MU-NLPC/Calc-aqua_rat huggingface dataset:
A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
Choices:
A) 12.8 kmph
B) 12.7 kmph
C) 12.6 kmph
D) 12.5 kmph
E) 12.3 kmph

Solution: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.   Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7   Solving the equation, the speed of man in still water is 12.5 kmph.   Answer:12.5 kmph
Answer: D
On January 12, 1980, it was Saturday. The day of the week on January 12, 1979 was – Choose the correct choice: A) Saturday B) Friday C) Sunday D) Thursday E) None of these

Solution: The year 1979 being an ordinary year, it has 1 odd day.   So, the day on 12th January 1980 is one day beyond on the day on 12th January, 1979.   But, January 12, 1980 being Saturday.   ∴ January 12, 1979 was Friday.   Answer Friday
Answer: B
In 100 litres mixture milk and water are in the ratio 3:2. After adding how many liters of water its ratio will become 3:4	Choices:
A) 48
B) 50
C) 62
D) 78
E) 100

Solution: Milk quantity = 3/5 * 60= 
3/5 * 60 = 36
36   water quantity= 100-36= 
100-36 = 64
64   new ratio of M:W= 36:64+x = 3:4   192+3x = 144   x = 48   48nswer is 48
Answer: A
On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is:  Choose the correct choice from the following answers.
A) 47619
B) 47719
C) 48619
D) 47649
E) 47659

Solution: By hit and trail, we find that    47619 * 7= 
 47619 * 7 = 333_333
333333.   7) 333333 (47619   333333   ----------------   0   47619NSWER:47619
Answer: A
The angle between the minute hand and the hour hand of a clock when the time is 8.30, is:  Choices:  A) 10º  B) 75º  C) 180º  D) 270º  E) 360º

Solution: Angle traced by hour hand in 17/2 hrs =(360/12	x 17/2)º = 255.   Angle traced by min. hand in 30 min. = (360/60	x 30)º = 180.   Required angle = (255 - 180)= 
(255 - 180) = 75
75º.   Answer 75º
Answer: B
A person P takes 4 hrs time to complete a job and Q takes 6 hrs to complete the same job if they work together how much time will they require to complete the job?
Pick:
A) 1.2 hrs  B) 1.8 hrs  C) 2.4 hrs  D) 3.0 hrs  E) None of these

Solution: Explanation:   P’s 1 hr work =1/4   Q’s 1 hr work =1/6   (P+Q)’s 1 hr work= 1/4 +1/6 =5/12=> time = 12/5= 
12/5 = 12/5 = around 2.4
2.4 hrs   Answer: Option 2.4 hrs
Answer: C
Amit, Sumit and Pramit go to a seaside town to spend a vacation there and on the first day everybody decides to visit different tourist locations. After breakfast, each of them boards a different tourist vehicle from the nearest bus-depot. After three hours, Sumit who had gone to a famous beach, calls on the mobile of Pramit and claims that he has observed a shark in the waters. Pramit learns from the local guide that at that time of the year, only eight sea-creatures (including a shark) are observable and the probability of observing any creature is equal. However, Amit and Pramit later recall during their discussion that Sumit has a reputation for not telling the truth five out of six times. What is the probability that Sumit actually observed a shark in the waters?	Choose the correct choice from the following options.
A) 1/36  B) 1/30  C) 5/36  D) 1/24  E) 1/28

Solution: Explanation :   The probability that Sumit actually sees a Shark, given that he claimed to have seen one.   =>P(He actually sees the shark and reports truth) / P(He claims of seeing a shark).   =>P(Sees the shark)P(Reports Truth)/(P(He sees a shark)P(reports truth)+P(Doesn't see) P(reports false).   =>(1/8×1/6)/(1/8×1.6+7/8×5/6)   =>1/36.   1/36nswer : 1/36
Answer: A
what is the sum of first 8 natural no.	Pick one.
A) 30	B) 24	C) 36	D) 33	E) 35

Solution: the formula for first n natural no. are=n(n+1)/2   here value of n=8   8(8+1)/2   =36   answer 36
Answer: C
The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is: Choose the correct choice
A) 2/3  B) 4/5  C) 4/8  D) 9/2  E) 3/7

