3=96157601   like this......   take only first two digit for n=1 99   n=2 98   n=3 97   n=4 96   ......................................................   n=10 90   n=11 89   so for n=11 number start with 8   11NSWER:11
Answer: A
If u clothes can be purchased for v dollars, how many clothes can be purchased for z dollars?	Choose the correct choice from the following answers.
A) u/z
B) z/uv
C) uv/z
D) uz/v
E) u/vz

Solution: Ans = uz/v
Answer: D
The area of a triangle is with base 4m and height 5m?	Select
A) 65 m2 B) 10 m2 C) 70 m2 D) 90 m2 E) 12 m2

Solution: 1/2 * 4 * 5= 
1/2 * 4 * 5 = 10
10 m2   Answer:10 m2
Answer: B
The sale price shirts listed for Rs.400 after successive discount is 10% and 5% is?	Choices:
A) 280  B) 290  C) 342  D) 250  E) 253

Solution: 400*(90/100)*(95/100)= 
400*(90/100)*(95/100) = 342
342   342
Answer: C
Two pipes can fill a cistern in 14 and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom, 32 minutes extra are taken for the cistern to be filled up. If the cistern is full, in what time would the leak empty it ?
Select.
A) 110 hours  B) 112 hours  C) 115 hours  D) 100 hours  E) None of these

Solution: Cistern filled by both pipes in one hour   = 1⁄14 + 1⁄16 = 15⁄112th   ∴ Both pipes filled the cistern in 112⁄15 hrs.   Now, due to leakage both pipes filled the cistern in   112⁄15 + 32⁄60 = 8 hrs.   ∴ due to leakage, filled part in one hour 1⁄8   ∴ part of cistern emptied, due to leakage in one hour   = 15⁄112 - 1⁄8 = 1⁄112th   ∴ in 112 hr, the leakage would empty the cistern.   Answer 112 hours
Answer: B
In how many ways can Ram choose a vowel and a constant from the letters of the word ALLAHABAD?
Options:
A) 4  B) 6  C) 9  D) 5  E) 3

Solution: Solution   In the letters of the word ALLAHABAD there is only 1 vowel available for selection (A). Note that the fact that A is available 4 times has no impact on this fact.   Also, there are 4 consonants available – viz. L, H, Band D. Thus, the number of ways of selecting a vowel and a consonant would be 1 × 4C1 = 4.   4nswer 4
Answer: A
The ratio of the areas of a square and rhombus whose base is same is:  Choose the correct choice
A) 1:2 B) 2:1 C) 1:1 D) 3:1 E) 2:3

Solution: SOLUTION :   The square and the rhombus are equal in area if they have a common base.   ANSWER IS 1:1
Answer: C
A sporting good store sells one type of baseball bat and one type of baseball. The cost for 2 bats and 4 balls is $200. The cost for 1 bat and 6 balls is $220, as well. If someone were to buy an equal number of bats and balls, at most how many bats can he purchase if he has a budget of $210 for the purchase?
Choose the correct choice.
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: IMO it should be C that is 3   reason:   formed an equation... bat = b ball = c   2b+4c=200   1b+6c=220   solving both we get b that is bat = 40 and c that is ball = 30   new equation 210 to be divided in equal   3b+3c=210   3*40 + 3*30= 
3*40 + 3*30 = 210
210   120 + 90= 
120 + 90 = 210
210
Answer: C
If the perimeter of square region W and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of W	Options.
A) 25:16  B) 24:25  C) 5:6  D) 4:5  E) 4:9

Solution: We know Perimeter of a square (Pw) = 4*side   Perimeter of a rectangle (Pr) = 2(length+breath)   Let us assume 40 to be the perimeter of the square (since we know each side of a square is equal and the perimeter is divisible by 4, also take in to account the length and breadth of the rectangle is in the ration 2k:3k = 5k; we can assume such a number)   Therefore,   Pw = Pr = 40   Area of the square = 100 sq. units   We know 2(length+breadth) = 40   i.e. length + breadth = 20 (or 5k = 20 given that l:b (or b:l) = 2:3)   Therefore length = 8, breath = 12   Area of the rectangle = 8*12= 
8*12 = 96
96 sq. units   Question asked= Area of the rectangle : Area of the square = 96:100 ==> 24:25=24:25
Answer: B
If x and y are numbers such that (x+4)(y-4)=0, what is the smallest possible value of x^2 + y^2 Pick: A) 0 B) 9 C) 12 D) 16 E) 18

Solution: From (x+4)(y-4)=0 it follows that either x=-4 or y=4. Thus either x^2=16 or y^2=16.   Now, if x^2=16, then the least value of y^2 is 0, so the least value of x^2 + y^2 = 16 + 0= 
16 + 0 = 16
16.   Similarly if y^2=16, then the least value of x^2 is 0, so the least value of x^2 + y^2 = 0 + 16= 
0 + 16 = 16
16.   Answer: 16.
Answer: D
24 people are there, they are shaking hands together, how many hand shakes possible, if they are in pair of cyclic sequence.
Choose the correct choice from the following choices:
A) 24
B) 23
C) 44
D) 45
E) 46

