MU-NLPC/Calc-aqua_rat huggingface dataset:
The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?  Pick.
A) 6 kmph	B) 7 kmph	C) 9 kmph	D) 4 kmph	E) 2 kmph

Solution: S = 1   M = x   DS = x + 1   US = x - 1   35/(x + 1) + 35/(x - 1) = 12   x = 6   6 kmphnswer: 6 kmph
Answer: A
The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.	Choose the most appropriate option
A) 87 B) 27 C) 25 D) 26 E) 24

Solution: Let the number of students who wrote the exam be x.   Total marks of students = 80 x.   Total marks of (x - 5) students = 90(x - 5)   80x - (5 * 40) = 90(x - 5)   250 = 10x => x = 25   Answer: 25
Answer: C
A and B finish the job in 15 days.while A,B and C can finish it in 5 days . C alone will finish the job in
Choose the correct choice
A) 4.50 days B) 3.50 days C) 6.0 days D) 7.5 days E) 5.50 days

Solution: Explanation:   5 = (15 * x)/(15 + x)   75+5x=15x   10x=75   X=7.5   Answer: Option 7.5 days
Answer: D
A car averages 55 mph for the first 4 hours of a trip and averages 70 mph for each additional hour. The average speed for the entire trip was 60 mph. How many hours long is the trip?
Answers.
A) 6
B) 8
C) 11
D) 12
E) 14

Solution: In 4hr journey = 55*4= 
55*4 = 220
220mph   Let in the next additional hour journey= 70*x =70x mph   So, (220+70x)/(4+x)= 60   => 220+70x = 240+60x   => 10x = 20   => x = 2h   So the trip is (4+x)=> 6 hours long   6NSWER:6
Answer: A
GOOD is coded as 164 then BAD coded as 21.if ugly coded as 260 then DUMP?
Choose the correct choice from the following.
A) 200 B) 210 C) 216 D) 225 E) 240

Solution: GOOD=(7+15+15+4)*4= 
(7+15+15+4)*4 = 164
164   BAD= (2+1+4)*3= 
(2+1+4)*3 = 21
21   UGLY= (21+7+12+25)*4= 
(21+7+12+25)*4 = 260
260   coding follows   (sum of position of alphabets)*(no. of letters in the given word)   so,   DUMP=(4+21+13+16)*4= 
(4+21+13+16)*4 = 216
216   ANSWER:216
Answer: C
We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $600. How many green hats did we buy? Choose the correct choice from the following choices:
A) A)36	B) B)90	C) C)40	D) D)42	E) E)44

Solution: Let B be the number of blue hats and let G be the number of green hats.   B+G=85.   B=85-G.   6B+7G=600.   6(85-G)+7G=600.   510-6G+7G=600.   G=600-510= 
600-510 = 90
90.   The answer is 90.
Answer: B
A part of certain sum of money is invested at 8% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?	Select the correct option:
A) 4:6
B) 3:2
C) 4:3
D) 4:1
E) 4:2

Solution: 12:8   = 3:2   Answer: 3:2
Answer: B
12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 6. Choose the correct answer.
A) 150 B) 152 C) 154 D) 159 E) 144

Solution: 159 = d * Q + R   159 = 17 * 9 + 6   159 = 153 + 6   159 = 159   ANSWER 159
Answer: D
If LCM of two number is 693, HCF of two numbers is 11 and one number is 99, then find other	Choose the correct choice from the following choices:
A) 34  B) 77  C) 12  D) 45  E) None of these

Solution: Explanation:   For any this type of question, remember   Product of two numbers = Product of their HCF and LCM   So Other number =   693×1199   = 77   Answer: Option 77
Answer: B
1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?	Choose the correct option.
A) 10.5  B) 12.5  C) 13.5  D) 11.5  E) 11

Solution: 1000*15 = 1200*x   x = 12.5   ANSWER 12.5
Answer: B
Viswak was born 3 years after his father's marriage. His mother is 8 years younger than his father but 20 years older than Viswak who is 10 years old. At what age did the father get married ? Choose one
A) 23 years  B) 25 years  C) 26 years  D) 24 years  E) 22 years

