MU-NLPC/Calc-aqua_rat huggingface dataset:
A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?
Choose the correct choice from the following
A) 833 1/7	B) 833 1/3	C) 833 1/2	D) 833 1/9	E) 833 1/5

Solution: If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.   If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.   How many grams he has to give instead of one kilogram(1000 gm).   120 gm ------ 100 gm   1000 gm ------ ?   (1000 * 100)/120 = 2500/3 = 833 1/3 grams.   Answer: 833 1/3
Answer: B
You buy a piece of land with an area of √900, how long is one side of the land plot?  Pick one
A) 28
B) 29
C) 30
D) 31
E) 32

Solution: Try filling the numbers into the answer y x y =   Find the closest to 900.   Answer 30
Answer: C
By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%? Answers
A) 8	B) 9	C) 7	D) 66	E) 2

Solution: 80% --- 12   120% --- ?     80/120 * 12= 
  80/120 * 12 = 8
8   8nswer:8
Answer: A
Of the 14 members of a dancing group,10 can perform modern dancing, 8 can perform traditional dancing, and 4 can perform both type of dancing. If one member is chosen at random, what is the probability that the member chosen will be someone who can not perform neither type of dancing? Pick one:
A) a) 1/5
B) b) 1/10
C) c) 1/7
D) d) 1/4
E) e) 0

Solution: You know how to solve for Total number of people who can perform at least one type of dancing:   Total = n(A) + n(B) - n(A and B)   Total people who can use at least one machine = 10 + 8 - 4= 
10 + 8 - 4 = 14
14   So all 14 people know how to perform at least one type of dancing. Hence, if you pick anyone, the probability is 0 that he/she wouldn't know how to perform any type of dancing   Answer (e) 0)
Answer: E
A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio R of milk and water in the resultant mixture?
Options:
A) 17 : 3	B) 9 : 1	C) 3 : 17	D) 5 : 3	E) 11: 2

Solution: he 20 litre mixture contains milk and water in the ratio of 3 : 2. Therefore, there will be 12 litres of milk in the mixture and 8 litres of water in the mixture.   Step 1.   When 10 litres of the mixture is removed, 6 litres of milk is removed and 4 litres of water is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the container. It is then replaced with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres of water.   Step 2.   When 10 litres of the new mixture is removed, 8 litres of milk and 2 litres of water is removed. The container will have 8 litres of milk and 2 litres of water in it. Now 10 litres of pure milk is added. Therefore, the container will have 18 litres of milk and 2 litres of water in it at the end of the second step. Therefore, the ratio of milk and water is 18 : 2 or 9 : 1.   Shortcut.   We are essentially replacing water in the mixture with pure milk.   Let W_o be the amount of water in the mixture originally = 8 litres.   Let W_r be the amount of water in the mixture after the replacements have taken place.   Then,{W_r}/{W_o}= (1-R/M)^n   where R is the amount of the mixture replaced by milk in each of the steps, M is the total volume of the mixture and n is the number of times the cycle is repeated.   Hence, {W_r}/{W_o} =(1/2)^2  =1/4   Therefore R,W_r ={W_o}/4= 8/4= 
8/4 = 2
2 litres.9 : 1
Answer: B
The price of 3 pens and 6 pencils is Rs. 1500. With the same money one can buy 1 pen and 12 pencils. If one wants to buy 23 pencils, how much shall he have to pay ? Choose the correct choice from the following choices.
A) 2400  B) 2300  C) 2200  D) 2100  E) 2000

Solution: Let the price of a pen and a pencil be Rs. x and Rs. y respectively.   Then, 3x + 6y = 1500 .... (i)   and x + 12y = 1500 .... (ii)   Divide equation (i) by 3, we get the below equation.   = x + 2y = 500. --- (iii)   Now subtract (iii) from (ii)   x + 12y = 1500 (-)   x + 2y = 500   ----------------   10y = 1000   ----------------   y = 100   cost of 23 pencils = 23*100= 
23*100 = 2_300
2300   Answer : 2300
Answer: B
The letters in the word "PLACES" are permuted in all possible ways and arranged in the alphabetical order.Find the word at 48 position.
Choose the most appropriate option:  A) AESPCL  B) ALCEPS  C) ALSCEP  D) AESPLC  E) AESPLD

