MU-NLPC/Calc-aqua_rat huggingface dataset:
How many 11-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example 12345654321. Choose the correct choice from the following answers
A) 100  B) 610  C) 729  D) 900  E) 900000

Solution: Take the task of building palindromes and break it intostages.   Stage 1: Select the 11th digit   We can choose 1, 2, 3, 4, 5, 6, 7, 8, or 9   So, we can complete stage 1 in9ways   Stage 2: Select the 10th 9th,8th, 7th, 6th digit   We can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9   So, we can complete stage 2 in10ways   IMPORTANT: At this point, the remaining digits are alreadylocked in.   Stage 3: Select the , 5th, 4th, 3rd, 2nd, 1st digit   So, we can complete this stage in1way.   By theFundamental Counting Principle(FCP), we can complete all 5 stages (and thus build a 11-digit palindrome) in(9)(10)(10)(10)(10)(10)(1)(1)(1)(1)(1)ways (= 900000 ways)   Answer: 900000
Answer: E
A batsman scored 150 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?	Pick one
A) 45(4/11) %  B) 60 %  C) 45(5/11) %  D) 44(5/11) %  E) None of these

Solution: Explanation :   Total runs scored = 150   Total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60   Total runs scored by running between the wickets = 150 - 60= 
150 - 60 = 90
90   Required %= (90/150) × 100 =60%   Answer : Option 60 %
Answer: B
The average monthly salary of 20 employees in an organisation is Rs. 1600. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ?
Choices:
A) 3700
B) 3890
C) 88798
D) 2789
E) 2891

Solution: Explanation:   Manager's monthly salary Rs. (1700 * 21 - 1600 * 20) = Rs. 3700.   3700nswer: 3700) 3700
Answer: A
If k is an integer and 2 < k < 6, for how many different values of k is there a triangle with sides of lengths 2, 6, and k?	Choices.
A) 0 B) 1 C) 2 D) 3 E) 4

Solution: (6-2) < k < (6+2)   4 < k < 8   thus k = 5, 6, 7   Since 2 < k < 6, then k can be 5.   The answer is 1.
Answer: B
A fill pipe can fill 1/2 of cistern in 20 minutes. In how many minutes, it can fill 1/2 of the cistern?	Select:
A) 5min	B) 10min	C) 15min	D) 20min	E) 25min

Solution: Required time = 20*2*1/2= 
20*2*1/2 = 20
20 minutes   Answer is 20min
Answer: D
A bag contains 4 red balls, 5 green balls and 6 white balls. A ball is drawn at
random from the box. What is the probability that the ball drawn is either red or green?  Choose the most appropriate option:
A) 2/5
B) 3/5
C) 1/5
D) 7/15
E) 8/15

Solution: Total number of balls = (4 + 5 + 6)= 
(4 + 5 + 6) = 15
15.   Therefore, n(S)= 15.   Let E1 = event of drawing a red ball.   and E2 = event of drawing a green ball.   Then, E1 n E2 = f.   P (E1 n E2) = P(E1) + P(E2) = (4/15 + 5/15) = 9/15 = 3/5.   ANSWER:3/5
Answer: B
The number of permutations of the letters of the word 'BUBBLEGUM' is?
Choose the correct option:  A) 9!/(2!)2  B) 9!/2!  C) 9!/3! 2!  D) 8!/3! 2!  E) 9!/2! 1! 1! 1!