Solution: Explanation:   Viswak's present age = 10 years.   His mother's present age = (10 + 20)= 
(10 + 20) = 30
30 years.   His father's present age= (30 + 8)= 
(30 + 8) = 38
38 years.   His father's age at the time of Viswak's birth= (38 - 10)= 
(38 - 10) = 28
28 years.   Therefore Viswak's father's age at the time of marriage= (28 - 3)= 
(28 - 3) = 25
25 years.   Answer: 25 years
Answer: B
If a person walks at 15 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is?  Choose the most appropriate option
A) 50 km
B) 76 km
C) 18 km
D) 60 km
E) 97 km

Solution: Let the actual distance traveled be x km. Then,   x/10 = (x + 20)/15   5x - 300 =>x = 60 km.   Answer: 60 km
Answer: D
If x and y are both odd prime numbers and x < y, how many distinct positive integer Q factors does 2xy have? Choose the correct choice from the following choices:	A) 3	B) 4	C) 6	D) 8	E) 12

Solution: Since 2xy prime Q factors are x^1*y^1*2^1, its total number or factors must be (1+1)(1+1)(1+1)=2^3=8. Thus, I think 8 would be the correct answer.
Answer: D
A grocer purchased 80 kg of sugar at 13.50 per kg and mixed it with 120 kg sugar at 16 per kg. At what rate should he sell the mixture to gain 17%?
Choose the correct choice from the following answers
A) 17 per kg B) 17.55 per kg C) 16.5 per kg D) 16 per kg E) None of these

Solution: C.P. of 200 kg of mixture = (80 × 13.50 + 120 × 16)   = 3000.   S.P. = 117% of 3000 = (117⁄100 × 3000) = 3510   ∴ Rate of S.P. of the mixture = (3510⁄200) per kg   = 17.55 per kg.   Answer 17.55 per kg
Answer: B
A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?  Choose the correct answer
A) 1 mins
B) 3 mins
C) 8 mins
D) 6 mins
E) 4 mins

Solution: D = 25 * 60 + 1500= 
25 * 60 + 1500 = 3_000
3000 m   T= 3000/60 * 18/5= 
3000/60 * 18/5 = 180
180 sec= 3 mins   Answer: 3 mins
Answer: B
Find out the wrong number in the given sequence of numbers.
1, 2, 6, 15, 31, 57 Choose the correct choice from the following choices
A) 2  B) 57  C) 15  D) 31  E) 91

Solution: 1(result) + (1*1) = 2.   2(result) + (2*2) = 6.   6(result) + (3*3) = 15.   15(result) + (4*4) = 31.   31(result) + (5*5) = 56.   Now we are getting 56 not 57.. So 57 is the wrong number of the given.   answer : 57
Answer: B
If C(n, 7) = C(n, 5), find n  Select.
A) 15 B) 12 C) 18 D) -1 E) -2

Solution: We know that C(n,r) = n! / r!(n - r)!   Now C(n,7) = C(n,5)   n! / 7! (n - 7)! = n! / 5! (n - 5)!   => 5! (n - 5)! = 7! (n - 7)!   => [5!] x [(n - 5)(n - 6)[(n - 7)!] = 7 x 6 x 5! x (n - 7)!   => n2 - 11n + 30 = 42   => n2 - 11n - 12 = 0   => (n - 12)(n + 1) = 0   => n = 12 or n = - 1   But n = - 1 is rejected as n is a non negative integer. Therefore, n = 12   ANSWER:12
Answer: B
A sum of money at simple interest amounts to Rs. 2240 in 2 years and to Rs. 2600 in 5 years. What is the principal amount  Choose the correct choice from the following answers:
A) 1000 B) 1500 C) 2000 D) 2500 E) 3500

Solution: Explanation:   SI for 3 year = 2600-2240= 
2600-2240 = 360
360   SI for 2 year 360/3 * 2= 
360/3 * 2 = 240
240   principal= 2240 - 240= 
2240 - 240 = 2_000
2000   Answer: Option 2000
Answer: C
Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections Q of the 4 items can Amanda make? Choose the correct option:
A) 9
B) 12
C) 14
D) 15
E) 60

Solution: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?   3! / 1!2! * 6! / 3!3!   Q=3*20= 
3*20 = 60
60   E. 60
Answer: E
A wheel rotates 10 times every minute and moves 30 cm during each rotation. How many metres does
the wheel move in two hour?
Choose the correct choice from the following answers:
A) 6 metre	B) 12 metre	C) 120 metre	D) 876 metre	E) 360 metre

