MU-NLPC/Calc-aqua_rat huggingface dataset:
A sum of money placed at C.I. interest doubles itself in 5 years. It will amount to eight times itself at the same rate of interest in?
Pick:
A) 20 years
B) 1 years
C) 15 years
D) 39 years
E) 39 years

Solution: Explanation:   P(1 + R/100)5 = 2P => (1 + R/100)5 = 2   Let P(1 + R/100)n = 8P   => (1 + R/100)n = 8 = 23 = {(1 + R/100)5}3   => (1 + R/100)n = (1 + R/100)15 => n = 15 Required time = 15 years.   Answer: Option 15 years
Answer: C
Set F consists of all the prime numbers between 10 and 25. What is the range of set F?  Select the correct option
A) 12	B) 13	C) 16.6	D) 17	E) 23

Solution: 12nswer of set F is 12=12
Answer: A
If a mixture is 5⁄9 alcohol by volume and 4⁄9 water by volume, what is the ratio of the volume of alcohol to the volume of water in this mixture? Choose the most appropriate option
A) 1/4	B) 3/4	C) 5/4	D) 6/4	E) 7/4

Solution: Should be a sub-600 level Q..   volume= {5/9}/{4/9}=5/4   5/4
Answer: C
when n divided by 3, the remainder is 2.
when n divided by 4, the remainder is 1
what is the the remainder when divided by 12	Choose the correct choice from the following.
A) 1	B) 3	C) 4	D) 5	E) 12

Solution: when n divided by 3, the remainder is 2.   This statement can be written as   n=3k+2 (where k is the quotient) ----1   similarly   when n is divided by 4, the remainder is 1   can be written as   n=4p+1 (here p is the quotient) ------2   from eq 1 and 2   3k+2=4p+1   or,   k=(4p-1)/3   substitute p= 1 , the result will give ----> k(4 -1)/3= 
(4 -1)/3 = 1
1 , the result will give ----> k=1   substitute back in the equations   in both the cases we have n=5   dividing n by 12 will give remainder 5 !!   ANSWER:5
Answer: D
The mean of set L does not exceed mean of any subset of set L. Which of the following must be true about set L?
I. Set L contains only one element
II. All elements in set L are equal
III. The median of set L equals the mean of set L
Choose the correct answer:
A) of the three qualities is necessary  B) II only  C) III only  D) II and III only  E) I, II, and III

Solution: The only necessary condition seems to be II.   If all nos are equal.... them mean of any subset is the same.   I is obviously ruled out ( e.g. L = {1,1,1} )   But III, what about 3?   It is not necessary in itself, rather, is automatically implied by II.   All sets that satsify II satisfy III=II and III only
Answer: D
The ratio of number of students studying Arts, Commerce and Science in a College is 7 : 5 :8. What is the new ratio of the number of students studying Arts, Commerce and Science respectively if there is an increase of 20%, 40% and 25% in the number of students studying Arts, Commerce and Science?
Choose the correct answer:
A) 18 : 35 : 50
B) 3 : 10 : 10
C) 4 : 8 : 5
D) 21 : 35 : 50
E) None of these

Solution: Suppose the number of students studying Arts, Commerce and Science be 7x, 5x and 8x respectively.   When their numbers are increased by 20%, 40% and 25% respectively the new ratio becomes   7x × 120% : 5x × 140% :   8x × 125% = 42 : 70 : 100   = 21 : 35 : 50   Answer 21 : 35 : 50
Answer: D
xy=1 then what is (4^(x+y)^2) / (4^(x-y)^2)	Choose one
A) 2
B) 4
C) 8
D) 256
E) 32

Solution: (x+y)^2 - (x-y)^2   (x+y+x-y)(x+y-x+y)   (2x)(2y)   4xy   4   4^4 = 256   Answer 256
Answer: D
A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Select:  A) 1:2  B) 1:9  C) 1:1  D) 1:9  E) 3:2