Solution: n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.   The letter pattern 'BUBBLEGUM' consists of 9 letters of which there are 3B's, 2U's, 1L, 1G and 1M.   Number of arrangements = 9!/3! 2!   Answer: 9!/3! 2!
Answer: C
A shop sells two variants of chocolates - one that costs $3 and the other that costs $5. If the shop sold $112 chocolates on a given day, how many different combinations of (number of $3 sold, number of $5 sold) exist?  Answers.
A) 6	B) 7	C) 8	D) 12	E) 15

Solution: $112 = 20*$5 + 4*$3   We can find other combinations by reducing the $5 chocolates by 3 (which is -$15)and increasing the $3 chocolates by 5 (which is +$15).   The number of $5 chocolates can be 20, 17, 14,...,2 for a total of 7 combinations.   The answer is 7.
Answer: B
A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?	Options.
A) 3:9
B) 3:4
C) 3:2
D) 3:1
E) 3:5

Solution: Explanation:   They should share the profits in the ratio of their investments.   The ratio of the investments made by A and 3:4 =   6000 : 8000 => 3:4   Answer:3:4
Answer: B
A retailer sells 10 shirts. The first 3 he sells for $20,$22 and $25. If the retailer wishes to sell the 10 shirts for an overall average price of over $20, what must be the minimum average price of the remaining 7 shirts?	Pick one:	A) $14.00	B) $16.00	C) $17.00	D) $19.00	E) $23.00

Solution: First 3 shirts are sold for $20,$22 and $25=$67.   To get average price of $20,total sale should be 10*$20=$200   So remaining 7 shirts to be sold for $200-$6710* 20= 
10* 20 = 200
$200   So remaining 7 shirts to be sold for $200-$67=$133   Answer should be 133/7200- 67= 
200- 67 = 133
$133   Answer should be   133/7= 
  133/7 = 19
$19.00 that is $19.00
Answer: D
Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 20 ounces of chocolate. How much chocolate is left over if he uses all the dough but only wants the cookies to consist of 10% chocolate?
Choose the correct answer:  A) 18  B) 20  C) 16  D) 22  E) 24

Solution: First, you must find the total weight of the mixture given that 80% of it will be dough.   90%*Total = 36 => (9/10)Total=36=> Total=360/9 => Total=40 oz,   From there, you must find 10% of the total 40 oz of the mixture.   10%*Total => (1/10)(40)= 4 oz choclate used,   Not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate. 20-4 = 16 oz chocolate left over.   Answer : 16
Answer: C
If 4 men can color 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in	Answers.
A) 1 day
B) 2 days
C) 3 days
D) 4 days
E) 5 days

Solution: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m   No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day.   1 day
Answer: A
A certain no. when divided by 20 leaves a remainder 25, what is the remainder if the same no.be divided by 15?	Choose the correct choice from the following choices: A) 3 B) 4 C) 6 D) 8 E) 9

Solution: Explanation:   20 + 25= 
20 + 25 = 45
45/15= 
45/15 = 3
3 (Remainder)   3
Answer: A
A box contains nine slips that are each labeled with one number: 1, 2, 3, 8, 13, 21, 34 and 55. Two of the slips are drawn at random from the box without replacement. What is the probability that the sum of the numbers on the two slips is equal to one of the numbers left in the box? Answers:	A) 7/72	B) 1/6	C) 7/36	D) 15/36	E) 1/7

Solution: Probability = No: of desired outcomes / Total No: of outcomes.   You are picking two slips out of 8 slips. So   Total No: of outcomes = 8C2 = 28   Desired outcome : sum of the numbers on the two slips is equal to one of the numbers left in the box. How many such outcomes are there?   If you look at the numbers closely, you will see that the following pair of numbers will give you the desired outcome.   (1,2) (8,13) (13,21) (21,34) . There are 4 such pairs. If the two numbers which I pick is from any of these 4 pairs, then I get my desired outcome.   So No: of desired outcomes = 4   Probability = 4/28=1/7   Answer :1/7
Answer: E
Kim has 7 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 14 shoes, what is the probability that she will select 2 shoes of the same color?
Choices.
A) 1/13 B) 1/15 C) 11/9 D) 1/10 E) 1/25

