MU-NLPC/Calc-aqua_rat huggingface dataset:
In a 1000 m race, A beats B by 50 m and B beats C by 100 m. In the same race, by how many meters does A beat C? Pick:  A) 145  B) 266  C) 276  D) 027  E) 266

Solution: By the time A covers 1000 m, B covers  (1000 - 50)= 
 (1000 - 50) = 950
950 m.   By the time B covers 1000 m, C covers  (1000 - 100)= 
 (1000 - 100) = 900
900 m.   So, the ratio of speeds of A and C=   1000/950 * 1000/900 = 1000/855 So, by the time A covers 1000 m, C covers 855 m.   So in 1000 m race A beats C by 1000 - 855= 
1000 - 855 = 145
145 m.   145nswer: 145
Answer: A
In how many ways can you line up 7 wrestlers in a row if one of them, The Undertaker, cannot be in the middle or at the either end?
Choose the correct choice from the following options.
A) 1,570  B) 2,880  C) 90  D) 192  E) 5,300

Solution: Since The Undertaker cannot be placed in the middle or at either end (3 spots), then he can choose 4 spots to sit. The remaining 6 apples can be placed in in 6! ways. Thus the # of arrangements is 4*6! = 2,880.   Answer: 2,880.
Answer: B
Benny goes to the market for buying some apples to be distributed between her nine kids equally.She takes 360 dollars with her .The cost of each apple is 4 dollars .How many apples does she buy to share them equally between her nine kids?
Select the correct option
A) 8
B) 9
C) 3
D) 7
E) 10

Solution: cost of each apple = 4 dollars   Apples that Benny can buy with the amount she has=360/4= 
360/4 = 90
90.   Apples that each kid gets evenly= 90/9= 
90/9 = 10
10 Apples.   So the answer is 10=10
Answer: E
What amount does an investor receive if the investor invests $3000 at 10% p.a. compound interest for two years, compounding done annually?
Options:	A) $3420	B) $3630	C) $3870	D) $4040	E) $4220

Solution: A = (1 + R/100)^n * P   (1.1)^2 * 5000 = 1.21 * 5000 = 3630   The answer is $3630.
Answer: B
Will must choose a 2-character computer password, consisting of 1 letter from the alphabet and 1 distinct digits, in any order.From how many different passwords can Will choose? Select:  A) 520  B) 1560  C) 4,680  D) 7,020  E) 14,040

Solution: 26C1*10C1 = 260   => 260 * 2= 
260 * 2 = 520
520   Option E is correct answer...but O520 is 520.
Answer: A
A train running at a speed of 60 kmph crosses a pole in 6 seconds.What is the length of the train? Choose the correct choice:
A) 120 m B) 180 m C) 100 m D) 150 m E) 160 m

Solution: 60 kmph=50/3 m/sec   50/3*6= 
50/3*6 = 100
100 m   ANSWER:100 m
Answer: C
P is able to do a piece of work in 10 days and Q can do the same work in 12 days. If they can work together for 5 days, what is the fraction of work left? Choose the correct choice from the following:  A) 7/12  B) 5/12  C) 1/12  D) 3/12  E) 1/2

Solution: Explanation :   Amount of work P can do in 1 day = 1/10   Amount of work Q can do in 1 day = 1/12   Amount of work P and Q can do in 1 day = 1/10+ 1/12 = 11/60   Amount of work P and Q can together do in 5 days = 5 × (11/60) =11/12   Fraction of work left = 1 – 11/12= 1/12   Answer : Option 1/12
Answer: C
Two equilateral triangles of side 12cm are placed one on top of another, such that a 6 pointed star is formed .if the six verticals lie on a circle what is the area of the circle not enclosed by the star ?
Select the correct option.
A) 68 B) 83 C) 57 D) 61 E) 62

Solution: area of star = √3/4 * (12)^2 + 3* √3/4 *(12/3)^2 = 48√3   if r be radius of circle then r=6/cos30 => r=12/√3 => r^2=48   area of circle = pi*48   area of the circle not enclosed by the star = 48*pi - 48√3 =48(3.14-1.732)= 68(approax)   68NSWER:68
Answer: A
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?	Choose the correct answer.
A) 12 days
B) 15 days
C) 18 days
D) 20 days
E) 22 days