Solution: Expl : Number of times wheel moves in 1 hour = 10 * 120= 
10 * 120 = 1_200
1200   :. Distance moves= (1200 *30)= 
(1200 *30) = 36_000
36000 cms   In metres= 360 metre   Answer: 360 metre
Answer: E
Look at this series: 31, 29, 24, 22, 17, ... What number should come next?  Pick one
A) 11	B) 15	C) 16	D) 17	E) 18

Solution: 15   15   This is a simple alternating subtraction series, which subtracts 2, then 5.
Answer: B
A Man travelled a distance of 80 km in 10 hours. He travelled partly on foot at 5 km/hr and partly on bicycle at 9 km/hr. What is the distance travelled on foot? Select:  A) 16 km  B) 14 km  C) 12 km  D) 10 km  E) None of these

Solution: Explanation:   Let the time in which he travelled on foot = x hour   Time for travelling on bicycle = (9 - x) hr   10 kmistance = Speed * Time, and Total distance = 80 km   So,   5x + 10(9-x) = 80   => 5x = 10   => x = 2   So distance traveled on foot = 5(2) = 10 km   Answer: Option 10 km
Answer: D
John makes $40 a week from his job. He earns a raise and now makes $70 a week. What is the % increase? Choose the correct choice from the following options:
A) 16% B) 16.66% C) 17.9% D) 18.12% E) 75%

Solution: Increase = (30/40)*100 = (3/4)*100= 
(3/4)*100 = 75
75%.   75%
Answer: E
At a conference, the only events scheduled for the day are seminars and breaks. All seminars are the same length and are 10 times as long as each break. A break must be between two consecutive seminars. If the first seminar begins at 9:00 a.m. and the third one ends at 11:20 a.m., how long will the conference last if there are a total of 6 seminars that day?	Choose the correct choice from the following choices
A) hours and 15 minutes  B) hours and 20 minutes  C) hours and 25 minutes  D) hours and 30 minutes  E) hours and 35 minutes

Solution: Well its like this S B S B S B S B S B S   the interval between 9 am to 11:40 am is 160 min having 3 seminars and 2 breaks .If 1 break is of 5 min than time for 3 seminars = 160 - 2*5= 
160 - 2*5 = 150
150   Time of 1 seminar=150 /3= 
150 /3 = 50
50 min .   So calculating for 6 seminars and 5 breaks ,total time comes out to be 5 hrs and 20 min .   Answer is hours and 20 minutes.
Answer: B
When n is divided by 19, the remainder is 7. When n is divided by 11, the quotient is equal to Z, and the remainder is equal to 7. Z must be divisible by which of the following numbers?
Choose one
A) 16	B) 18	C) 20	D) 19	E) 22

Solution: N = 19 q + 7   N = 11 z + 76   Equating   19 Q + 7 = 11z+7   11z=19q   11z/19 = q   since q is an integer Z must be divisible by 19.   Hence 19
Answer: D
In the formula A = (2r)^3, if r is halved, then A is multiplied by ? Options:
A) 64
B) 1/8
C) 1
D) 8
E) 1/64

Solution: Say r=2 => A1 = 64   when r=1; V2 = 8   V2 = 1/8*V1.   Answer : 1/8
Answer: B
In a 8 x 8 chess board what is the total number of squares.
Pick.
A) 238  B) 204  C) 678  D) 169  E) 161

Solution: Ans: The total number of squares in a n x n chess board is equal to "the sum of first n natural number squares"   i.e., n(n+1)(2n+1)6n(n+1)(2n+1)6   So Substituting 8 in the above formula we get 204   Answer:204
Answer: B
Two circular signs are to be painted. If the radius of the larger sign is three times that of the smaller sign, how many times more paint is needed to paint the larger sign? (We can assume that a given amount of paint covers the same area on both signs.)	Choose the correct choice from the following answers:
A) 3
B) 9
C) 12
D) 15
E) 18

Solution: Let R be the radius of the smaller sign.   The area A of the smaller sign is A = piR^2.   The area of the larger sign is pi(3R)^2=9piR^2=9A.   Since the area is 9 times larger, we need 9 times more paint for the larger sign.   The answer is 9.
Answer: B
If 20 machine can finish a job in 36 days, then how many more machines would be needed to finish the job in one -third less time?	Choose the correct option
A) a. 4	B) b. 8	C) c. 10	D) d. 12	E) e. 16