Solution: Can be tackled in this way as well: Probability of selecting any 1 out of 14 shoes = 14/14= 
14/14 = 1
1   Probability of selecting the next shoe (out of 14 available) having the same color= 1/14 (as after selecting the 1st one, there is only 1 another shoe left with the same color).   Thus the total probability = 1*1/13=1/13.   1/13 is the correct answer.
Answer: A
A train 225 m in length crosses a telegraph post in 15 seconds. The speed of the train is?	Options.
A) 37 kmph B) 34 kmph C) 32 kmph D) 38 kmph E) 76 kmph

Solution: S = 225/25 * 18/5   = 32 kmph   Answer: 32 kmph
Answer: C
A trader owes a merchant $10000 due 1 year hence. The trader wants to settle the account after 2 months. If the rate of interest 12% per annum, how much cash should he pay? Choose one:
A) $9090.90
B) $9010.90
C) $7090.90
D) $8090.90
E) $9000.90

Solution: Required money	= P.W. of $10000 due 10 months hence   = $((10000*100) / 100+ (12*10/12) )   = $9090.90   $9090.90NSWER:$9090.90
Answer: A
Which of these lines in the xy-plane does not contain any point with two negative coordinates? Choose the correct answer
A) y = 3x	B) y = x + 7	C) y = x^2 - 4	D) y = x^3 + 3x	E) y = x^6

Solution: x^6 is 0 when x is 0 and positive for all other values of x.   The answer is y = x^6.
Answer: E
Each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and the average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 15 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed? Select the correct option:
A) 10
B) 12
C) 14
D) 16
E) 18

Solution: If the average of 10-pound and 20-pound boxes is 18, the ratio of 10-pound boxes:20-pound boxes is 1:4.   So out of 20 boxes, 4 are 10-pound boxes and 16 are 20-pound boxes.   If the average of 10 and 20-pound boxes is to be 15, the ratio of 10-pound boxes:20-pound boxes should be 1:1.   The number of 10 pound boxes remains the same so we still have 4 of them.   To get a ratio of 1:1, the number of 20-pound boxes must be 4.   We need to remove 12 of the 20-pound boxes.   The answer is 12.
Answer: B
The cash realised on selling a 14% stock is Rs.104.25, brokerage being 1/4% is? Choose the correct choice from the following answers.
A) 104 B) 106 C) 102 D) 192 E) 122

Solution: Cash realised= Rs. (104.25 - 0.25)   = Rs. 104.   104nswer: 104
Answer: A
The triplicate ratio of 2:5 is?	Answers
A) 1:0  B) 8:125  C) 1:7  D) 1:2  E) 1:1

Solution: 23: 53 = 8:125   Answer: 8:125
Answer: B
There are 2000 students in a school and among them 10 % of them attends chess class. 50% of the students who are in the chess class are also enrolled for swimming. No other students are interested in swimming so how many will attend the swimming class if all enrolled attends?  Choose the correct option.
A) 1
B) 10
C) 100
D) 50
E) 20

Solution: 10% of 2000 gives 200. so 200 attends chess and 50% of 200 gives 100   so 100 enrolled for swimming   Answer: 100
Answer: C
If y is an integer, then y(y - 1)( y- k) must be evenly divisible by three when k is any of the following values EXCEPT
Choose one:
A) -4	B) -6	C) -1	D) 2	E) 5

Solution: if we put k=-1 we get:   y(y-1)(y+1) rearrange:(y-1)y(y+1)   so it looks like a sequenc,   if we assume that y=2 and put number from the answer then we get:   (y – 1)y(y – k)   k=5 =1.2.-3   k=2 =1.2.0   k=-1 =1.2.3   k=-4 =1.2.6   but when we put   k=-6 =1.2.8 not satisfied   so,the answer is -6
Answer: B
The grocer ordered deliveries of apples on each weekday. The numbers of apples he ordered per day were 80, 30, 100, 90 and x. If the median apple delivery was 10 apples larger than the average (arithmetic mean) number of apples delivered, which of the following could be x?	Select the correct option:
A) 50 B) 55 C) 60 D) 65 E) 70

