MU-NLPC/Calc-aqua_rat huggingface dataset:
A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
Answers:  A) 59002  B) 59028  C) 59128  D) 59000  E) 59122

Solution: Explanation:   Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.   Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.   Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)   Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.   Income of A = Twice the income of B   (2500 + 18000 + P) = 2(P)   P = 20500   Total profit = 2P + 18000   = 2*20500 + 18000= 
2*20500 + 18000 = 59_000
59000   Answer:59000
Answer: D
If −2≤f≤0 and n > 19, which of the following CANNOT be the value of fn?
Choose the correct choice from the following options:	A) -48	B) -38	C) -20	D) 0	E) 19

Solution: value of fn not equal to -19=19 -19....Rest all are achievable
Answer: E
Arun went for a movie nine days ago. He goes to watch movies only on Thursdays. What day of the week is today?
Options.
A) Wednesday  B) Saturday  C) Friday  D) Sunday  E) None of these

Solution: Explanation :   Clearly it can be understood from the question that 9 days ago was a Thursday   Number of odd days in 9 days = 2 (As 9-7= 
9-7 = 2
2, reduced perfect multiple of 7 from total days)   Hence today= (Thursday + 2 odd days) = Saturday. Answer : Option Saturday
Answer: B
After offering a discount of 37.5%, Pankaj sold the rice at a profit of 25%. Had he offered a discount of 41.67%, his profit or loss percent would have been:-
Choices:
A) 16.66% profit
B) 12% loss
C) 29.17% loss
D) 8.33% profit
E) None of these

Solution: Explanation :   Let the Marked Price of the rice = 8p,   And the discount is 37.5% i.e 37.5%=(3/8)MP.   Thus, the Selling Price is:-   =>8p-(3/8)8p=5p.   =>5p=CP(25/100)x25.   =>CP=4p.   If he had offered a discount of 41.67%=5/12.   S.P=8p-(5/12)X8p.   =>14p/3.   The profit is:-   =>(14p/3)-4p.   =>2p/3.   Hence, the required profit percentage is :-   =>(2p/3)x100/4p.   =>(100/6)%.   =>16.66%.   16.66% profitnswer : 16.66% profit
Answer: A
A building contractor employs 20 male, 15 female and 5 child workers. To a male worker he pays Rs.25 per day, to a female worker Rs.20 per day and a child worker Rs.8 per day. The average wage per day paid by the contractor is? Pick:	A) 19	B) 21	C) 23	D) 25	E) 27

Solution: Explanation:   20 15 5   25 20 8   500 + 300 + 40= 
500 + 300 + 40 = 840
840/40= 
840/40 = 21
21   21
Answer: B
At a loading dock, each worker on the night crew loaded 1/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?
Choose the correct option
A) 1/2  B) 2/5  C) 3/5  D) 4/5  E) 5/6

Solution: Method: X = No. of boxes loaded by day crew.   Boxes by night crew = 1/4 * 4/5 X = 1/5 X   % loaded by day crew = X/(X + 1/5X) = 5/6   Answer 5/6
Answer: E
The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 100, then their difference is  Choose the correct choice from the following choices:
A) 19	B) 10	C) 28	D) 27	E) 29

Solution: Let the numbers be x and (100-x).   Then,   \inline \fn_jvn \Rightarrow \inline \fn_jvn x^{2}-100x+2475=0   \inline \fn_jvn \Rightarrow (x-55) (x-45) = 0   \inline \fn_jvn \Rightarrow x = 55 or x = 45   \inline \fn_jvn \therefore The numbers are 45 and 55   Required difference = (55-45)= 
(55-45) = 10
10   Answer:10
Answer: B
Alex takes a loan of $9,000 to buy a used truck at the rate of 9 % simple Interest.Calculate the annual interest to be paid for the loan amount.
Select the correct option
A) 680 B) 810 C) 800 D) 730 E) 750