Solution: You might think of this in a management context - we can use the principle of 'person-hours' to solve any problem where we have identical workers. So, using simpler numbers, suppose you know that 6 identical employees, working simultaneously, would finish a job in 5 hours. Then that job requires 6*5= 
6*5 = 30
30 total hours of person-work. If instead you wanted the job done in 3 hours, you'd assign   30/3= 
  30/3 = 10
10 employees to do the job, because you want to get a total of 30 hours of work from the employees.   We can solve this problem identically. If 20 machines (identical ones, I assume) work simultaneously for 36 days, they will do a total of 20*36 machine-days of work. So the job requires 20*36 days of machine work in total. We instead want the job done in 1/3 less time, so in 24 days. So we'll need 20*36/24= 
20*36/24 = 30
30 machines, or 10 additional machines.   c. 10
Answer: C
In terms of percentage profit, which among following the best transaction. Choose the correct choice:	A) C.P. 36, Profit 17	B) C.P. 50, Profit 24	C) C.P. 40, Profit 19	D) C.P. 60, Profit 29	E) C.P. 70, Profit 39

Solution: Explanation:   Hint: Calculate profit percent as   Profit% = (profit/cost) * 100   ANSWER IS C.P. 60, Profit 29
Answer: D
A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?	Choose the most appropriate option
A) 18 days  B) 20 days  C) 24 days  D) 30 days  E) 32 days

Solution: 2c = ¼ + 1/6 – 1/3 = 1/12   c = 1/24 => 24 days   ANSWER:24 days
Answer: C
A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2460?
Choose the correct choice from the following
A) 14028  B) 14029  C) 14027  D) 14000  E) 14298

Solution: 25*12: 30*12: 35*8   15:18:14   14/47 * 47000= 
14/47 * 47000 = 14_000
14000   Answer: 14000
Answer: D
Two cars A and B are running towards each other from different places 88 km apart. If the ratio of the speeds of the cars A and B is 5 : 6 and the speed of the car B is 90 km per hour then after how long will the two meet each other? Choose the correct choice from the following options:
A) 2263 minutes  B) 24 minutes  C) 32 minutes  D) 36 minutes  E) None of these

Solution: Speed of the car A = 5⁄6 × 90 = 75 km/hr   \ Reqd time = 88/90+75×60=32minutes   Answer 32 minutes
Answer: C
If A can do a work in 8 days and B can do the same work in days,in how many days A and B together can finish the work  Choose the correct choice.
A) 3 3/7	B) 4 3/7	C) 5 3/7	D) 6 3/7	E) None of these

Solution: no of days taken to finish the work=8*6/(8+6)   Instead of solving this directly take the LCM of 8 and 6   8*6/(8+6)=LCM(8,6)/(LCM(8,6)/8 + LCM(8,6)/6)=24/(3+4)=24/7=3 3/7   3 3/7nswer 3 3/7
Answer: A
On Saturday, the original price of a shirt was discounted by 20%. On Monday, the price of the shirt was marked up p percent so that the new price on Monday was 20% more than the original price before the discount. What is the value of p?
Pick:
A) 20%	B) 30%	C) 33 1⁄3%	D) 40%	E) 50%

Solution: Let Original price be O   Saturday price = 0.8 x O   Monday price = 1.P x 0.8x O   Monday price is 20 percent higher than original.price   So 1.P x 0.8 X O = 1.2 x O   1.P = 1.5   Hence P = 50 %   ANSW50%R:50%
Answer: E
The ratio of length of two refill is 9:8.2nd refill got damaged when only half length of 2nd refill get used.The ratio of total no. of pages written by both refill.	Select the correct option:	A) 8:3	B) 6:5	C) 9:8	D) 9:4	E) 5:4

Solution: the no. of page written is directly proportional to length of refill.   so, initial no. of page to be write =9x,8x.   now,2nd refill only can write 4x page   so new ratio of page written =9x/4x=9:4.   answer 9:4
Answer: D
if {x+y}/{x-y}= 4/3 and x≠0, then what percentage (to the nearest integer) of x+3y is x–3y ? Pick one:	A) 40%	B) 30%	C) 55%	D) 36%	E) None of these