Solution: for words AC**** possible ways for arranging * will be 4!=24   now next seq in alphabatical order will be AE**** so....   same way for AE**** possible ways for arranging * will be 4!=24   ..   ..   Thus, 48th element will be last element in AE**** that means AE followd by reverse alphabatical order! which is AESPLC   ANSWER:AESPLC
Answer: D
In some quantity of alcohol, 50% of pure alcohol and 30% of is water. If 20liters of pure alcohol is added, then the strength of alcohol solution becomes 20%. The original quantity was?	Pick:  A) 1.42liters  B) 2.5liters  C) 3liters  D) 5.6liters  E) 7liters

Solution: Let the original quantity be x liters   alcohol solution in x liters = 30/100 *x = 3x/10 kg   (3x/10)/(x+20) = 20/100   3x = x/5 + 4   14x = 20   x = 1.42liters   1.42litersnswer is 1.42liters
Answer: A
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?	Pick one.
A) 24000	B) 25100	C) 25150	D) 25200	E) 25400

Solution: Explanation:   Number of ways of selecting 3 consonants from 7   = 7C3   Number of ways of selecting 2 vowels from 4   = 4C2   Number of ways of selecting 3 consonants from 7 and 2 vowels from 4   = 7C3 × 4C2   =   (   7   ×   6   ×   5   3   ×   2   ×   1   )   ×   (   4   ×   3   2   ×   1   )   =   210   =(7×6×53×2×1)×(4×32×1)=210   It means we can have 210 groups where each group contains total 5 letters (3 consonants and 2 vowels).   Number of ways of arranging 5 letters among themselves   =   5   !   =   5   ×   4   ×   3   ×   2   ×   1   =   120   =5!=5×4×3×2×1=120   Hence, required number of ways   =   210   ×   120   =   25200   25200)
Answer: D
f(x) is defined as the largest integer n such that x is divisible by 2^n. Which of the following numbers is the biggest?
Choose the correct choice from the following
A) f(24)
B) f(42)
C) f(62)
D) f(76)
E) f(84)

Solution: So, we have an integer x. It has some power of 2 in its prime factorization (2^n) and f(x) is the value of that n. Basically f(x) is the power of 2 in prime factorization of x.   For example, if x is say 40, then f(x)=3. Why? Because the largest integer n such that 40 is divisible by 2^n is 3: 40/2^3=5, or 40=2^3*5 --> the power of 2 in prime factorization of 40 is 3.   Hence all we need to do to answer the question is to factorize all options and see which one has 2 in highest power.   A. f(24) --> 24 = 2^3*3   B. f(42) --> 42 = 2*21   C. f(62) --> 62 = 2*31   D. f(76) --> 76 = 2^2*19   E. f(84) --> 84 = 2^2*21   f(24)nswer: f(24).
Answer: A
In a certain series, each term is m greater than the previous term. If the 16th term is 660 and the 13th term is 600, what is the first term?	Choose the correct choice from the following.
A) 120	B) 180	C) 360	D) 300	E) 360

Solution: a + 15m = 660 (16th term)   a + 12m = 600 (13th term)   You get a = 360 and m = 20   Answer:360
Answer: C
A 10 Liter mixture of milk and water contains 30 percent water. Two liters of this mixture is taken away. How many liters of water should now be added so that the amount of milk in the mixture is double that of water?  Pick one:
A) 3.3  B) 3.4  C) 0.4  D) 4.9  E) 3.87

Solution: Explanation:   Two liters were taken away So we have only 8 liters of mixture.   Amount of milk in 8 liters of mixture = 8 × 70% = 5.6 liters   Amount of water in 8 lit of mix = 8 - 5.6= 
8 - 5.6 = 2.4
2.4 liters.   Half of milk i.e half of 5.6= 2.8 liters.   We need   (2.8 - 2.4)= 
  (2.8 - 2.4) = 0.4
0.4 lit   Answer: 0.4
Answer: C
10 friends meet for movie 20 for picnic and 5 for games 4 for movie & picnic 2 for movie & games, 0 for picnic & games, 2 for all, how many are students are there in all?
Choose one.
A) 30 B) 31 C) 32 D) 33 E) 34