Solution: From the details given in the problem Principle = P = $9,000 and R = 9% or 0.09 expressed as a decimal.   As the annual Interest is to be calculated, the time period T =1.   Plugging these values in the simple Interest formula,   I = P x T x R   = 9,000 x 1 x 0.09   = 810.00   Annual Interest to be paid = $810   answer :810
Answer: B
According to the directions on the can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12 ounces cans of the concentrate are required to prepare 272 6 ounces servings of orange juice? Select the correct option.
A) a) 25	B) b) 34	C) c) 50	D) d) 67	E) e) 100

Solution: Its B.   Total juice rquired = 272*6= 
272*6 = 1_632
1632 ounce   12 ounce concentate makes= 12 * 4= 
12 * 4 = 48
48 ounce juice   Total cans required= 1632/48= 
1632/48 = 34
34.   Answer b) 34
Answer: B
If the LCM of 7, 10, 3, and x is 210, which of the following could be x?	Choose the correct choice:
A) 13
B) 6
C) 21
D) 2
E) 14

Solution: Using elimination method, eliminate the option to arrive at 21   if x is replaced by 21 and the L21M is calculated you arrive at 210   21
Answer: C
The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 51
kmph, find the speed of the stream?	Answers.
A) 16 kmph B) 19 kmph C) 14 kmph D) 17 kmph E) 13 kmph

Solution: The ratio of the times taken is 2:1.   The ratio of the speed of the boat in still water to the speed of the stream   = (2+1)/(2-1)= 
(2+1)/(2-1) = 3
3/1= 
3/1 = 3
3:1   Speed of the stream= 51/3= 
51/3 = 17
17 kmph.   Answer: 17 kmph
Answer: D
(w^2+x^2)x(y^2+z^2) is always divisible by which of the max no. Where w;x;y;z are odd integers?
Pick:
A) 20	B) 8	C) 4	D) 2	E) 6

Solution: ((odd)^2+(odd)^2)*((odd)^2+(odd)^2)   (even)*(even)   2*2   4   ANSWER:4
Answer: C
A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 40 minutes. When both pipes are opened, find when the cistern will be full?  Choose the correct choice from the following answers
A) 17 minutes	B) 87 minutes	C) 40 minutes	D) 27 minutes	E) 11 minutes

Solution: 1/20 - 1/40 = 1/40   40 minutes   Answer:40 minutes
Answer: C
A 150 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?	Choose the correct answer:  A) 220 meter  B) 225 meter  C) 230 meter  D) 350 meter  E) None of these

Solution: Explanation:   As trains are running in opposite directions so their relative speed will get added   So, Relative speed = 120 +80= 
120 +80 = 200
200 kmph= 200*(5/18) = 500/9 m/sec   Let the length of other train is x meter then   x+150 /9=500 /9   =>x+150=500   =>x=350   So the length of the train is 350 meters   Option 350 meter
Answer: D
Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in scheme B?
Select the correct option: A) Rs.6400 B) 2878 C) 2899 D) 2660 E) 2701

Solution: Let the sum invested in scheme A be Rs. x and that in scheme B be Rs. (13900 - x). Then,   (x * 14 * 2)/100 + [(13900 - x) * 11 * 2]/100 = 3508   28x - 22x = 350800 - (13900 * 22)   6x = 45000 => x = 7500   So, sum invested in scheme B = (13900 - 7500) = Rs. 6400.Rs.6400nswer:Rs.6400
Answer: A
In how many ways Chief Minister and Minister be elected from a team of 6 members? Options
A) 124 B) 29 C) 30 D) 154 E) 165

Solution: To do this, if captain is elected first, then we have 6 ways of doing this.   For election of vice-captain, we have only 5 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)   So, the ans is 6*5= 
6*5 = 30
30 ways.   30
Answer: C
In shop contains some articles each of a cost of $5. He sold them at a price of $10. If the shop keeper has a order of 150 articles, how much profit he will get?	Select the correct option.
A) 200 B) 250 C) 750 D) 1000 E) 500