Solution: Look at the options available   Value of x seems to 50 < = x < = 70   A. 50   B. 55   C. 60   D. 65   E. 70   So position of x is second   30 , x , 80 , 90 , 100   Median = 80   Median number of apples was 10 points higher than the average, so average = 70   30 + x + 80 + 90 + 100 = 350   x = 50 = 50nswer = 50
Answer: A
In the simple subtraction problem below some single digits are replaced by letters .Fined the value of 7A+5D+6CD?	Choose the correct choice from the following options.
A) 288 B) 3799 C) 277 D) 278 E) 240

Solution: 15 - 7= 
15 - 7 = 8
8 So D= 8   10 + (C -1) - 8 = 4 So C = 3   10 + (5-1) - B = 7 So B = 7   (A-1) - 1 = 6 So A = 8   7A + 5D + 6CD = 56 + 40 + 144= 
56 + 40 + 144 = 240
240   Answer:240
Answer: E
There are 3 teams each with 6 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice?	Choose the correct choice:
A) 50  B) 23  C) 108  D) 28  E) 45

Solution: There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 36 possibilities (6*6) since each team has 6 players. So there are a total of 108 possibilities (36*3). I hope this method is easier for you to understand.
Answer: C
For any 8 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3?
I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number.
II. Dividing each of the numbers by 3 and then adding the results together.
III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. Choose the correct answer.
A) I only B) II only C) I and II only D) II and III only E) None of the above

Solution: Let the 3 numbers be x, y and z.   Question: Which of the following is equivalent to (x + y + z)/3   I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number. --> Not always equivalent Eg: 111 and 141   II. Dividing each of the numbers by 3 and then adding the results together. --> x/3 + y/3 + z/3 = (x + y + z)/3 --> Equivalent   III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. --> (6x + 6y + 6z)/9 = 2(x + y + z)/3 --> Not equivalent   Answer: None of the above
Answer: E
A father is now three times as old as his son. Seven years back, he was four times as old as his son. The age of the son (in years) is Choices:
A) A)12
B) B)15
C) C)18
D) D)20
E) E)21

Solution: Explanation:   Let son's age be x years. Then, father's age = (3x) years.   Seven years ago, father's age = (3x - 7) years and son's age = (x - 7) years.   So, 3x - 7 = 4 (x - 7)=> 3x - 7 = 4x - 28=> x = 21.   Answer: 21
Answer: E
In a group of 86 students, each student is registered for at least one of three classes – History, Math and English. Twenty-eight students are registered for History, twenty-three students are registered for Math, and forty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?  Choose the correct answer:	A) 3	B) 10	C) 9	D) 8	E) 7

Solution: 3 U B U C = 3 + B + C - 3B-BC-3C + 3BC   86 = 28 + 23+ 44 -3B-BC-3C +3 => 3B+BC+3C = 12   Exactly Two classes = 3B+BC+3C - 33BC = 12 -3*3= 
12 -3*3 = 3
3   Hence 3
Answer: A
If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is Choose the correct choice from the following:
A) 50 km	B) 56 km	C) 70 km	D) 80 km	E) 90 km

Solution: Let the actual distance travelled be x km.   Then x/10=(x+20)/14   --> 14x = 10x + 200   --> 4x = 200   --> x = 50 km.   50 kmnswer : 50 km.
Answer: A
A test paper has 10 questions each worth 4 marks. While taking the test, a student realises that he has attempted questions worth 16 marks. Assuming that whatever question he attempts is completely correct, how many more questions should he attempt so that he is able to secure 90 percent marks?	Choices:
A) 4 B) 5 C) 6 D) 7 E) 8