Solution: T = 192/32= 
192/32 = 6
6 h   T= 6 - 3= 
6 - 3 = 3
3   Time Ratio= 6:3 = 2:1   Speed Ratio = 1:2   1:2nswer: 1:2
Answer: A
A researcher computed the mean, the median, and the standard deviation Q for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change?  Choose the correct choice from the following answers:
A) The mean only	B) The median only	C) The standard deviation only	D) The mean and the median	E) The mean and the standard deviation

Solution: If we add or subtract a constant to each term in a set the standard deviation Q will not change..   If we add (or subtract) a constant to each term in a set the mean and the median will increase (decrease) by the value of that constant.   Answer: The mean and the median.
Answer: D
If X = Y/Z+1, -1 < Z < 0 and 2 < Y, which of the following is correct? Choose the correct choice from the following options.
A) 1 < X <2 B) 0 < X <-2. C) -4 < X < 0 D) 0 < X <-4 E) X < -20

Solution: Y is +ve & Z is -ve   For min. value max. numerator and minimize denominator   take Y=2.1 & Z=-0.9   X=2.1/(-0.9+1) X=2.1/1.9   1 < X <2   1 < X <2ns 1 < X <2
Answer: A
If O is the center of the circle in the figure above and the area of the unshaded sector is 5, what is the area of the shaded region?
Choose the correct answer:	A) 25/√π	B) 30/√π	C) 20	D) twenty five (25)	E) 30

Solution: 60/360 = 1/6   1/6 of total area = 5   5/6 of total area = 5*5= 
5*5 = 25
25   ANSWER:twenty five (25)
Answer: D
Two assembly line inspectors, Lauren and Steven, inspect widgets as they come off the assembly line. If Lauren inspects every fourth widget, starting with the fourth, and Steven inspects every third, starting with the third, how many of the 98 widgets produced in the first hour of operation are not inspected by either inspector?	Choices.
A) 50	B) 52	C) 53	D) 55	E) 56

Solution: Widgets inspected by Lauren: ((96-4)/4)+1=23+1= 
23+1 = 24
24   Widgets inspected by Steven: ((96-3)/3)+1=31+1= 
31+1 = 32
32   Widgets inspected by both: ((96/12)+1=9   Total : 24+32 -9=45   hence, widgets not inspected: 98-45= 
98-45 = 53
53   Option 53
Answer: C
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?  Pick one.
A) 36 sec	B) 30 sec	C) 13 sec	D) 19 sec	E) 12 sec

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.   36 secnswer:36 sec
Answer: A
In a series of football matches, the probability that Team P wins a match against Team Q is 1/3 and the probability that the match ends in a draw is 1/5. If the two teams play five matches, what is the probability that all five matches end in a draw?
Select the correct option.
A) 1/1625  B) 1/2225  C) 1/3125  D) 1/4225  E) 1/5425

Solution: P(5 draws)=(1/5)^5=1/3125   The answer is 1/3125.
Answer: C
A man gets a simple interest of Rs.600 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.  Options.
A) Rs.500	B) Rs.250	C) Rs.307.5	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.600   (P)(8)(5)/100 = 600   P = 1500   Rs.307.5.I on Rs.2P i.e., Rs.2500 at 5% p.a in two years   =3000{ [1 + 5/100]2 - 1} = 3000{ 212 - 202 /202}   = 3000/400(441 - 400)   = Rs.307.5   ANSWER:Rs.307.5
Answer: C
A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?	Choose the correct option.
A) 167 ways  B) 828 ways  C) 627 ways  D) 108 ways  E) 622 ways

Solution: The boy can select one trouser in nine ways.   The boy can select one shirt in 12 ways.   The number of ways in which he can select one trouser and one shirt is   9 * 12= 
  9 * 12 = 108
108 ways.   Answer:108 ways
Answer: D
A factory produces 5500 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?  Choose the correct choice from the following choices
A) 1375 toys
B) 2375 toys
C) 3375 toys
D) 4375 toys
E) 5375 toys

Solution: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 4 days) by 4.   5500 ? 4 = 1375 toys   correct answer 1375 toys
Answer: A
The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?	Choose the correct choice from the following answers.
A) 20 kmph B) 40 kmph C) 27 kmph D) 28 kmph E) 22 kmph