Solution: n(A U B U C)=n(A) + n(B) + n(C) - n(A INTERSECTION B) - n(A INTERSECTION C) - n(C INTERSECTION B) + n(A INTERSECTION B - INTERSECTION C)   Hence,   Total no. of Students = 10 + 20 + 5 - 4 - 0 - 2 + 2= 
10 + 20 + 5 - 4 - 0 - 2 + 2 = 31
31.   ANSWER:31
Answer: B
The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 33 ft long. What is the distance traveled by the cart, when the front wheel has done five more revolutions than the rear wheel?
Choose the correct choice from the following options:	A) 20 ft	B) 25 ft	C) 750 ft	D) 900 ft	E) 1650 ft

Solution: Point to note: Both the wheels would have traveled the same distance.   Now consider, no. of revolutions made by back wheel as x, which implies that the number of revolutions made by the front wheel is (x+5).   Equating the distance traveled by front wheel to back wheel: (x+5)*30 = x * 33. (Formula for calculating the distance traveled by each wheel is: # of revolutions * circumference.)   Solving this eqn. gives x=50.   Sub x=50 either in (x+5)*30 or in x * 33 to get the distance, which is 1650. So the correct choice is 1650 ft.
Answer: E
60 percent of movie theatres in Town X have 2 screens or less. 20% of those theatres sell an average of more than $300 worth of popcorn per showing. 56 percent of all the movie theatres in Town X sell $300 or less of popcorn per showing. What percent of all the stores on the street have 4 or more screens and sell an average of more than $300 worth of popcorn per day? Choose one
A) 12 B) 18 C) 32 D) 40 E) 44

Solution: Lets take numbers here.   Assume that the total number of movie theaters in the town = 100   Then number of movie theaters with 3 screens or less = 60   => Number of movie theaters with 4 screens or more = 40   Movie theaters with 3 screens or less selling popcorn at more than $300 = 20% of 60 = 12   Number of movie theaters selling popcorn at $300 or less = 56   => Number of movie theaters selling popcorn at more than $300 = 100-56= 
100-56 = 44
44   Of these 44 theaters, 12 are those with 3 screens or less   Therefore 40 (44-12) must be those with four screens or more   40 is the answer
Answer: D
In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points R is in the same quadrant as the fourth vertex of the square?  Pick:
A) (-5, -3) B) (-5, 3) C) (5, -3) D) (3, -5) E) (3, 5)

Solution: The question:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points R is in the same quadrant as the fourth vertex of the square?   I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means   Vertex #1 = (c, d) is in QII (that is, negative x and positive y)   Vertex #2 = (c, -d) is in QIII (that is, both xy negative)   Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive)   That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =(3, 5).
Answer: E
The length of a rectangle is four times its width. If the area is 100 m2 what is the length of the rectangle? Pick:  A) 20  B) 40  C) 50  D) 80  E) 60

Solution: Let L be the length and W be the width of the rectangle. Hence   L = 4 W   We now use the area to write   100 = L ? W   Substitute L by 4 W in the equation above   100 = 4 W ? W = 4 W2   Solve for W and find L   4 W2 = 100   W2 = 25 , W = 5 and L = 4 W = 20 m   correct answer 20
Answer: A
How many integral divisors does the number 120 have?
Choose the correct option.
A) 14  B) 16  C) 12  D) 20  E) None of these

Solution: Explanatory Answer   Express the number in terms of its prime factors   120 = 2(3) * 3 * 5.   The three prime factors are 2, 3 and 5.   The powers of these prime factors are 3, 1 and 1 respectively.   Find the number of factors as follows   To find the number of factors / integral divisors that 120 has, increment the powers of each of the prime factors by 1 and then multiply them.   Number of factors = (3 + 1) * (1 + 1) * (1 + 1) = 4 * 2 * 2= 
4 * 2 * 2 = 16
16.   Choice 16
Answer: B
The value of land increases by x% during June and decreases by y% during July. If the value of the land is the same at the end of July as at the beginning of June, what is y in terms of x? Options:
A) 200x/(100+2x) B) 100x/(100+x) C) x(2+x)/(1+x)2 D) x(200+x)/10000 E) 2x/x+2x