Solution: Total money after selling articles = 150*10= 
150*10 = 1_500
1500   cost price= 150*5= 
150*5 = 750
750   profit= 750   correct option is 750
Answer: C
With # andeach representing different digits in the problem below, the difference between #and ## is 623. What is the value of?
#
-##
___
623 Choices
A) 7	B) 8	C) 9	D) 10	E) 11

Solution: 100x   -(10x +x)   -----------   89 x= 667   x = 7   7
Answer: A
40 + 5 * 12 / (180/3) = ?  Answers.
A) 23
B) 78
C) 27
D) 61
E) 41

Solution: Explanation:   40 + 5 * 12 / (180/3) = 40 + 5 * 12 / (60)   = 40 + (5 * 12)/60 = 40 + 1= 
40 + 1 = 41
41.   Answer:41
Answer: E
Four of the five parts numbered (a), (b), (c), (d) and (e) in the following equation are exactly, equal. Which of the parts is not equal to the other four? The number of that part is the answer. Answers:
A) 375.789 + 41.28 – 115.249 B) 6.45 × 120.8 – 477.34 C) 1015.71 – 738.416 + 24.526 D) 853.12 + 109.73 – 661.03 E) 132.8 × 3.5 – 152.98

Solution: Others are equal to 301.82.   Answer 132.8 × 3.5 – 152.98
Answer: E
A Certain item costs to Harris $50. At what price must the merchant sell this item in order to make a profit of 10% ?	Answers.
A) $50	B) $55	C) $65	D) $60	E) $50

Solution: Cost Price = $50   Profit % = 10   Selling Price = ?   Selling Price = (100 + profit %) * Cost Price /100   = (100 + 10) * 50 / 100= 
(100 + 10) * 50 / 100 = 55
55   Answer is $55
Answer: B
How many words can be formed from the letters of the word ‘EXTRA’ so that the vowels are never together?	Choose the correct choice from the following choices
A) 72 B) 24 C) 48 D) 120 E) 30

Solution: The given word contains 5 different letters.   Taking the vowels EA together, we treat them as one letter.   Then, the letters to be arranged are XTR (EA).   These letters can be arranged in 4! = 24 ways.   The vowels EA may be arranged amongst themselves in 2! = 2 ways.   Number of words, each having vowels together = (24x2) = 48 ways.   Total number of words formed by using all the letters of the given words   = 5! = (5x4x3x2x1) = 120.   Number of words, each having vowels never together = (120-48)= 
(120-48) = 72
72   72NSWER 72 72
Answer: A
A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum? Choose the correct choice:
A) 7
B) 5
C) 4
D) 3
E) 2

Solution: 3 --- 1725   5 --- 1875   --------------   2 --- 150   N = 1 I = 75 R = ?   P = 1725 - 225= 
1725 - 225 = 1_500
1500   75= (1500*1*R)/100   R = 5%   Answer: 5
Answer: B
Sum of the squares of 3 no.'s is 99 and the sum of their products taken two at a time is 131. Find the sum?
Answers:
A) 20  B) 24  C) 19  D) 28  E) 30

Solution: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 99 + 2* 131   a + b + c = √361 = 19   19
Answer: C
Two numbers are in the ratio of 1 : 2. If 8 be added to both, their ratio changes to 3 : 5. The greater number is
Options
A) 20	B) 24	C) 28	D) 32	E) 36

Solution: Let the ratio be X : Y,   Given X/Y = 1/2 ,   (X + 8)/(Y + 8) = 3/5   => X = 16   And Y = 32   ANSWER:32
Answer: D
If 0 < a < b and k = (5a + 5b)/b , which of the following must be true? Choose the correct choice from the following answers:
A) k < 2 B) k < 7 C) k < 9 D) k > 9 E) k > 11