Solution: Speed downstream = 60 + 20= 
60 + 20 = 80
80 kmph   Speed upstream= 60 - 20= 
60 - 20 = 40
40 kmph   Answer:40 kmph
Answer: B
There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.? Choose the correct choice:
A) 87  B) 98  C) 12  D) 27  E) 28

Solution: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.   a2 = 784 = (4)(196) = (22).(142)   a = (2)(14) = 28   a = 2l, l = a/2 = 14   l = (7/3)s   Therefore s = (3/7)(l) = 6 Circumference of the smaller circle   = 2∏s = 12∏ cm.   Answer:12
Answer: C
The length and width of a rectangle are integer values. What is the area of the smallest such rectangle that can be inscribed in a circle whose radius is also an integer Pick
A) 12	B) 24	C) 46	D) 48	E) 60

Solution: If we consider all pythagorean triplets with integral values, we have the following results:-   (3,4,5),(6,8,10)........   The diameter of the circle is 5 in the 1st case and 10 in the 2nd.   But the question says that radius of the circle is also an integer hence the 1st triplet will be ruled out.   We are left with the 2nd triplet where radius of the circle=5,   Hence the sides of the rectangle are 6 and 8 making the area =46.   46
Answer: C
Solving a linear equation with several occurrences of the variable, solve for w. Simplify answer as much as possible.
(7w + 6)/6 + (9w +8)/2 = 22
Choose the correct choice from the following answers.
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: (7w + 6)/6 + (9w +8)/2 = 22   or, [7w + 6 + 3(9w + 8)]/6 = 22   or, 7w + 6 + 27w + 24 = 132   or, 34w + 30 = 132   or, 34w = 132 - 30   or, 34w = 102   or, w = 102/34   Therefore, w = 3   Answer: 3
Answer: C
What is the square root of 81, divided by 3?	Choose the correct option:
A) 9  B) 36  C) 122  D) 3  E) 1

Solution: Square root is a number times itself   Square root of 81=6, 9/3=3   (3)3
Answer: D
Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $ 56 more. What was his original selling price?	Choices
A) $770  B) $660  C) $700  D) $1100  E) $880

Solution: Let the original purchase price be X   So original selling price at 10% profit = 1.1X   If product is purchased at 10% less of original = 0.9X   Profit of 30% on this price = 1.3(0.9X)   He would have received $56 more in second scenario => 1.3(0.9X) - 1.1X = 56   => 0.07X = 56   => X = $800   Original purchase price = $800   Hence, original selling price (at 10% of profit) = 1.1(800) = $880   Option $880
Answer: E
Cricket match is conducted in US. The run rate of a cricket game was only 3.2 in first 10 over. What should be the run rate in the remaining 40 overs to reach the target of 222 runs?	Choices.
A) 6  B) 6.25  C) 7.25  D) 7.5  E) 4.75

Solution: Required run rate = 222 - (3.2 x 10) =	190 = 4.75   40	40   4.75
Answer: E
Two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 48 kmph respectively. In how much time will they cross each other, if they are running in the same direction?	Select: A) 72 sec B) 132 sec C) 157.5 sec D) 252 sec E) None

Solution: Solution   Relative Speed	= (48 - 40 )= 
(48 - 40 ) = 8
8 kmph=(8 x 5 / 18)m/sec   = (40 / 18 ) m/sec   Time taken	= (350 x 18 / 40) sec   = 157.5 sec.   Answer 157.5 sec
Answer: C
A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock?
Choose the correct choice from the following choices:	A) 23277	B) 20000	C) 28778	D) 28788	E) 18881

Solution: Let the total worth of the stock be Rs. x.   The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50   The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50   Total SP = 11x/50 + 38x/50 = 49x/50   Overall loss = x - 49x/50 = x/50   x/50 = 400 => x = 20000   Answer: 20000
Answer: B
If a real number x is chosen at random in the interval [0,5] and a real number y is chosen at random in the interval [0,7], what is the probability that x < y?
Choose the correct choice from the following answers
A) 5/7	B) 2/3	C) 9/14	D) 4/5	E) 7/8