Solution: Since the test paper has 10 questions each worth 4 marks, the maximum marks he can get is 40.   His aim is to secure 90 % marks, this means he wants to secure 90% of 40 = 36 marks.   Out of the 36 marks, he has already attempted questions worth 16 marks, so he should attempt questions worth   36 - 16= 
  36 - 16 = 20
20 more marks.   As every question is worth 4 marks, so to secure 20 more marks he should attempt (20/4)= 
(20/4) = 5
5 more questions.   Ans 5
Answer: B
The average age of three boys is 48 years and their ages are in proportion 2:5:5. What is the age in years of the youngest boy?  Choose the correct choice from the following options:
A) 30
B) 23
C) 24
D) 26
E) 40

Solution: 2x + 5x + 5x = 144   x =12   2x = 24   Answer: 24
Answer: C
The cash realised on selling a 14% stock is Rs.106.25, brokerage being 1/4% is
Options:	A) 123	B) 106	C) 100	D) 156	E) 240

Solution: Explanation:   Cash realised= Rs. (106.25 - 0.25)   = Rs. 106.   Answer: 106
Answer: B
A jogger running at 9 kmph along side a railway track is 270 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger? Select
A) 3.6 sec	B) 18 sec	C) 36 sec	D) 39 sec	E) None of these

Solution: Speed of train relative to jogger   = (45 – 9) km/h = 36 km/h   = (36 × 5⁄18) m/sec = 10 m/sec   Distance to be covered = (270 + 120)= 
(270 + 120) = 390
390 m.   ∴ Time taken= (390⁄10) sec = 39 sec.   Answer 39 sec
Answer: D
Find the average of all prime numbers between 80 and 100	Choose the correct choice from the following answers:
A) 88 B) 60 C) 80 D) 89.6 E) 92

Solution: Prime numbers between 80 and 100 are 83, 89, 97   Required average = (83+ 89+ 97)/3 = 269/3 = 89.6   Answer is 89.6
Answer: D
In a birthday party, every person shakes hand with every other person. If there was a total of 28 handshakes in the party, how many persons were present in the party?  Pick
A) 6	B) 7	C) 8	D) 9	E) 10

Solution: Suppose there are nn persons present in a party and every person shakes hand with every other person. Then, total number of handshakes   = n82=n(n−1)/2   n(n−1)=28×2n(n−1)=56   n=8   ANSWER 8 8
Answer: C
A train passes a man standing on the platform. If the train is 180 meters long and its speed is 72 kmph, how much time it took in doing so?
Choose the correct choice from the following.
A) 6 ½ sec	B) 4 ½ sec	C) 9 sec	D) 8 sec	E) 2 ½ sec

Solution: D = 180   S = 72 * 5/18= 
72 * 5/18 = 20
20 mps   T= 180/20= 
180/20 = 9
9 sec   Answer: 9 sec
Answer: C
The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by3 months. Find the age of the teacher. Choose one.
A) 22 years  B) 23 years  C) 24 years  D) 25 years  E) 26 years

Solution: avg of 39 student = 15 yrs   Total age of 39 students=39*15= 
39*15 = 585
585 yrs   Avg age of 39 students + teacher=15+3/12= 
15+3/12 = 61/4 = around 15.25
15.25 yrs   so the total age of (39 student+1 teacher) or 40 persons=   40*15.25= 
40*15.25 = 610
610 yrs   so age of teacher=610-585= 
610-585 = 25
25 years   ANSWER:25 years
Answer: D
A boat running downstream covers a distance of 44 km in 8 hours while for covering the same distance upstream, it takes 10 hours. What is the speed of the boat in still water?  Choose the correct answer
A) 5 kmph	B) 4.95 kmph	C) 6 kmph	D) 7 kmph	E) 8 kmph

Solution: Explanation:   Speed downstream = 44/8= 
44/8 = 11/2 = around 5.5
5.5 kmph   Speed upstream= 44/10= 
44/10 = 22/5 = around 4.4
4.4 kmph   Speed of the boat in still water= (5.5+4.4)/2= 
(5.5+4.4)/2 = 4.95
4.95 kmph   Answer: Option 4.95 kmph
Answer: B
Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007	Choose the most appropriate option
A) 967532
B) 977522
C) 984424
D) 997454
E) 1083875

Solution: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)   = P (1 + 15/100)(1 - 35/100)(1 + 45/100)   = 1083875   1083875
Answer: E
Two numbers are in the ratio 3 : 4. If the sum of numbers is 63, find the numbers.	Choose the correct choice from the following options:
A) 27 and 36. B) 25 and 30. C) 23 and 44. D) 63 and 12. E) 12 and 36.