Solution: Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify.   As for your question, it is very simple and straightforward with number plug in.   Assume a=1 and b=2 as a < b, you get k = (5+10)/2 = 7.5. This eliminates all but option k < 9 , making it the correct answer.
Answer: C
In My, Xiang sold 15 used cars. For these 15 used cars the range of selling prices was 15,000 and the lowest selling price was 3,000. In June, Xiang sold 10 cars. For these 10 cars the range of selling was 16,000 and the lowest selling price was 6,100. What was the range of selling prices for the 25 used car sold by xiang in May and June?	Pick
A) 15,600 B) 15,750 C) 16,820 D) 18,100 E) 19,200

Solution: for 10 cars - 16000+ 6100 = 22,100   for 15 cars - 15000+ 3000 = 18,000   max = 22,100 min 4500   answer is approx 19100.   Option 19,200 is closest.
Answer: E
Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?  Choose the correct choice from the following choices:
A) 27 B) 24 C) 62 D) 78 E) 25

Solution: There are five letters in the given word.   Consider 5 blanks ....   The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.   The number of words = 3! = 6.   Answer:24
Answer: B
Which of the following must be divisible by 4, given that y is a positive integer? Pick:
A) (y−1)*y*(y+3) B) y^2*(y−3) C) y(y^2−2) D) y(y+2)^3 E) (y−2)·(y+1)·(y+3)

Solution: option A) (y−1)*y*(y+3)- assume y any positive integer e.g 5, plug it into the various options and check if the result . hence answer should be (y−1)*y*(y+3)
Answer: A
In a class of 40 students, 10 did not opt for math. 15 did not opt for science and 2 did not opt for either. How many students of the class opted for both math and science?	Choose the most appropriate option:
A) 13	B) 15	C) 7	D) 17	E) 18

Solution: 40 students total   10 did not opt for math   15 did not opt for science   2 did not opt for either   Total of 30 students in math and 13 did not opt for sci but did for math   30-13=7   7 students of the class opted for both math and science   Answer:   C. 7
Answer: C
In how many ways can a cricket eleven be chosen out of a batch of 15 players?
Select:  A) 1365  B) 1523  C) 2165  D) 1012  E) 2135

Solution: Required number of ways = 15C11 = 15C (15-11) = 15C4   15C4 = (15*14*13*12)/(4*3*2*1)= 
(15*14*13*12)/(4*3*2*1) = 1_365
1365   1365nswer is 1365
Answer: A
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability W that the team will have exactly 2 women?	Choose the correct choice from the following answers
A) 1/14	B) 1/7	C) 2/7	D) 3/7	E) 1/2

Solution: 5C2 * 3C2 -> it gives combination of exactly 2 women and 2 men.   8C4 -> gives total possibilities of 4 people from 5 women and 3 men.   Probability = 5C2*3C2 / 8C4 = 3/7   SECOND METHOD:   Probability of two women -> 5/8 * 4/7.   probability of two men -> 3/6 * 2/5.   Probability: (5/8 * 4/7) * (3/6 * 2/5) = 1/14.
Answer: D
Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many four letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter? Answers
A) 2,145
B) 6,435
C) 326,040
D) 12,870
E) 25,740

Solution: Since we are given atleast one symmetric letter in the three letter word we can take the following cases   1. All four   2. One symmetry and other three non   3. Two symmetry and other two non   4. Three symmetry and one non   4. All the three letters can be arranged in 24 ways   ( 11c4 + 11c1 * 15c3 + 11c2 * 15c2 + 11c3 *15c1 ) * 6   (330 +5005 + 5775+2475 ) * 24   326,040   IMO option C is the correct answer..   OA please...will correct if I missed anything.. 326,040
Answer: C
The average (arithmetic mean) of 4 different integers is 72. If the largest integer is 90, what is the least possible value of the smallest integer?  Choose the most appropriate option:
A) 1	B) 19	C) 21	D) 30	E) 33