Solution: Since x is in [0,5] and y is in [0,7] we can draw a rectangle in the coordinate plane with vertices (0, 0), (5, 0), (0, 7), and (5, 7).   The points above the line y=x satisfy x < y.   The part of the rectangle below y=x has an area of 12.5   The whole rectangle has an area of 35.   P(x < y) = (35-12.5)/35 = 22.5/35 = 45/70 = 9/14   The answer is 9/14.
Answer: C
Three bottles whose capacities are as 5 : 3 : 2 are completely filled with milk mixed with water. The ratio of milk to water in the mixture of bottles are as 3 : 2, 2 : 1 and 3 : 1 respectively. Find the percentage of water in the new mixture obtained when 1/3rd of first, 1/2 of second and 2/3rd of the third bottle is taken out and mixed together Pick:
A) 66.66%
B) 50%
C) 16.66%
D) 33.33%
E) 36.33%

Solution: Let the percentage of water be X   The quantity of new mixture = (5X/3) + (3X/2 )+ (4X/3) = 27X/6 = 9X/2.   Percentage of milk = (5X/3) x (3/5) + (3X/2) x (2/3) + (4X/3) x (3/4) = 3X   Percentage of water = (5X/3) x (2/5) + (3X/2) x (1/3) + (X/2) x (2/3) = 3X/2   Percentage of water = (3X/2)/(9X/2) x 100   = 100/3   = 33 (1/3)%   ANSWER:33.33%
Answer: D
The total of a company's assets in 1994 was 100% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of the company's assets in 1992 was N dollars, what were the company's assets in 1994? Choose one:
A) 5N  B) 7N  C) 10N  D) 15N  E) 20N

Solution: In 1992, the company's assets were N.   In 1993, the company's assets were N + 4N = 5N.   In 1994, the company's assets were 5N + 5N = 10N.   The answer is 10N.5  + 5= 
5  + 5 = 10
10N.   The answer is 10N.
Answer: C
If A and B get profits of Rs.5,000 and Rs.2,000 respectively at the end of year then ratio of their investments are
Choose the correct choice from the following answers
A) 4:1 B) 1:4 C) 5:2 D) 2:3 E) 2:5

Solution: Ratio = 5000/2000 = 5 : 2   Answer : 5:2
Answer: C
If the cost price of 44 chocolates is equal to the selling price of 24 chocolates, the gain percent is :
Choices:
A) 83.55%  B) 83.33%  C) 80%  D) 83.39%  E) 84.33%

Solution: Explanation :   Solution: Let C.P. of each chocolate be Re. 1. then, C.P. of 24 chocolates = Rs. 24;   S.P. of 24 chocolates =Rs. 44.   .'. Gain% = 20*100/24 =83.33%   Answer : 83.33%
Answer: B
If x and y are positive integers, and 1 is the greatest common divisor of x and y, what is the greatest common divisor A of 2x and 3y? Choose the correct choice
A) A=1 B) A=Cannot be determined C) 2 D) 5 E) 6

Solution: My explanation: from question stem we know that nothing is common between X and Y , X and Y are two prime numbers eg: X=2, Y=3 and their GCD(2,3) =1 and so 2X and 3Y will have a GCD(2X,3Y) = 1 . what if either X or Y was 1, eg: X=1,Y=4 then GCD(1,4) =1 , but GCD(2,12) = 2.   and hence answer A=Cannot be determined
Answer: B
The original price of a certain TV set is discounted by d percent, and the reduced price is then discounted by 2d percent. If P is the original price of the TV Set, which of the following represents the price of the television set after the two successive discounts?
Choose the correct choice.
A) P(1 - 0.03x + 0.02x^2)	B) P(1 - 0.03d + 0.0002d^2)	C) P(1 - 0.03x + 0.002x^2)	D) P(1 - 2x^2)	E) P(1 - 3x + 2x^2)