Solution: A’s two day’s work = 2/20 = 1/10   (A + B + C)’s one day’s work = 1/20 + 1/30 + 1/60 = 6/60 = 1/10   Work done in 3 days = (1/10 + 1/10) = 1/5   Now, 1/5 work is done in 3 days   Therefore, Whole work will be done in (3 x 5) = 15 days.   ANSWER:18 days
Answer: C
The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
Choices:  A) 4years  B) 5years  C) 6years  D) 7years  E) 8years

Solution: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.   Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50   5x = 20   x = 4.   Age of the youngest child = x = 4 years.   answer :4years
Answer: A
A tradesman is marketing his goods 20% above the cost price of the goods. He gives 10% discount on cash payment, find his gain percent.
Choose the correct option
A) 12%
B) 8%
C) 15%
D) 18%
E) None of these

Solution: Let the C.P. of the goods be 100   ⇒ Marked price of the goods = 120   Discount = 10% ⇒ S.P. is 90% of 120 = 108   ∴ Gain = (108 – 100) i.e. 8%.   Answer 8%
Answer: B
A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 90, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined? Choose one:
A) 74
B) 75
C) 76
D) 77
E) 79

Solution: ratio is 4:6:5 , numbers are 4x, 6x, 5x   total scores of each class is (65*4x + 6x * 90 + 77*5x) = 260x+540x+385x = 1185x   total number of students 260 +540 +385= 
260 +540 +385 = 1_185
1185x   total number of students= 15x   average = 1185x/15x = 79   79 is the answer1185 /15= 
1185 /15 = 79
79   79 is the answer
Answer: E
The average weight of 10 students decreases by 6 kg when one of them weighing 120 kg is replaced by a new student. The weight of the student is Choose the correct choice:
A) 62 kg
B) 60 kg
C) 70 kg
D) 72 kg
E) None of these

Solution: Explanation :   Let the weight of student be x kg.   Given, Difference in average weight = 6 kg   => (120-x)/10 = 6   => x = 60   Answer : 60 kg
Answer: B
At milk factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce? Answers
A) 8/17 B) 1/2 C) 8/9 D) 9/8 E) 17/8

Solution: At milk factory, Let the first shift have 3 employee and each produce 3 widgets, so the total number of widgets produced by the first shift is 3*3= 
3*3 = 9
9;   Then the second shift would have 4 employees and each second shift employee would produce   3*2/3= 
  3*2/3 = 2
2 widgets, so the total number of widgets produced by the second shift employees would be   4*2= 
  4*2 = 8
8;   The ratio of the second shift production to the total is 8/(9+8)=8/17.   8/17nswer: 8/17.
Answer: A
The price of a jacket is reduced by 10%. During a special sale the price of the jacket is reduced another 30%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?  Choose one:
A) 32.5 B) 58.7 C) 48 D) 65 E) 67.5

Solution: 1) Let the price of jacket initially be $100.   2) Then it is decreased by 10% , therefore bringing down the price to $90.   3) Again it is further discounted by 30%, therefore bringing down the price to $63.   4) Now 67.5 has to be added byX %in order to equal the original price.   63 + ( X% ) 63 = 100.   Solving this eq for X, we get X = 58.7   Ans is 58.7
Answer: B
An author received $0.80 in royalties for each of the first 100,000 copies of her book sold, and $0.80 in royalties for each additional copy sold. If she received a total of $260,000 in royalties, how many copies of her book were sold?  Choose the correct choice:
A) 130,000
B) 300,000
C) 325,000
D) 400,000
E) 420,000

Solution: Total royalties for first 100.000 books = .8*100,000= 80,000   Total royalties for the rest of the books = 260,000-80,000 = 180,000   Remaining books = 180,000/0.8 = 225,000   Total books = 225,000+100,000 = 325,000 Answer 325,000
Answer: C
If P represents the product of the first 16 positive integers, then P is not a
multiple of:	Choose one.
A) a) 99
B) b) 84
C) c) 133
D) d) 65
E) e) 57