Solution: Explanation:   Let the required fraction be x. Then 1/x-x=9/20   1-x^2/x=9/20   20 - 20x^2 = 9x   20x^2 + 9x - 20 = 0   20x^2 + 25x - 16x - 20 = 0   5x(4x + 5) - 4(4x + 5) = 0   (4x + 5)(5x - 4) = 0   x =4/5   ANSWER 4/5
Answer: B
Find the highest value of 'a' so that 365a24 is divisible by 8. Choices:  A) 9  B) 8  C) 0  D) 2  E) 1

Solution: Explanation:   Given, number is divisible by 8 only if 'a24' is divisible by 8.   .: highest value of a is '8'.   Answer: Option 8
Answer: B
What is the scope including 1/61+1/62+1/63+......+1/70? Choose the correct answer.
A) 1/7~1/6 B) 1/5~1/4 C) 1/4~1/3 D) 1/3~1/2 E) 1/2~1

Solution: For Maximum value : It should be less than 1/61 + 1/61 +1/61... 10 times = 10/61 ~ 1/6   For Minimum Value : It should be greater than 1/70+ 1/70+ 1/70 .. 10 times = 10/70 = 1/7   Thus, the answer should lie between 1/7 and 1/6. Correct ans : 1/7~1/6.
Answer: A
All of the stocks on the over-the-counter market are designated by either a 4-letter or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
a.
b.
c.
d.
e.  Options:
A) 2(26^5)
B) 26(26^4)
C) 27(26^4)
D) 26(26^5)
E) 27(26^5)

Solution: no of different stocks for 4-letter code = 26^4   no of different stocks for 4-letter code = 26^5   total = 26^4 + 26^5 = 26^4(26+1) = 27(26^4)   ANS:27(26^4)
Answer: C
At what rate percent per annum will a sum of money double in 16 years.	Choose the correct option:
A) 2.45%
B) 5.62%
C) 5.35%
D) 6.9%
E) 6.25%

Solution: Let principal = P   then S.I. = P   T= 16yrs   Rate = (100*P)/(p*16) = 25/4= 
25/4 = 25/4 = around 6.25
6.25% p.a.   Answer is 6.25%
Answer: E
Two boards are being cut for a construction project. If the total length of the boards is 100 inches and the shorter board is 5 inches less than half the length of the longer board, what is the length of the shorter board?	Choose the correct answer
A) 25 inches B) 30 inches C) 35 inches D) 65 inches E) 70 inches

Solution: There are two boards...let it be T1(bigger) and T2(shorter one)   Now given total is T1 + T2 = 100..   also given that T2 = T1/2 -5 ..sub this value in the above eq   We get T1 + (T1-10)/2 = 200   => 3 T1 = 210 => T1 = 70..and T2 = 30...   Answer: option 30 inches is correct answer
Answer: B
The Royal Hawaiian Hotel decorates its Rainbow Christmas Tree with non-flashing white lights and a series of colored flashing lights - red, blue, green, orange, and yellow. The red lights turn red every 20 seconds, the blue lights turn blue every 30 seconds, the green lights turn green every 45 seconds, the orange lights turn orange every 60 seconds, and yellow lights turn yellow every 1 minute and 20 seconds. The manager plugs the tree in for the first time on December 1st precisely at midnight and all lights begin their cycle at exactly the same time. If the five colored lights flash simultaneously at midnight, what is the next time Q all five colored lights will all flash together at the exact same time?	Options:
A) 0:03 AM	B) 0:04 AM	C) 0:06 AM	D) 0:12 AM	E) 0:24 AM

Solution: Time taken by each light to on   Red = 20 secs   Blue = 30 secs   Green = 45 secs   Orange = 60 secs   Yellow = 80 secs   We need to take LCM to find the time all five colored lights will flash together.   LCM = 720 secs   =12 mins   =0.12 AM   Ans = 0:12 AM
Answer: D
Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 more months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?
Choose the correct choice from the following:	A) 21:32	B) 32:21	C) 12:17	D) 17:12	E) 11:10

Solution: Explanation:   Here capital is not the same.   Suresh invested 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio   =(20000Ã—6+15000Ã—6)=(20000Ã—6+15000Ã—6)   Kiran invested Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ratio   =(30000Ã—4+50000Ã—4)=(30000Ã—4+50000Ã—4)   Suresh : Kiran   =(20000Ã—6+15000Ã—6)=(20000Ã—6+15000Ã—6) :(30000Ã—4+50000Ã—4):(30000Ã—4+50000Ã—4)   =(20Ã—6+15Ã—6):(30Ã—4+50Ã—4)=(20Ã—3+15Ã—3):(30Ã—2:50Ã—2)=105:160=21:32   21:32NSWER IS 21:32
Answer: A
On his first 4 tests, Rajeev received an average score of X points. If on his fifth test, he exceeds his previous average score by 25 points, what is his average score for his first 5 tests?	Select.
A) X+6 B) X+7 C) X D) X+5 E) X+2