Solution: Youcansolve this problem with number plugging.   Say the original price was $10 and d=50. Then after the first reduction the price would become $5 and after the second reduction of   2*50= 
  2*50 = 100
100% the rprice would become $0.   Now, since P is not zero, then the expression in the brackets must be zero for d=50. Only answer choice B works.   Answer: B.   On this problem - number pluggin is not giving me the answer.. I initially used d = 10, then 2d = 20 and P = 100. Answer should after both consecutive discounts = 72. I plug in the respective values and I keep getting 68. Can you double check my math.   100 (1-0.03(10) + 0.0002 (10)^2)   100 (1-0.3 + 0.0002 (100))   100 (0.7 + 0.02)   100 (0.68) = 68????   double check my math. Am I missing something? I also plugged in your numbers and still did not get zero as final answer with choice P(1 - 0.03d + 0.0002d^2)..
Answer: B
Of 300 surveyed students, 20% of those who read book A also read book B and 50% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B?
Choose the correct choice from the following answers:
A) 120
B) 125
C) 130
D) 135
E) 150

Solution: Say the number of students who read book A is A and the number of students who read book B is B.   Given that 20% of those who read book A also read book B and 50% of those who read book B also read book A, so the number of students who read both books is 0.2A=0.5B --> A=2.5B.   Since each student read at least one of the books then {total}={A}+{B}-{Both} --> 300=2.5B+B-0.5B --> B=100, A=2.5B=250 and {Both}=0.5B=50.   The number of students who read only book A is {A}-{Both}=250-50= 
250-50 = 200
200;   The number of students who read only book B is {B}-{Both}=100-50= 
100-50 = 50
50;   The difference is  200-50= 
 200-50 = 150
150.   Answer: 150.
Answer: E
John have a 630ml mixture of milk and water in the ratio 7:2. How much water must be added to make the ratio 7:3? Options.
A) 50 ml
B) 60 ml
C) 70 ml
D) 80 ml
E) 90 ml

Solution: concentration of water in mixture1 =29 (since the ratio of milk and water = 7:2) ...(1)   concentration of water in pure water= 1 ...(2)   Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3   => concentration of water in mixture2 =310   By rule of alligation,   concentration of water in mixture1 (29)   concentration of water in pure water (1)   Mean concentration   (310)   1−310=710   310−29=790   => Quantity of mixture1 : Quantity of water   =710:790=110:190=1:19   Given that Quantity of mixture1 = 630 ml   => 630 : Quantity of water =1:19   => Quantity of water =630×19=70 ml   70 ml
Answer: C
By investing Rs. 1620 in 8% stock,Michael earns Rs. 135.The stock is then quoted at :  Choose the correct choice from the following choices:
A) Rs. 80 B) Rs. 96 C) Rs. 106 D) Rs. 108 E) Rs. 109

Solution: Solution   To earn Rs. 135, investment = Rs. 1620.   To earn Rs. 8, investment = Rs. (1620/135X8)= Rs. 96.   ∴ Market value of Rs. 100 stock = Rs. 96.   Answer Rs. 96
Answer: B
The least number which must be subtracted from 509 to make it exactly divisible by 9 is:	Select:
A) A)2  B) B)3  C) C)5  D) D)5  E) E)6

Solution: On dividing 509 by 9, we get remainder= 5   Therefore, required number to be subtracted= 5   Answer: 5
Answer: C
A watch was sold at a loss of 10%. If the watch was sold for $28 more, there would have been a gain of 4%. What is the cost price?	Choose the correct choice from the following choices.
A) $180
B) $200
C) $220
D) $240
E) $260

Solution: 0.9x + 20 = 1.04x   0.14x = 28   x = 200   The answer is $200.
Answer: B
In Net's hair salon 54% of the customers dye their hair blond, 36% dye their eyebrows blond and 35% straighten their hair. 20% of the customers have none of these three procedures, while 12% take all of these three procedures. What percent of the customers come for exactly 2 of these 3 procedures?  Choose the correct choice from the following answers.
A) 5%	B) 9%	C) 12%	D) 15%	E) 21%