Solution: a) 99 = 9*11   b) 84 = 4*7*3   c) 133 =19*7   d) 65 = 5*13   e) 57 =19*3   since 19 is not there in first 15 positive numbers it is the only possibility   c) 133
Answer: C
A person sold two cows each for Rs.9900. If he gained 10% on one and lost 20% on the other, then which of the following is true ?
Choose the correct choice from the following answers:
A) He lost Rs. 200	B) He gained Rs. 200	C) Neither he gained nor lost	D) None of the above	E) He gained Rs. 300

Solution: Explanation:   In first he got Rs. 990   But in second he lost Rs. 1980   So he lost Rs. 990.   ANSWER IS None of the above
Answer: D
What is the average of xx, 2x2x, and 66?	Pick one
A) x+2x  B) x+2  C) x+2x+2  D) 2x+2  E) 2x

Solution: By the definition of an average, we get:   x+2x+63=3x+63x+2x+63=3x+63   =3(x+2)3=x+2.=3(x+2)3=x+2.   Hence, the answer is x+2x+2 or Option x+2x+2
Answer: C
A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once. How many times does the teacher go to the zoo?  Select:
A) 10	B) 12	C) 15	D) 20	E) 30

Solution: Two students can be selected from 6 in 6C2 =15 ways.   Therefore, the teacher goes to the zoo 15 times.   Option 15 is answer
Answer: C
What percent of 60 is 90? Answers
A) 133 1⁄3 B) 75 C) 150 D) 33 1⁄3 E) 25

Solution: To find out the % of 90 in 60   Do 90/60 = 150%   Answer 150)
Answer: C
In a bread recipe, the ratio of water to flour is 13 to 20. There is 168 g more flour than water. How much flour does the recipe call for?  Choose the correct choice from the following options.
A) 400 g
B) 440 g
C) 480 g
D) 510 g
E) 525 g

Solution: Let x equal the amount of water, and y equal the amount of flour.   We know that x = 13/20y.   We also know that x = y-168.   So we can simplify:   y-168 = 13/20y   So to isolate y, we get:   7/20y = 168   And to solve for y:   y = 480   Answer: 480 g
Answer: C
Five persons - A, B, C, D and E are being compared in weight and height. The second heaviest person. D is the shortest. A is the 2nd tallest and shorter than E, The heaviest person is the third tallest person. There is only one person shorter than B, who is lighter than E and A respectively. What is the position of A in height and weight respectively?  Choose the correct choice from the following options:
A) 2nd,4th  B) 4th,3rd  C) 2nd,1st  D) 5th,3rd  E) 2nd,5th

Solution: Explanation:   A is the second tallest person. There is only one person shorter than B. So, B is the fourth tallest person. D is the shortest and second heaviest.   A is shorter than E. So, the third tallest person is C. Who is the heaviest person. B is lighter than E and A respectively. So, the final arrangement is as follows.   A is the second tallest and the fourth heaviest person.   2nd,4thNSWER IS 2nd,4th
Answer: A
I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss? Options
A) Rs.28	B) Rs.280	C) Rs.140	D) Rs.70	E) Rs.15

Solution: x*(85/100) = (480 - x)119/100   x = 280   Answer: Rs.280
Answer: B
Evaluate combination
100C98=100!/(98)!(2)!
Choose one.
A) 4950
B) 1510
C) 4170
D) 3170
E) None of these

Solution: Explanation:   nCr=n!/(r)!(n−r)!   100C98=100!/(98)!(2)!   =100∗99∗98!/(98)!(2)!   =100∗99/2∗1   =100∗99/2∗1=4950   Option 4950
Answer: A
A certain company expects quarterly earnings of $0.80 per share of stock, half of which will be distributed as dividends to shareholders while the rest will be used for research and development. If earnings are greater than expected , shareholders will receive an additional $0.04 per share for each additional $0.10 of per share earnings. If quarterly earnings are $1.10 per share, what will be the dividend paid to a person who owns 300 shares of the company's stock? Select the correct option:
A) $92	B) $96	C) $156	D) $120	E) $240