Solution: Sum of the terms of the ratio = 3 + 4= 
3 + 4 = 7
7   Sum of numbers= 63   Therefore, first number = 3/7 × 63 = 27   Second number = 4/7 × 63 = 36   Therefore, the two numbers are 27 and 36.   27 and 36.nswer is 27 and 36.
Answer: A
The residents of the town Q participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of town Q, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?  Choose the most appropriate option:
A) - 30
B) - 20
C) - 18
D) - 12
E) - 6

Solution: (21-6*2)<number of hours that Pat watched television last week <(21-6*1)   =9<L<15   Only option - 6 (12) satisfies this condition.
Answer: E
The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group?  Choose the correct choice from the following answers
A) 17	B) 26	C) 15	D) 97	E) 12

Solution: Total members in the group = 7   Average amount = Rs. 20   Total amount with them = 7 * 20   = Rs. 140   One number has Rs. 50. So, the amount with remaining 6 people   = 140 - 50 = Rs. 90   The average amount with them = 90/6   = Rs.15.   Answer:15
Answer: C
A work as fast as B. If B can complete a work in 20days independently,the number of days in which A and B can together finish the work in?
Choose the most appropriate option.
A) 2days  B) 3days  C) 4days  D) 5days  E) 6 2/3days

Solution: Ratio of rates of working of A and B = 2:1   ratio of times taken = 1:2   A's 1day work = 1/10   B's 1day work = 1/20   A+B 1day work = 1/10 + 1/20  +  1= 
 +  1 = 1
1/10 + 1/20= 3/20 => 20/3 = 6 2/3   A and B can finish the work in 6 2/3days   Answer is 6 2/3days
Answer: E
There are 10 orators A, B, C, D, E, F, G, H, I and J. In how many ways can the arrangements be made so that A always comes before B and B always comes before C.	Options:  A) 10! / 3!  B) 8! / 6!  C) 5! x 3!  D) 8! / (5! x 3!)  E) 8! / (5! x 4!)

Solution: Select any three places for A, B and C. They need no arrangement amongst themselves as A would always come before B and B would always come before C.   The remaining 7 people have to be arranged in 7 places.   Thus, 10C3 x 7! =10! / 3!   10! / 3!NSWER:10! / 3!
Answer: A
A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?  Pick
A) 37 1/2 days
B) 22 days
C) 31 days
D) 22 days
E) 25 1/2 days

Solution: Work done by 37 1/2 days in 20 days = 80/100 = 8/10 = 4/5   Work done by 37 1/2 days in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)   Work done by 37 1/2 days and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by 37 1/2 days and B)   Work done by 37 1/2 days and B in 1 day = 1/15 ---(2)   Work done by B in 1 day = 1/15 – 1/25 = 2/75   => B can complete the work in 75/2 days = 37 ½ days   Option 37 1/2 days
Answer: A
The present average age of a family of five members is 26 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest)  Choices:  A) 22 years  B) 25 years  C) 20 years  D) 28 years  E) 12 years

Solution: Present total age of the members = 26(5) = 130 years.   Present age of the youngest member = 10 years   Present total age of the remaining four members = 130 -10= 
130 -10 = 120
120 years   Their average age at the time of the birth of the youngest member= [120 - (4 * 10)] / 4 = 30 - 10= 
30 - 10 = 20
20 years.   Answer: 20 years
Answer: C