Solution: Total of 1st 4 tests= 4X   5th test score = X + 25   Total of all 5 tests = 5X + 25   Average = X + 5   Answer : X+5
Answer: D
A sum of money lent out at S.I. amounts to Rs. 720 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is? Choose the correct choice from the following answers:  A) 600  B) 288  C) 2768  D) 287  E) 191

Solution: S.I for 5 years = (1020 - 720) = Rs. 300.   S.I. for 2 years = 300/5 * 2 = Rs. 120.   Principal = (720 - 120) = Rs. 600.   600nswer: 600
Answer: A
If a and b are integers and (a*b)^5 = 32y, y could be:	Options.
A) 16
B) 1
C) 8
D) 12
E) 24

Solution: Distribute the exponent.   a^5 * b^5 = 32 y   Find the prime factorization of 32. This is 2^5 *1.   we need 1   The answer is 1.
Answer: B
A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 108 km downstream Choose one
A) 5 hours  B) 4 hours  C) 3 hours  D) 2 hours  E) None of these

Solution: Explanation :   Speed of the boat in still water = 22 km/hr   speed of the stream = 5 km/hr   Speed downstream = (22+5)= 
(22+5) = 27
27 km/hr   Distance travelled downstream= 108 km   Time taken = distance/speed = 108/27= 
108/27 = 4
4 hours. Answer : Option 4 hours
Answer: B
A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?	Select: A) 21/145 B) 36/145 C) 23/141 D) 21/132 E) None of these

Solution: The probability that first ball is white:   =12C130C1=12C130C1   =1230=1230   =25=25   Since, the ball is not replaced; hence the number of balls left in bag is 29.   Hence, the probability the second ball is black:   =18C129C1=18C129C1   =1829=1829   Required probability,   =(25)×(1829)=(25)×(1829)   =36/145   36/145
Answer: B
An electric motor makes 2,800 revolutions per minutes. How many degrees does it rotate in one second?	Choose the correct choice from the following answers:
A) 18.000 d/sec
B) 16.800 d/sec
C) 38.000 d/sec
D) 26.000 d/sec
E) 35.000 d/sec

Solution: 2800 revolutions / minute   = 2800*360 degrees / 60 seconds   = 16,800 degrees / second   16.800 d/sec
Answer: B
Four of the following five parts (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.	Options
A) 30 × 14 ÷ 7 × 5  B) 10 3 – 100 × 7  C) 5√3600  D) 450 ÷ 50 × 50 – 5 × 30  E) 10 × 3 + 120 × 2

Solution: Other parts are equal to 300.   Answer 10 × 3 + 120 × 2
Answer: E
If x and y are positive numbers and z = xy^2, a 40 percent increase in x and a 20 percent decrease in y would result in which of the following changes in z?  Choose the correct choice from the following answers.
A) decrease of 6.5% B) decrease of 10.4% C) increase of 4.3% D) increase of 12.8% E) increase of 16.7%

Solution: After the changes, z = 1.4x*(0.8y)^2 = (1.4*0.64)xy^2 = 0.896*z   The answer is decrease of 10.4%.
Answer: B
Total of ages of A,B and C at present is 80 years. If ratio of this ages is 2 : 2 : 4 what will be the age of C after 3 years? Choose the most appropriate option.
A) 43 years B) 42 years C) 40 years D) 37 years E) None of the above

Solution: 2+2+4=9   4*(80/8)= 
4*(80/8) = 40
40yrs   after 5yrs=43   43 yearsNSWER:43 years
Answer: A
The average runs scored by a batsman in 20 matches is 40. In the next 10 matches the batsman scored an average of 13 runs. Find his average in all the 30 matches?  Select.
A) 31  B) 34  C) 46  D) 47  E) 57