Solution: EPS Actual> EPS expected.   each gets and additional .12 per share.   Thus .52*300 --> $156   answer is $156
Answer: C
During the second quarter of 1984, a total of 2,976,000 domestic cars were sold. If this was 18% greater than the number sold during the first quarter of 1984, how many were sold during the first quarter ? Choose the correct choice from the following answers:
A) 714,240  B) 2,261,760  C) 2,522,033  D) 3,690,240  E) 3,915,790

Solution: Let number of cars sold in 1st quarter = x   Number of cars sold in 2nd quarter = 18% greater than the number sold during the first quarter = (1 + 18/100)= 
(1 + 18/100) = 59/50 = around 1.18
1.18 x   1.18 x= 2,976,000   => x = 2,522,033   So, answer will be 2,522,033
Answer: C
John Traveled from point A to B in 4 merter per sec and from B to A in 6 meter per sec. What is his average speed?	Pick.
A) 4.6m/s B) 4.8m/s C) 5.2m/s D) 5.4m/s E) 5.8m/s

Solution: Since the distance traveled is same, we can apply direct formula= 2XS1XS2/(S1+S2)   2X4X6/10= 4.8. '4.8m/s' is the answer.
Answer: B
In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 172 votes. Find the total number of valid votes? Choices.
A) 430 B) 287 C) 267 D) 262 E) 927

Solution: Let the total number of valid votes be x.   70% of x = 70/100 * x = 7x/10   Number of votes secured by the other candidate   = x - 7x/100 = 3x/10   Given, 7x/10 - 3x/10   = 172 => 4x/10 = 172   => 4x = 1720 => x   = 430.   430nswer:430
Answer: A
A man can row upstream at 8 kmph and downstream at 13 kmph. The speed of the stream is	Choose the correct option.
A) 2.5 km/hr B) 4.2 km/hr C) 5 km/hr D) 10.5 km/hr E) None

Solution: Solution   Speed of stream	= 1 / 2 (13 - 8 )kmph   = 1/2 x 5   =5 /2= 
5 /2 = 5/2 = around 2.5
2.5   2.5 km/hrnswer 2.5 km/hr
Answer: A
What is 120% of 13/24 of 840?  Pick
A) 436 B) 478 C) 512 D) 546 E) 620

Solution: 120% * 13/24 * 360 = 1.2 * 13 * 35= 
1.2 * 13 * 35 = 546
546   The answer is 546.
Answer: D
There are 81 people in a certain community who belong to the local golf club, tennis club or both clubs. If twice as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs? Pick:
A) 4	B) 7	C) 27	D) 21	E) 37

Solution: let's find the range of Both and hence the range of x. Minimum value of Both: Say there is no overlap in the two sets. 81 = x + 2xx = 27In this case Both = 0 Maximum value of Both: Say there is maximum overlap between the two sets. One set has x so it could be a subset of the set 2x.81 = 2xBut x cannot be a decimal so (x-1) could be the overlap (= Both) and there could be 1 in only the Golf club.81 = 2 x + x - (x - 1)x = 40In this case Both = 40 - 1= 
40 - 1 = 39
39 So Both lies between 0 and 39 Only option (E) satisfies this condition. ANSW37R:37
Answer: E
In a mixture of 60 liters, the ratio of milk and water is 2:1. What amount of water must be added to make the ratio of milk and water as 1:2?	Pick one: A) 65 liters B) 68 liters C) 60 liters D) 26 liters E) 27 liters

Solution: 2:1 --- 60   1:2   2:4   ---------------   3   3 ----------- 60   3 ----------- ? => 60 liters   Answer: 60 liters
Answer: C
Pavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan.	Choose the correct choice from the following options:
A) 240 km B) 225 km C) 452 km D) 300 km E) 290 km

Solution: D   300 km   Let the distance travelled be x km.   Total time = (x/2)/30 + (x/2)/25 = 11 => x/60 + x/50 = 11 => (5x + 6x)/300 = 11 => x = 300 km
Answer: D
The average of 11 numbers is 10.7. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
Choose the correct choice from the following choices
A) 9 B) 9.2 C) 10 D) 13.7 E) 12