Solution: n for cyclic hand shake and n-1 for linear handshake.   so here no of hand shake is 24.   24NSWER:24
Answer: A
In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?
Pick one.
A) 30 B) 20 C) 40 D) 57 E) 63

Solution: A   30   There is a meal for 200 children.   150 children have taken the meal.   Remaining meal is to be catered to 50 children.   Now, 200 children 120 men.   50 children = (120/200)x 50 = 30 men.
Answer: A
In a 6 digit ID number, what is the probability of exactly four digits are the digit 0?
Select the correct option:
A) 9/2000	B) 81/20000	C) 12/36001	D) 81/16000	E) 84/3600

Solution: Total number of 6 digit numbers = 9*10*10*10*10*10 = 9,00,000   No. of ways of arranging 4 digits as 0 = 5C4=5.   Arrangements are as follows. Here X can be any digit other than 0   1) XX000X ==> no. of ways - 729   2) XXX000 ==> no. of ways - 729   3) X0XX00 ==> no. of ways - 729   4) XX00X0 ==> no. of ways - 729   5) X00XX0 ==> no. of ways - 729   Probability = (729*5)/90000   =81/20000   Ans - 81/20000
Answer: B
On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction Q of the total distance did he cover while the sun was shining on him?
Choose the correct choice from the following answers
A) 1/4
B) 4/5
C) 1/5
D) 1/6
E) 1/7

Solution: If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is Q=2/14 = 1/7. Answer: 1/7
Answer: E
A, B, C, D, E, F are the only six families in Indira Nagar. A, B, C, D, E and F has 7, 8, 10, 13, 6, and 10 member in their families respectively. If 1 member from all the six families left their respective families to accommodate themselves in the hostel of IIM Lucknow, then the average number of member now in each family of Indira nagar is	Choose the most appropriate option:
A) 8 B) 9 C) 10 D) 13 E) 15

Solution: 8nswer   Required average   = (( 7 - 1 ) + ( 8 - 1 ) + ( 10 - 1 ) + ( 13 - 1 ) + (6 - 1) +( 10 - 1 ) )/ 6   = ( 7 + 8 +10 + 13 + 6 + 10 ) / 6 - ( 6 x 1 ) / 6   =9 - 1= 
9 - 1 = 8
8   Correct Option: 8
Answer: A
Two taps can fill a tank in 12 and 18 minutes respectively. Both are kept open for 2 minutes and the first is turned off. In how many minutes more will the tank be filled ?	Choose one
A) 15 min.  B) 20 min.  C) 11 min.  D) 13 min.  E) None of these

Solution: Part filled by first tap in one min = 1⁄12th   Part filled by second tap in one min = 1⁄18th   Now, 2[1⁄12 + 1⁄18] + unfilled part = 1   ⇒ unfilled part = 13⁄18th   ∵ 1⁄18th part of tank is filled by second tap in 1 min.   ∴ 13⁄18th part of tank is filled by second tap in 1 min.   = 18 × 13⁄18 min = 13 min.   Answer 13 min.
Answer: D
A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?	Choose the correct choice from the following choices:  A) 5  B) 6  C) 7  D) 8  E) 9

Solution: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.   π(16)2 * h = (4/3)π (12)3 => h = 9 cm   Answer: Option 9
Answer: E
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
Answers.
A) 176 m	B) 198 m	C) 197 m	D) 150 m	E) 168 m

Solution: Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 15   => y = x/15   x + 100 / 25   = x / 15   x = 150 m.   Answer:150 m
Answer: D
The quantities S and T are positive and are related by the equation S=K/T, where k is a constant. If the value of S increases by 40 percent, then the value of T decreases by what percent?	Choose the correct choice from the following answers
A) 25%	B) 33 ¹/₃%	C) 50%	D) 66 ²/₃%	E) 75%

Solution: We can assign numbers:   lets say S = 2, K = 6 (constant) and T = 3 (so that S=K/T)   Now increasing S by 40% gives S=3, K remains constant, so T = 2 (6/2=3)   decrease in T= 1, percent decrease in T = (1/3)*100 = 33.33%   Answer 33 ¹/₃%
Answer: B
If 10 litres of an oil of Rs.55 per litres be mixed with 5 litres of another oil of Rs.66 per litre then what is the rate of mixed oil per litre? Choose the correct choice.
A) Rs.49.17	B) Rs.51.03	C) Rs.58.66	D) Rs.55.33	E) None of the above

Solution: 55*10= 
55*10 = 550
550   66*5= 
66*5 = 330
330   880/15= 58.66   ANSWER:Rs.58.66
Answer: C
What should be added to 4872 so that it may become a perfect square?
Choose the correct choice from the following answers: A) 24 B) 25 C) 26 D) 27 E) 28

Solution: 70x70=4900   4900-4872= 
4900-4872 = 28
28   If added to 28 get perfect square   answer=28
Answer: E