Solution: Total of Integers=72*4= 
72*4 = 288
288   Lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer.   But all integers are distinct. So if the largest integer is 90, then the middle 2 will be 88 and 89   Lowest of least possible integer= 288-(90+89+88)=288-267= 
288-267 = 21
21   Answer: 21
Answer: C
The average of 9 results is 50. The average of first four results is 52 and average of last four results is 49 . what is the fifth result?	Choose the correct choice from the following options:  A) 22  B) 27  C) 29  D) 46  E) 92

Solution: Total of results = 50 x 9 = 450   Total of first four results = 52 x 4 = 208   Total of Last four results = 49 x 4 = 196   Hence the fifth result = 450 - (208 + 196)= 
450 - (208 + 196) = 46
46   Answer:46
Answer: D
A can do a piece of work 60 days. B can do work in 90 days. In how many days they will complete the work together?	Choose the correct answer:
A) 36 days B) 32 days C) 19 days D) 17 days E) 18 days

Solution: LCM = 180, Ratio= 60:90=2:3   No of days= 180/(2 + 3) = 180/5= 
180/5 = 36
36 days   36 daysNSWER:36 days
Answer: A
How many positive integers less than 500 can be formed using the numbers 1,2,3,and 5 for digits, each digit being used only once. Choose the correct choice from the following choices:
A) 34 B) 677 C) 197 D) 177 E) 191

Solution: Single digit numbers = 4   Double digit numbers = 4 x 3 = 12   Three digit numbers = 3 x 3 x 2 x 1 = 18   Total = 34   34nswer:34
Answer: A
Five men and nine women can do a piece of work in 10 days. Six men and twelve women can do the same work in 8 days. In how many days can three men and three women do the work?	Choose the correct choice from the following answers
A) 50 days B) 23 days C) 20 days D) 65 days E) 22 days

Solution: (5m + 9w)10 = (6m + 12w)8   => 50m + 90w = 48w + 96 w => 2m = 6w => 1m = 3w 5m + 9w = 5m + 3m = 8m   8 men can do the work in 10 days.   3m +3w 5  + 3= 
5  + 3 = 8
8m   8 men can do the work in 10 days.   3m +3w= 3m + 1w = 4m   So, 4 men can do the work in (10 * 8)/4 3  + 1= 
3  + 1 = 4
4m   So, 4 men can do the work in (10 * 8)/4= 
(10 * 8)/4 = 20
20 days.   Answer: 20 days
Answer: C
A computer manufacturer produces a certain electronic component at a cost of $100 per component. Shipping costs for delivering the components are $4 per unit. Further, the manufacturer has costs of $24,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 100 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
Choices
A) 278  B) 366  C) 349  D) 335  E) 295

Solution: $24500 is a fixed cost   Each component is $104 ($100 to produce, $4 to ship)   Manufacturer will be producing and selling 100 components   so therefore the equation to find price would be   100*p = 24500+(100*100)+(100*4)   p = (24500+10000+400)/100= 
(24500+10000+400)/100 = 349
349   Answer: 349
Answer: C
Amit and Ananthu can do a work in 15 days and 30 days respectively. Amit started the work and left after 3 days. Ananthu took over and completed the work. In how many days was the total work completed?
Options:
A) 28 days  B) 20 days  C) 23 days  D) 25 days  E) 27 days

Solution: Amit’s one day’s work= 1/15   Amit’s 3 day’s work = 1/15 *3 = 1/5   Work left= 1-1/5 = 4/5   Ananthu’s one day’s work= 1/30   Ananthu can do work in = 4/5 *30= 
4/5 *30 = 24
24 days   So total days= 24+3= 
24+3 = 27
27 days   ANSW27 daysR:27 days
Answer: E
There are 225 female managers in a certain company. Find the total number of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers. Pick one:
A) 300	B) 400	C) 562.5	D) 600	E) None of these