Solution: Explanation:   1 to 11 = 11 * 10.7= 
11 * 10.7 = 117.7
117.7   1 to 6= 6 * 10.5= 
6 * 10.5 = 63
63   6 to 11= 6 * 11.4= 
6 * 11.4 = 68.4
68.4   63 + 68.4= 
63 + 68.4 = 131.4
131.4 – 117.7= 13.7   6th number = 13.7   13.7)
Answer: D
Two pipes A and B can fill a tank in 15 min and 21 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank? Choose the correct choice
A) 14 min 19 sec
B) 14 min 42 sec
C) 14 min 20 sec
D) 14 min 40 sec
E) 15 min 12 sec

Solution: :   Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15   Remaining part = 1 - 7/15 = 8/15   Part filled by B in 1 minute = 1/21   1/21 : 8/15 :: 1 ; x   x = 8/15 * 1 * 21 = 11 1/5 min = 11 min 12 sec.   The tank will be full in (4 min. + 11 min. 12 sec) = 15 min 12 sec.Answer: 15 min 12 sec
Answer: E
A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?  Choose the correct choice from the following
A) 15 days	B) 12 days	C) 10 days	D) 9 days	E) 8 days

Solution: Explanation:   3/12 + (3 + x)/16 = 1   x = 9 days   Answer: 9 days
Answer: D
A number when divided by D leaves a remainder of 8 and when divided by 3D leaves a remainder of 21 . What is the remainder left, when twice the number is divided by 3D? Select.
A) 13	B) 12	C) 3	D) 2	E) 42

Solution: making eqn as per the question   a=Dx+8......1   a=3Dy+21....2   multiplying 3 in eqn 1 we get eqn 3   3a=3Dx+24....3   a=3Dy+21......2   now subtract 2 from 3 we get..   2a=3D(x-y)+3   so here's the remainder we got is 3   ANSWER:3
Answer: C
A batsman makes a score of 90 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?	Select the correct option: A) 39 B) 35 C) 42 D) 40.5 E) 42

Solution: let the average after 16th inning =x   then total run after 16th inning=16x   then total run after 17th inning=16x+90   then average run after 17th inning=(16x+90)/17   (16x+90)/17=x+3 => 16x+90 = 17x+51 => x=39   x=39;   average after 17th inning =39+3= 
39+3 = 42
42   ANSW42R:42
Answer: E
On a certain road, 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 60% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on that road exceed the posted speed limit?
Pick one
A) 10.5%  B) 12.5%  C) 15%  D) 25%  E) 30%

Solution: suppose there are X motorists.   10% of them exceeded the speed limit and received the ticket, i.e. X/10.   Again, suppose total no. of motorists who exceeded the speed limit are Y.   60% of Y exceeded the speed limit but didn't received the ticket, i.e. 3Y/5.   it means 2Y/5 received the ticket.   hence, 2Y/5 = X/10   or Y/X=1/4   or Y/X * 100= 1/4 * 100= 
1/4 * 100 = 25
25%   25%
Answer: D
A shopping cart contains only apples, oranges, and pears. If there are four times as many oranges as apples, and five times as many pears as oranges, then the apples are equivalent to what fraction of the pears?	Pick:
A) 1/8
B) 1/9
C) 1/12
D) 1/16
E) 1/20

Solution: O = 4A   P = 5O = 20A   A = P/20   The answer is 1/20.
Answer: E
Which of the following correctly lists the data sets in order of least to greatest standard deviation?
I. 2, 2, 2 3, 3, 2
II. 32, 32, 32, 30, 30, 32
III. 37, 38, 39, 40, 44, 42
Choose the correct choice from the following options.
A) I, II, III	B) I, III, II	C) II, I, III	D) II, III, I	E) III, II, I

Solution: (D) To answer a question such as this, you DO NOT need to know how to calculate standard deviation. You simply need to understand how to compare standard deviations of different sets. The more spread out the numbers are, the greater the standard deviation will be. Even one or two numbers that are much larger or smaller than the others will cause the standard deviation to rise drastically.   sequence lowest to highest = I,II,III   I, II, III
Answer: A
How many 3-letter words can be formed using the letters of the English alphabet that contain 1 different vowels and 2 different consonants?  Choose the correct choice from the following choices.
A) 4!*5c2 *21c2  B) 4!*5c3 *21c2  C) 3!*5c1 *21c2  D) 5!*5c2 *21c2  E) 6!*5c2 *21c2