Solution: Total score of the batsman in 20 matches = 800.   Total score of the batsman in the next 10 matches = 130.   Total score of the batsman in the 30 matches = 930.   Average score of the batsman = 930/30= 
930/30 = 31
31.   31nswer:31
Answer: A
A reduction of 50% in the price of apples would enable a man to obtain 50 more for Rs.50, what is reduced price per dozen? Choose the correct option
A) 1	B) 3	C) 6	D) 7	E) 10

Solution: 6   50*(50/100)= 
50*(50/100) = 25
25 --- 50   ? --- 12=> Rs.6
Answer: C
A bowl contains pecans, cashews, and almonds in a ratio of 5 : 8 : 12, respectively. If some of the nuts of one of the three types are removed, which of the following could be the ratio of pecans to cashews to almonds remaining in the bowl?
i. 1 : 2 : 3
ii. 2 : 3 : 4
iii. 4 : 7 : 10	Choose the correct choice from the following.
A) II only B) I only C) III only D) II,III only E) I,III only

Solution: i. The ratio 2 : 3 is the same as the given ratio 8 : 12. If one pecan were removed, the new ratio would be 4 : 8 : 12, or 1 : 2 : 3.   ii. None of the nuts currently have a ratio of 3 : 4. The cashews and almonds do have a ratio of 2 : 3, but there are not enough pecans in the bowl to complete the ratio.   iii. The ratio 4 : 10 is the same as the given ratio 6 : 15. To see this, multiply the ratio by 3/2 . The new ratio is 6 : 10.5 : 15. Unfortunately, this means that there are fewer cashews that this ratio would require. Removing cashews won’t create the desired ratio.   Answer : I only
Answer: B
The edges of a cuboid are 6 cm, 5 cm and 6 cm. Find the volume of the cuboid?  Choose the correct choice:
A) 120	B) 160	C) 210	D) 368	E) 180

Solution: 6*5*6= 
6*5*6 = 180
180   Answer: 180
Answer: E
The time on a clock is 20 minutes past 4. What is the angle between the hands of the clock? Choose the correct choice from the following.
A) 60 degrees B) 20 degrees C) 45 degrees D) 50 degrees E) 10 degrees

Solution: The hour hand rotates 360 degrees in twelve hours.   The hour hand rotates 30 degrees in one hour.   The hour hand rotates 5 degrees in ten minutes.   At this time, the hour hand has rotated 130 degrees.   The minute hand rotates 360 degrees in 60 minutes, or 60 degrees in ten minutes.   At this time, the minute hand has rotated 120 degrees.   The difference is 130 - 120= 
130 - 120 = 10
10 degrees.   The answer is 10 degrees.
Answer: E
The length of a rectangular landscape is 8 times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/6rd of the total landscape. What is the length of the landscape?
Choose the most appropriate option
A) 180  B) 270  C) 340  D) 140  E) 240

Solution: Sol. x * 8x = 6 * 1200   x = 30   Length = 8 * 30= 
8 * 30 = 240
240   240
Answer: E
a and b are positive integers less than or equal to 9. If a and b are assembled into the six-digit number ababab, which of the following must be a factor of ababab Select
A) 2
B) 4
C) 5
D) 6
E) none of the above

Solution: 464646 when divided by 2 gives the result 232323   CONCEPT: Rule of Divisibility of 2 isIf sum of the digits of the Number is divisible by 2 then the number will be divisible by 2   SUm of the digits of No. which is divisible by 2 hence the Number 464646 will be divisible by 2   2
Answer: A
A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?	Select.
A) 16 2/3 days	B) 13 1/3 days	C) 17 1/3 days	D) 16 1/2 days	E) 18 1/2 days

Solution: Explanation:   5/30 + 20/x = 1   x = 24   1/30 + 1/24 = 3/40   40/3 = 13 1/3 days   Answer: 13 1/3 days
Answer: B
If the radius of a circle that centers at the origin is 5, how many J points on the circle have integer coordinates?
Choose the correct option:
A) 4
B) 8
C) 12
D) 15
E) 20

Solution: I understand this might not be required but I used the equation of a circle.   Since the origin is at 0, x^2+y^2=5^2.   X,Y could be +/- (0,5 or 5,0) - 4 possibilities.   X,Y could be +/- (3,4 or 4,3) - 8 possibilities.   Ans: J=12
Answer: C
The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 8 points after 5 games, what is the least number of the remaining matches it has to win to reach the 40-point mark by the end of the tournament?  Choose the correct choice:	A) 6	B) 7	C) 8	D) 9	E) 10