Solution: as per question stem 2/5M (Portion of Men employees who are managers) + 225 (Portion of Female employees who are managers) = 2/5T (Portion of Total number of employees who are managers), thus we get that 2/5M+225= 2/5T, or 2/5(T-M)=225, from here we get that T-M=562.5, that would be total number of female employees and the answer (562.5)
Answer: C
Mona and Donald fly to Rome for the weekend. They take cash only in notes of $10 and notes of €10. Mona carries three times the amount of euros Donald carries. She also carries as many dollars as Donald carries. The number of €10 notes they take is double the number of $10 notes they take. If Donald carries a total of 39 notes (of either $10 or €10,) then what is the total number of notes (of either $10 or €10,) they take?	Pick:
A) 130	B) 80	C) 100	D) 120	E) 150

Solution: let e10 =x no. d10 =y no. donald is having x+y notes mona carries 3x+y again x =2y or donald x+y =39   or 3y =39 y =13 ;x =26 , total notes they carry = 104+26= 
104+26 = 130
130   130
Answer: A
If two positive numbers are in the ratio 1/8 : 1/7, then by what percent is the second number more than the first?
Choose the most appropriate option.
A) 14.3%.  B) 70%.  C) 60%.  D) 68%.  E) 80%.

Solution: Given ratio = 1/8 : 1/7 = 7 : 8   Let first number be 7x and the second number be 8x.   The second number is more than first number by 1x.   Required percentage = 1x/7x * 100 = 14.3%.   14.3%.nswer: 14.3%.
Answer: A
John can complete a given task in 16 days. Jane will take only 12 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 5 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together?	Choose the correct answer:
A) 62  B) 64  C) 66/7  D) 10  E) 68/7

Solution: In such questions, you need to start from the end. Last 5 days John works alone and completes 5 * (1/16) = 5/16 of the work.   So 11/16 of the work should have been completed by the two of them together before Jane left.   Their combined rate of work is 1/16 + 1/12 = 7/48   Time taken to complete 11/16 of the work = (11/16)/(7/48) = 33/7 days.   So total number of days taken to complete the work =33/7 + 5 = 68/7 days.   68/7
Answer: E
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Choose the correct choice from the following options: A) 25200 B) 2543 C) 2344 D) 233445 E) 52757

Solution: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) = (7C3 x 4C2) = ( 7 x 6 x 5 x 4 x 3 ) 3 x 2 x 1 2 x 1 = 210. Number of groups, each having 3 consonants and 2 vowels = 210. Each group contains 5 letters. Number of ways of arranging 5 letters among themselves = 5! = 5 x 4 x 3 x 2 x 1 = 120. Required number of ways = (210 x 120) = 25200.   25200nswer:25200
Answer: A
The average expenditure of the hotel when there are 10 guests is Rs. 60 per guests and the average expenditure is Rs.40 when there are 20 Guests. If it is known that there are some fixed expenses irrespective of the number of guests then the average expenditure per guest whe there are 40 guests in the hotel.  Choose the correct answer:
A) 30 B) 88 C) 26 D) 18 E) 11

Solution: Explanation:   Let the fixed expenditure of the hotel be Rs.x and the variable expenditure ( which is dependent on the guest ) is Rs.y , then   x + 10y = 600 ---------(1)   x + 20y = 800 ----------(2)   \inline \Rightarrow 10y = 200   y = Rs. 20 and x= 400   Hence the total expenditure when there are 40 guests = 400 + 40 x 20 = 1200   \inline \therefore average expenditure = \inline \frac{1200}{40} = Rs. 30   30nswer: 30
Answer: A
The tens digit of a two-digit number is two more than its unit digit. The two-digit number is 7 times the sum of the digits. Find the units digits?
Choose the correct choice from the following answers:
A) 1
B) 2
C) 6
D) 8
E) 7

Solution: Let the two-digit number be 10a + b   a = b + 2 --- (1)   10a + b = 7(a + b) => a = 2b   Substituting a = 2b in equation (1), we get   2b = b + 2 => b = 2   Hence the units digit is: 2.   Answer: 2
Answer: B