Solution: The simplest pairing is a 25% increase will be offset by a 20% decrease.   Here's the proof:   Starting value = 100   25% increase = 100 + (.25)(100) = 125   20% decrease = 125 - (.2)(125) = 100   Ending value = 100   So we would be looking for an answer that equals 20 when A=25. While the answers might appear 'complex', you can actually avoid much of the 'math' if you just fill in the parts and take a good look at what you have...   Answer A: (200)(25)/(150) ... since 200>150, this answer will be greater than 25. ELIMINATE A.   Answer B: (100)(25)/125) = (100)(1/5) = 20 This is a MATCH.   Answer C: (25)(27)/(26)2 ... nothing 'cancels out', so this cannot = 20. ELIMINATE C.   Answer D: (25)(225)/10000... the 'units' digit of the numerator is a 5; when dividing by 10,000, this won't end in a 0. ELIMINATE D.   Answer E:  (50/25) + 50= 
 (50/25) + 50 = 52
52. ELIMINATE E.   100x/(100+x)
Answer: B
power windows: 60%
anti-lock brakes: 25%
CD player: 45%
The table above shows the number of vehicles at Bill's car dealership that have certain features. No vehicle has all three features, but 10% have power windows and anti-lock brakes, 15% have anti-lock brakes and a CD player, and 22% have power windows and a CD player. What percent of the vehicles at Bill's car dealership have a CD player but no power windows or anti-lock brakes? Choose the correct choice from the following options.
A) 25
B) 8
C) 11
D) 3
E) 0

Solution: Answer: B   Were looking for the number of cars with a CD player but no other features. We know that 40% of the cars have a CD player, 15% have a CD player and anti-lock brakes, while 22% have a CD player and power windows. Since no car has all three features, those account for all of the possibilities except for what were looking for.   If a car has a CD player, it must either have anti-lock brakes, power windows, or no other features. Since the total of cars with a CD player is 45%, we can set up the following equation:   45=15+22+x   x=8, choice 8.
Answer: B
30 quintals is what percent of 2 metric tonnes ? Answers: A) 15% B) 1.5% C) 150% D) 30% E) None

Solution: Answer   Required percent = {30/(2 x 10)} x 100 % = 150%   150%orrect Option: 150%
Answer: C
Q is a set of nine distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be? Choose the correct choice
A) 2	B) 3	C) 4	D) 5	E) 7

Solution: 2 + 3 + 5 + 7 +11 + 13 + 17 + 23 + 29 = 100 ( sum is even)   Least number = 2   2
Answer: A
Three positive integers a, b, and c are such that their average is 12 and a ≤ b ≤ c. If the median is (a + 5), what is the least possible value of c?	Choose the correct choice:
A) 11	B) 13	C) 15	D) 17	E) 19

Solution: Solution   Given Data   3 positive integers   Average of a, b, and c = 12.   So, a+b+c3a+b+c3 = 36 or a + b + c = 36   a ≤ b ≤ c   Median = (a + 5)   Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c   Therefore, b = a + 5   Objective To find the least value of 'c'   Theoretically, the least value of c is when c = b.   Therefore, a + (a + 5) + (a + 5) = 36 (b and c are equal and b, the median, is a + 5)   Or 3a = 26 or a = 8.66   So, b = c = 8.66 + 5= 
8.66 + 5 = 13.66
13.66   However, we know that these numbers are all integers.   Therefore, a, b, and c cannot take these values.   So, the least value for c with this constraint is NOT likely to be when c= b   Let us increment c by 1. Let c = (b + 1)   In this scenario, a + (a + 5) + (a + 6) = 36   Or 3a = 25. The value of the numbers is not an integer in this scenario as well.   Let us increment c again by 1. i.e., c = b + 2   Now, a + (a + 5) + (a + 7) = 36   Or 3a = 24 or a = 8.   If a = 8, b = 13 and c = 15.   The least value for c that satisfies all these conditions is 15.   15orrect answer is choice 15.
Answer: C
A number, x is chosen at random from the set of positive integers less than 12. What is the probability that (9/x) > x?  Answers:
A) 1/11  B) 2/9  C) 2/11  D) 2/3  E) 7/9