Solution: To get 40 points as end of season we need another 32 points or more from remaining 15 matches:   Option A= 6*3+9*1= 
6*3+9*1 = 27
27   Option B=7*3 + 8*1= 
7*3 + 8*1 = 29
29   Option C=8*3+7*1= 
8*3+7*1 = 31
31   Option 9=9*3+6*1= 
9*3+6*1 = 33
33   hence option 9-9
Answer: D
For the past n days, the average (arithmetic mean) daily production at a company was 70 units. If today's production of 90 units raises the average to 75 units per day, what is the value of n ? Choose the correct answer.
A) 30 B) 18 C) 10 D) 9 E) 3

Solution: (average production for n days) * n = (total production for n days) --> 70n=(total production for n days);   (total production for n days) + 90 = (average production for n+1 days) * (n+1) --> 70n + 90 = 75 * (n+1) --> n=3.   Answer: 3.
Answer: E
Pens are bought at a rate of 8 for Rs 100.To make a profit of 60%,these must be sold at  Choose the correct choice from the following answers.
A) 5 for Rs100 B) 6 for Rs 100 C) 9 for Rs 200 D) 8 for Rs 100 E) None

Solution: C.P. of 8 Pens = Rs100   S.P. of 8 Pens = 160% of Rs 100 = Rs160   For Rs.160 , Pens sold = 8.   For Rs. 100,Pens sold=(8/160)*100= 
(8/160)*100 = 5
5   5 for Rs100nswer: Option 5 for Rs100
Answer: A
If s and t are positive integers such that s/t = 36.42, which of the following could be the remainder when s is divided by t ? Choose the correct choice from the following choices:
A) 42
B) 43
C) 83
D) 20
E) 45

Solution: s/t= 36.42   s = 36.42t   s = (36 + 0.42)t   s = 36t + (42/100)t   s = 36t + (21/50)t   So remainder will be multiple of 21. The only multiple of 21 is 42.   Ans. 42
Answer: A
The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half yearly is	Pick one:
A) 6.06%	B) 6.07%	C) 6.08%	D) 6.09%	E) None

Solution: Solution   Amount of Rs.100 for 1 year when compounded half yearly   = Rs.[100 x (1+3/100)2]   = Rs. 106.09%.   Effective rate	= (106.09 - 100)%   = Rs. 6.09%.   Answer 6.09%
Answer: D
A pipe can fill a cistern in 44 minutes. Find the time in which 1/11 part of the cistern will be filled?	Pick:
A) 4min
B) 2min
C) 3min
D) 1min
E) 10min

Solution: Full cistern filled in = 44 minutes   1/11 part filled in = 44*1/11= 
44*1/11 = 4
4minutes   4minnswer is 4min
Answer: A
In how many different ways can the letters of the word 'SENDING' be arranged in such a way that the vowels always come together?
Choices
A) A)360  B) B)480  C) C)720  D) D)5040  E) of these

Solution: The word 'SENDING' has 7 different letters.   When the vowels EI are always together, they can be supposed to form one letter.   Then, we have to arrange the letters SNDNG (EI).   Now, 6 (5 + 1 = 6) letters can be arranged in 6! = 720 ways.   The vowels (EI) can be arranged among themselves in 2! = 2 ways.   Required number of ways = (720 x 2) = 1440.   ANSWER:480
Answer: B
P works twice as fast as Q. If Q alone can complete a work in 12 days, P and Q can finish the work in --- days	Choose the correct choice
A) 1 B) 2 C) 3 D) 4 E) 4.5

Solution: Work done by Q in 1 day = 1/12   Work done by P in 1 day = 2 × (1/12) = 1/6   Work done by P and Q in 1 day = 1/12 + 1/6 = ¼   => P and Q can finish the work in 4 days   Option 4
Answer: D
What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x Choose the correct choice from the following:
A) 1	B) 3	C) 4	D) 5	E) 6

Solution: 46080 /12= 
46080 /12 = 3_840
3840   3840 /10= 
3840 /10 = 384
384   384 /8= 
384 /8 = 48
48   48 /6= 
48 /6 = 8
8   8/4= 
8/4 = 2
2   2 /2= 
2 /2 = 1
1   1
Answer: A
if a person want to earn 500 extra from his principal amount in 3 year and rate of interest in market is 3%.how much principal amount he have to spend?	Choose the correct choice from the following answers:	A) 3500	B) 4444.44	C) 3000	D) 5555.55	E) 6000