Solution: Explanation :   =>(x+y)/(x-y)=4/3.   =>(x/y)+1/(x/y)−1=4/3.   Cross-multiplying this equation yields   =>3x/y+3=4x/y−4.   Solving for x/y yields x/y=7.   Now, the percentage of x+3y the expression x−3y makes is   =>x−3y /x+3y∗100   Dividing both the numerator and the denominator of the expression by y, gives:-   =>((x/y)−3/(x/y)+3))×100.   =>((7−3)/(7+3))×100.   =>40%.   40%nswer : 40%
Answer: A
How long does a train 200 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
Choose the correct choice from the following: A) 82.1 sec B) 12.1 sec C) 16.1 sec D) 13.1 sec E) 16.6 sec

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec   Total distance covered= 200 + 132= 
200 + 132 = 332
332 m.   Required time= 332/20= 
332/20 = 83/5 = around 16.6
16.6 sec.   Answer:16.6 sec
Answer: E
Two trains leave the same train station at 6:00 am and 6:30 am and they travel at 100 kph and 120 kph respectively. How many kilometers from the train station will the two trains be together?
Options:
A) 300 B) 320 C) 340 D) 360 E) 380

Solution: At 6:30, the first train is 50 km ahead.   The second train gains 20 km each hour.   The time it takes the second train to catch the first train is 50 /20= 
50 /20 = 5/2 = around 2.5
2.5 hours.   In this time, the second train travels   2.5*120= 
  2.5*120 = 300
300 km.   The answer is 300.
Answer: A
One hour after Matthew started waking from e to y, a distance of 45km, Johnny started walking along the same road from y to e. Matthew's walking rate was 3 km per hour and Johnny's was 4km per hour, how many km had Johnny walked when they met? Pick:  A) 24  B) 23  C) 22  D) 21  E) 19.5

Solution: Just an alternative method...   After the first hour the distance e is 42 km (45-3). Now the problem can be treated as if bothof them started at the same time. Since the speeds are in the ratio 3 : 4, the distances will also be in the same ratio. Splitting 42 in that ratio we get 18 : 24. So answer is 24.   Hence 24.
Answer: A
what is the Max number of rectangular boxes, each measuring 4 inches by 6 inches by 10 inches, that can be packed into a rectangular packing box measuring 16 inches by 18 inches by 30 inches, if all boxes are aligned in the same direction?	Choose the correct choice from the following:
A) 36	B) 14	C) 12	D) 15	E) 11

Solution: The 4 inch side should be aligned to the 16 inch side ( 4 layer)   6 inch side should be aligned to the 18 inch side. (3 layer)   and 10 inch side should be aligned to the 30 inch side.(3 layer)   Maximum number of rectangles =4*3*3= 
4*3*3 = 36
36   36nswer is 36
Answer: A
In an arithmetic progression the difference between the any two consecutive terms is a constant. What is the arithmetic mean of all of the terms from the first to the 29th in an arithmetic progression if the sum of the 13th and 17th terms of the sequence is 102?
Choose the correct choice from the following answers:
A) 43
B) 47
C) 51
D) 55
E) 59

Solution: Let x be the difference between any two consecutive terms.   The mean of a sequence like this is the middle term, thus the 15th term in the sequence.   Then the mean of the 14th and 16th term is also equal to the overall mean, because the 14th term is (15th term - x) and the 16th term is (15th term + x).   Similarly the mean of the 13th and 17th term is also equal to the mean.   etc...   Thus the mean is   102/2= 
  102/2 = 51
51   The answer is 51.
Answer: C
Hariprasad and Madhusudan started a business, investing sums in the ratio of 2 : 3. If Hariprasad had invested an additional amount of 10,000 the ratio of Hariprasad's investment to Madhusudan's investment would have been 3 : 2. What was the amount invested by Hariprasad?
Choose one
A) 8000	B) 12000	C) 9000	D) Data inadequate	E) None of these

Solution: Let the initial investments of Hariprasad and Madhusudan be 2x and 3x,respectively.   From the question,   2x+10000/3x=32   or, 4x + 20000 = 9x   \ x = 4000   \ 8000mount invested by Hariprasad = 2x = 8000   8000nswer 8000
Answer: A
In 1950, Richard was 4 times as old as Robert. In 1955, Richard was 3 times as old as Robert. In which year was Richard 1.5 times as old as Robert?  Choices:	A) 1960	B) 1965	C) 1970	D) 1975	E) 2000