Solution: Let a total of 100 people visit the salon.   Total = 100   Dye hair blonde (A) = 54 % = 54   Dye 21%yebrows blonde (B) = 36% = 36   Straighten Hair (C) = 35% = 35   Neither = 20% = 20   All Three = 12% =12   Total = A+B+C - (Sum of 21%xactly Two group overlaps) - 2*(All three) + Neither   100 = 54+36+35 - (Sum of 21%xactly Two group overlaps) - 2*12 + 20   (Sum of 21%xactly Two group overlaps) = 9   %of customers coming for exactly 2 of the 3 procedures = 21%   21%
Answer: E
Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 60 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?	Choose the correct choice from the following answers.
A) 22 B) 27 C) 40 D) 99 E) 12

Solution: Relative speed = 60 + 30= 
60 + 30 = 90
90 km/hr.   90 * 5/18= 
90 * 5/18 = 25
25 m/sec.   Distance covered= 500 + 500= 
500 + 500 = 1_000
1000 m.   Required time= 1000/25= 
1000/25 = 40
40 sec.   Answer: 40
Answer: C
An unbiased die is tossed .find the probability of getting a multiple of 3  Pick one.
A) 3/7
B) 4/9
C) 1/3
D) 3/5
E) 2/7

Solution: Here S={1,2,3,4,5,6}   Let E be the event of getting the multiple of 3   then ,E={3,6}   P(E)=n(E)/n(S)=2/6=1/3   Ans: 1/3
Answer: C
There are 20 balls which are red, blue or green. If 7 balls are green and the sum of red balls and green balls is less than 13, at most how many red balls are there? Options: A) 4 B) 5 C) 6 D) 7 E) 8

Solution: Explanation :   GIVEN:   RED + GREEN + BLUE = 20   GREEN = 7   SOLUTION:   R + G < 13   THEREFORE R + 7 < 13   SO r < 6   ANS: AT most 5 red balls   B. 5   Hence (B) is correct.   Answer : 5
Answer: B
A dishonest dealer claims to sell a product at its cost price. He uses a counterfeit weight which is 20% less than the real weight. Further greed overtook him and he added 15% impurities to the product. Find the net profit percentage of the dealer?	Choose the correct choice from the following options: A) 46.85% B) 43.75% C) 50% D) 56.25% E) 36%

Solution: The dealer uses weight which is 20% less than the real weight. or (1- 1/5) or 4/5 of real weight.   It means that he is selling $4 worth of product for $5.   The dealer then further added 20% impurities to the product.   It means that he is selling $5 worth of product for $5.75.   So his profit is $5.75-$4 = $1.75   and his profit percent is   (1.75/4)*100 5.75- 4= 
5.75- 4 = 1.75
$1.75   and his profit percent is    (1.75/4)*100= 
 (1.75/4)*100 = 43.75
43.75%   Answer:- 43.75%
Answer: B
A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?  Pick: A) 65 sec B) 89 sec C) 100 sec D) 150 sec E) 120 sec

Solution: Speed =	240/24 m/sec = 10 m/sec.   Required time = (240 + 650)/10= 
(240 + 650)/10 = 89
89 sec.   Answer: Option 89 sec
Answer: B
A train 605 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
Select the correct option:  A) 81  B) 16  C) 33  D) 54  E) 12

Solution: Speed of train relative to man = 60 + 6= 
60 + 6 = 66
66 km/hr.= 66 * 5/18 = 55/3 m/sec.   Time taken to pass the men = 605 * 3/55= 
605 * 3/55 = 33
33 sec.   Answer: 33
Answer: C
From the top of a 9 metres high building AB, the angle of elevation of the top of a tower CD is 30º and the angle of depression of the foot of the tower is 60º. What is the height of the tower?  Choose the most appropriate option:
A) 11
B) 12
C) 88
D) 27
E) 10

Solution: We have to find the value of CD. We use Sine rule to find the answer easily. Sine rule is aSinA=bSin12=cSinCaSinA=bSin12=cSinC   In triangle 12DE, 9Sin60=xSin309Sin60=xSin30   So 93–√2=x12⇒x=93–√932=x12⇒x=93   In triangle 12CD, CDSin30=93–√Sin60CDSin30=93Sin60   CD12=93–√3–√2⇒CD=3CD12=9332⇒CD=3   So height of the tower = 9 + 3= 
9 + 3 = 12
12   Answer:12
Answer: B