Solution: Number x has to be chosen from numbers 1-11   (9/x) > x   => 9 > x^2   =>x^2 - 9 < 0   x can have 2 values only 1 , 2   Therefore , probability = 2 / 11   Answer 2/11
Answer: C
The least number which should be added to 28523 so that the sum is exactly divisible by 3, 5, 7 and 8 is Choose the correct option.
A) 40 B) 37 C) 35 D) 45 E) 48

Solution: LCM of 3,5,7 and 8 = 840   28523/840 = 33 remainder = 803   least no which should be added = 840-803= 
840-803 = 37
37   ANSWER 37
Answer: B
What is the sum of all even numbers from 1 to 601? Choose the correct answer.
A) 122821
B) 281228
C) 90300
D) 122850
E) 128111

Solution: Explanation:   600/2= 
600/2 = 300
300   300 * 301= 
300 * 301 = 90_300
90300   Answer: 90300
Answer: C
The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 5300, what is the length of the plot in metres?	Choose the correct choice from the following answers:
A) 333  B) 200  C) 288  D) 276  E) 1999

Solution: Let length of plot = L meters, then breadth = L - 20 meters   and perimeter = 2[L + L - 20] = [4L - 40] meters   [4L - 40] * 26.50 = 5300   [4L - 40] = 5300 / 26.50= 
5300 / 26.50 = 200
200   4L= 240   L = 240/4= 
240/4 = 60
60 meters.   Answer: 200
Answer: B
The ratio of the number of females to males at a party was 1:2 but when 7 females and 7 males left, the ratio became 1:3. How many people were at the party originally?	Choose the correct choice from the following answers.
A) 28
B) 32
C) 36
D) 42
E) 50

Solution: The total number of people are x females + 2x males.   3*(x-7) = 2x - 7   x = 14   There were 3x = 42 people at the party originally.   The answer is 42.
Answer: D
The total cost of a vacation was divided among 3 people. If the total cost of the vacation had been divided equally among 5 people, the cost per person would have been $50 less. What was the total cost cost of the vacation?  Choose the correct choice from the following answers:
A) $200
B) $375
C) $400
D) $500
E) $600

Solution: C for cost.   P price per person.   C= 3*P   C=5*P-250   Substituting the value of P from the first equation onto the second we get P = 125.   Plugging in the value of P in the first equation, we get C= 375. Which leads us to answer choice $375
Answer: B
If a number N is chosen at random from the set of two-digit integers whose digits are both prime numbers, what is the probability R that N is divisible by 3?  Pick one.
A) 1/3	B) ¼	C) 9/25	D) 5/16	E) 0

Solution: Prime digits are: 2, 3, 5, 7   Total number of 2 digit #s with both digits prime are:   4*4= 
  4*4 = 16
16   out of these numbers divisible by 3= 33, 27, 57, 72 and 75. I had to find the numbers manually using the 4 numbers above.   => prob = 5/16.   Ans D. Took me 3:20 mins.
Answer: D
In a camp, there is a meal for 100 men or 200 children. If 150 children have taken the meal, how many
men will be catered to with the remaining meal ?
Choose the correct choice from the following answers.
A) 25 men  B) 32 men  C) 34 men  D) 30 men  E) None of these

Solution: Explanation:   There is meal for 200 children. 150 children have taken the meal.   Remaining meal is to be catered to 50 children.   Now, 200 children = 100 men   So, 50 Children = 100/200 * 50= 
100/200 * 50 = 25
25 men   25 mennswer: 25 men
Answer: A
When you multiply a number by 4 and
then subtract 8, the result is the same as
if you first subtracted 4 from the same
number and then multiplied by 12. What
is the number?
Answers
A) A)5 B) B)13 C) C)19 D) D)31 E) E)10