Solution: In 1950: Ri = 4 Ro -------------- eq1   In 1955: Ri +5 = 3(Ro+5)---------eq2   Thus in 1950, solving eq1 and eq2   Ro= 10 , Ri =40   Now for each year we can calculate:   2000: Ri= 60, Ro = 90   Thus Ans:2000
Answer: E
In a hot dog eating contest the average number of hot dogs that were eaten by boys was 7 each, and the average number eaten by girls was 5 each. If the total number of hot dogs eaten during the contest was 50, what was the total number of boys and girls in the contest?  Choose the correct choice.
A) 6
B) 7
C) 8
D) 9
E) 10

Solution: We can determine quickly that total number should range between 50/7<= N <= 50/5 , so ans should be between 7 and 10.   Now solving the expression 7A+5B =50   decreasing 50 by multiples of 7 and checking divisibility of that number by 5, we get   5 boys and 3 girls will total 50 hot dogs, 5*7 + 3*5 = 50   Hence total number is  5 + 3= 
 5 + 3 = 8
8   Ans 8
Answer: C
A certain restaurant offers 8 different salads, 6 different main courses, 6 different desserts. If customers choose one salad, one main course and two different desserts for their meal, how many different meals are possible?  Choose the most appropriate option.
A) 120	B) 240	C) 480	D) 600	E) 1200

Solution: MAGOOSHOFFICIAL SOLUTION:   To count the number of meals, we have to count the possibilities for the three components, and then, according to theFundamental Counting Principle, we multiply. For more on the FCP, seethis blog.   For salads, there are 8 possibilities. Done.   For main courses, there are 5 different possibilities. Done.   For desserts, there are 6 choices, but we pick two different choices. This would be 6C2. To calculate this, we can usethe shortcut, nC2 = (n*(n-1))/2.   6C2 = (6*5)/2= 
(6*5)/2 = 15
15   So, there are 15 combinations of two different desserts.   For the number of meals, we multiply  8*6*15= 
 8*6*15 = 720
720   120nswer= 120
Answer: A
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 650 sq. feet, how many feet of fencing will be required?	Choose the correct choice:
A) 34
B) 40
C) 85
D) 88
E) None

Solution: EXPLANATION   We have: l = 20 ft and lb = 650 sq. ft.   So, b = 32.5 ft.   Length of fencing = (l + 2b) = (20 + 65)= 
(20 + 65) = 85
85 ft.   Answer 85
Answer: C
If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price? Choose the most appropriate option:
A) 1533  B) 1543  C) 1500  D) 1278  E) 1202

Solution: Explanation:   Let the cost price of an article be Rs. x.   (19% of x) - (12% of x) = 105   19x/100 - 12x/100 = 105 => 7x = 105 * 100   => x = 1500   Cost price = Rs. 1500   Answer:1500
Answer: C
A shipment of 1500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived 1/3 of the heads were sold, each at 25% above the cost per head. The following day the rest were sold at a price equal to 5% less than the price each head sold for on the day before. What was the total gross profit on this shipment. Pick.
A) $100 B) b $115 C) c $120 D) d $125 E) e $135

Solution: Purchase cost = 600/1500= 
600/1500 = 2/5 = around 0.4
$ 0.4   25% above the cost per head= (125/100)*0.4= 
(125/100)*0.4 = 0.5
$ 0.5   2/3 of the heads were sold means 1/3*1500= 
1/3*1500 = 500
500 ,Selling amount for 500 cabbage= 500 * 0.5= 
500 * 0.5 = 250
$ 250   Remaining were sold at a price equal to 10% less than the price each head sold for on the day before i.e , (95/100)*0.5= $ 0.475   Hence selling cost for the remaining cabbage = 1000 * 0.475= 
1000 * 0.475 = 475
$ 475   Total selling cost= 475 + 250= 
475 + 250 = 725
$ 725   Gross profit= $ 725 - $ 600 = $ 125   Hence Answer is d $125
Answer: D
30 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work ?  Pick.
A) 20  B) 77  C) 36  D) 25  E) 13

Solution: Explanation:   Less Men, means more Days {Indirect Proportion}   Let the number of days be x   then,   27 : 30 :: 18 : x   [Please pay attention, we have written 27 : 30 rather than 30 : 27, in indirect proportion, if you get it then chain rule is clear to you :)]   {\color{Blue} x=\frac{30\times 18}{27}}   x = 20   So 20 days will be required to get work done by 27 men.   20nswer: 20
Answer: A