Solution: combination for 1 vowels out of 5 =5c1 ways   combination for 2 consonants of 21 = 21c2 ways   Additionally the arrangement can be = 3!   total arrangements =3!*5c1 *21c2   3!*5c1 *21c2
Answer: C
If (x+4)2−−−−−−−√=3(x+4)2=3, which of the following could be the value of x−4x−4?	Choices
A) -11
B) -7
C) -4
D) -3
E) 5

Solution: X+4)2=9(X+4)2=9   (X−4+8)2=9(X−4+8)2=9   let X-4 = -11   (-11+8)2=9(-11+8)2=9   Now, sub answer choices in -11   -11) (−11+8)2=(−3)2=9(−11+8)2=(−3)2=9   -11 is your answer
Answer: A
what is the smallest number should be added to 5377 so that the sum is completely divisible by 7?
Pick one:
A) 5
B) 4
C) 6
D) 2
E) 1

Solution: Solution: Divide 5377 with 7 we get remainder as 1. so, add 6 to the given number so that it will divisible by 7.   Answer 6
Answer: C
Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?	Pick
A) 1 B) 8 C) 9 D) 2 E) 7

Solution: Explanation:   Amy can travel clockwise or anticlockwise on the diagram.   Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.   Similarly, anticlockwise sh   Answer: 8) 8
Answer: B
if each of its sides of a rectangle is increased by 18%, what is the percentage increase in the area of the rectangle, ?	Choose the most appropriate option
A) 39.24%
B) 38.24%
C) 36.24%
D) 37.24%
E) 38.24%

Solution: 39.24%ssume original length = 100m by 50m   original area = 100*50= 
100*50 = 5_000
5000   18% increase on each side   l= 100 + 18= 
100 + 18 = 118
118   w= 50 + 9= 
50 + 9 = 59
59   new area= 118*59= 
118*59 = 6_962
6962   increase in area= 6962 - 5000= 
6962 - 5000 = 1_962
1962   %increase=39.24%   39.24%nswer 39.24%
Answer: A
If 4 : 6 :: x : 36, then find the value of x	Choices
A) 24	B) 22	C) 28	D) 30	E) 18

Solution: Explanation:Treat 4:6 as 4/6 and x:36 as x/36, treat :: as = So we get 4/6 = x/36=> 6x = 144=> x = 24 Option 24
Answer: A
One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?
Choose the correct choice from the following answers.
A) Rs. 30,000
B) Rs. 50,000
C) Rs. 60,000
D) Rs. 90,000
E) Rs. 70,000

Solution: N/3=P/2   N+P=150000   60000   ANSWER:Rs. 60,000
Answer: C
A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in? Choose the correct choice from the following answers.
A) 22 1/2	B) 22 1/3	C) 23	D) 23 1/2	E) 23 1/3

Solution: Ratio of times taken by A and B = 1 : 3.   The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.   If difference of time is 2 days, B takes 3 days.   If difference of time is 60 days, B takes 3	x 60 = 90 days.   2   So, A takes 30 days to do the work.   A's 1 day's work =	1   30   B's 1 day's work =	1   90   (A + B)'s 1 day's work = 1	+	1 =	4	=	2   30	90	90	45   A and B together can do the work in	45	= 22	1	days.   2	2   22 1/2nswer is 22 1/2
Answer: A
Ten circular coins are thrown on the street so that no two of them
overlap or touch, and no three of them have a tangent line in common.
What is the total number of lines which are tangent to two of the coins?
Choose the correct option
A) 60 B) 100 C) 180 D) 240 E) 360

Solution: There are n(n-1)=2 different ways   of choosing 2 objects from a given collection   of n objects. Thus, there are   10*9/2= 
  10*9/2 = 45
45   different ways of choosing 2 of the 10 coins.   For each selection of two coins, one can form 4   tangent lines as shown at the right. Therefore,   the answer is   4*45= 
  4*45 = 180
180.   correct answer 180
Answer: C