Solution: s.i=p*r*t/100   500=p*3*3/100   50000/9=p   p=5555.55   answer 5555.55
Answer: D
The 7th grade French and Spanish classes each have 14 students in them, and there are four students in the 7th grade taking both languages. If everyone in the 7th grade is in at least one of the two language classes, how many students are taking just one of the two classes?
Choose the correct choice from the following choices:
A) 20 B) 21 C) 22 D) 23 E) 24

Solution: French class + Spanish class = 28 students.   Four students are in both classes so they were counted twice.   The number of students taking just one class is 28 - 2(4) = 20.   The answer is 20.
Answer: A
If Albert’s monthly earnings rise by 36%, he would earn $495. If, instead, his earnings rise by only 25%, how much (in $) would he earn this month? Select the correct option
A) 643	B) 652	C) 454	D) 460	E) 490

Solution: =495/1.36∗1.25   =454=454   Answer is 454
Answer: C
Reema took a loan of Rs 900 with simple interest for as many years as the rate of interest. If she paid Rs. 729 as interest at the end of the loan period, what was the rate of interest.
Pick one.
A) 5%
B) 6%
C) 7%
D) 8%
E) 9%

Solution: Explanation:   Let rate = R% then Time = R years.   =>900∗R∗R /100=729   =>R2=81   =>R=9%   Option 9%
Answer: E
How many 4-digit Y numbers (ABCD) can be formed such that |A – D| = 2? Choose one.
A) 2,000 B) 1,900 C) 1,800 D) 1,600 E) 1,500

Solution: 1) A=0 and D-8   2) A and D as 1 and 9..so 3*100= 
3*100 = 300
300 extra ways ans  1800-300= 
 1800-300 = 1_500
1500.   we are looking for |A-D|=2 so any of the two can be bigger..   these two can have values (1,3) ; (2,4) so on till (7,9) so total 7*2 = 14..   another arrangement could be A as 2 and D as 0... D as 2 and A as 0 is not possible as number will become 3 digits..   so the ways A and D can be placed = 14+1= 
14+1 = 15
15 ways..   B and C can be placed in 10*10 ways..   Total Y= 15*10*10=1500.1,500
Answer: E
A man gets a simple interest of Rs.400 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate.
Choose the correct choice from the following choices:
A) Rs.500 B) Rs.250 C) Rs.205 D) Rs.5062.50 E) None of these.

Solution: Let the principal be Rs.P   S.I at 5% p.a in 8 years on Rs.P = Rs.400   (P)(8)(5)/100 = 400   P = 1000   Rs.205.I on Rs.2P i.e., Rs.2000 at 5% p.a in two years   =2000{ [1 + 5/100]2 - 1} = 2000{ 212 - 202 /202}   = Rs.205   ANSWER:Rs.205
Answer: C
A thief steals at a car at 1.30 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?  Choose one:
A) 1 p.m  B) 3 p.m  C) 4. p.m  D) 5 p.m  E) 6 p.m

Solution: C   4 p.m   Suppose the thief is overtaken x hrs after 1.30 p.m.   Then, distance covered by the owner in (x - 1/2) hrs.   60x = 75(x - 1/2) => x = 5/2 hrs.   So, the thief is overtaken at 4. p.m.
Answer: C
The radius and height of a right circular cone are in the ratio 3 : 4. If its volume is 96∏ cm³, what is its slant height?	Choices.
A) 8 cm B) 10 cm C) 12 cm D) 14 cm E) None

Solution: Sol.   Let the radius and the height of the cone be 3x and 4x respectively. Then,   1/3 * ∏ * (3x)² * 4x = 96∏ ⇔ 36x³   = (96 * 3) ⇔ x³ = [96 * 3 / 36= 
96 * 3 / 36 = 8
8 ⇔ x= 2   &ther4 Radius = 6 cm, Height = 8 cm.   Slant height = √6² + 8 ² cm = √100 cm = 10 cm.   Answer 10 cm
Answer: B
A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?  Choose the correct choice from the following options:
A) 359m	B) 3320m	C) 350m	D) 3598m	E) 310m

Solution: Speed = [300 / 18] m/sec = 50/3 m/sec.   Let the length of the platform be x meters.   Then, x + 300 / 39 = 50/3   3(x + 300) = 1950 è x = 350m.   Answer: 350m
Answer: C