Solution: Let x equal the number and then change the words into an equation and solve for x:   4x – 8 = 12(x – 4)   4x – 8 = 12x – 48   40 = 8x   5 = x   correct answer 5)5
Answer: A
Find four consecutive even integers so that the sum of the first two added to twice the sum of the last two is equal to 742.
Choose the correct answer:
A) 120 ,122 , 124 ,126  B) 120 ,122 , 124 ,128  C) 120 ,121 , 122 ,123  D) 123 ,125 , 127 ,129  E) None of these

Solution: Let x, x + 2, x + 4 and x + 6 be the four integers. The sum of the first two   x + (x + 2)   twice the sum of the last two is written as   2 ((x + 4) + (x + 6)) = 4 x + 20   sum of the first two added to twice the sum of the last two is equal to 742 is written as   x + (x + 2) + 4 x + 20 = 742   Solve for x and find all four numbers   x = 120 , x + 2 = 122 , x + 4 = 124 , x + 6 = 126   120 ,122 , 124 ,126nswer 120 ,122 , 124 ,126
Answer: A
A group of three girls and three boys have tickets for six adjacent seats in one row of a theater. If the three boys will not sit in three adjacent seats, how many possible different seating arrangements are there for these 6 theatre-goers?	Answers.
A) 6! – 2!3!2!  B) 6! – 6!3!  C) 7 × 2!3!2!  D) 6! – 4!3!  E) 2!3!2!

Solution: There are 3 boys and 3 girls , we want to calculate the seating arrangements if three boys do not sit together, like MMM.   Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 6 persons without restriction. Thus we'll get the # of arrangements asked in the question.   1. Total # of arrangements of 6 is 6!.   2. # of arrangements when 3 boys are seated together, like MMM;   Among themselves these 3 boys can sit in 3! # of ways,   Now consider these 3 boys as one unit like this {MMM}. We'll have total of 4 units: {MMM}{W}{W}{W} The # of arrangements of these 4 units is 4!.   Hence total # of arrangements when 3 men sit together is: 3!4!.   # of arrangements when 3 boys do not sit together would be: 6!-3!4!.   Answer: 6! – 4!3!
Answer: D
Point A is moving along 32 inch circle at a rate of 8 inches per second. Two seconds after A starts, point B moves from the same starting point on the circle at 12 inches per scond. What is the shortest time that B could take in order to coincide with A?
Choose the correct option
A) 4 seconds
B) 3 seconds
C) 2 seconds
D) 1 second
E) 0.8 seconds

Solution: we don't need to assume here the direction.we need to find which will take less time   so there are 2 cases   1)both moving in same direction...then time would be 4 seconds   2)both moving in opposite direction then time would be 0.8 seconds   as we need the shortest time it would be the second case   Answer:0.8 seconds
Answer: E
Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 30% profit?	Choose the most appropriate option
A) 16.39	B) 16.33	C) 16.35	D) 16.3	E) 16.32

Solution: C.P. of 50 kg wheat = (30 * 11.50 + 20 * 14.25) = Rs. 630.   S.P. of 50 kg wheat = 130% of Rs. 630 = 130/100 * 630 = Rs. 819.   S.P. per kg = 819/50 = Rs. 16.38 = 16.30.   Answer: 16.3
Answer: D
A family consists of grandparents, parents and three grand children. The average age of the grandparents is 67 years, that of the parents is 38 years and that of the grandchildren is 6 years. What is the average age of the family? Select the correct option:
A) 28 4â„7 years B) 31 5â„7 years C) 32 4â„7 years D) 27 1â„2 years E) None of these

Solution: Required average = (67Ã—2+38Ã—2+6Ã—3/2+2+3)   =228/7   = 32 4â„7 years   Answer 32 4â„7 years
Answer: C
Find the simple interest on Rs.500 for 9 months at 6 paisa per month? Choose the correct choice from the following answers.
A) 277	B) 270	C) 288	D) 266	E) 121

Solution: I = (500*9*6)/100= 
(500*9*6)/100 = 270
270   Answer: 270
Answer: B