MU-NLPC/Calc-aqua_rat huggingface dataset:
Ayesha's father was 29 years of age when she was born while her mother was 23 years old when her brother three years younger to her was born. What is the difference between the ages of her parents? Choose the most appropriate option.
A) 2 years B) 4 years C) 6 years D) 8 years E) 9 years

Solution: Mother's age when Ayesha's brother was born = 23 years.   Father's age when Ayesha's brother was born = (29 + 3)= 
(29 + 3) = 32
32 years.   Required difference= (32 - 23)= 
(32 - 23) = 9
9 years. Answer: Option 9 years
Answer: E
There are three secretaries who work for four departments. If each of the four departments have one report to be typed out, and the reports are randomly assigned to a secretary, what is the probability Q that all three secretary are assigned at least one report?
Options:
A) 8/9
B) 64/81
C) 4/9
D) 16/81
E) 5/9

Solution: I got the same answer: Here's my reasoning   First Report you have 3 choices   Second Report you have 2 choices   Third Report you have 1 choice   Fourth report 3 choices again   Then total number of ways is: 3*2*1*3=3^2*2   This is not correct. You have assumed that the 4th report must go to someone who already has a report. There is no such constraint. You can easily give the 1st and 2nd reports to secretary 1, 3rd report to secretary 2 and 4th report to secretary 3. But you have ignored all such cases.   The number of ways of ensuring at least one report goes to each secretary is 44/92 (select 2 reports out of 4 which go to the same person)*34/91 (select the person who must type 2 reports)*2! (since you have 2 reports left which you must distribute to the 2 remaining people such that each person gets one) = 36   Required probability Q = 36/81.4/9
Answer: C
A train passes a station platform in 31 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?	Choose the most appropriate option:
A) 165 m B) 240 m C) 300 m D) 365 m E) 280 m

Solution: Speed = 54 x	5/18	m/sec = 15 m/sec.   Length of the train = (15 x 20)m = 300 m.   Let the length of the platform be x metres.   Then,	(x + 300)/31	= 15   x + 300 = 465   x = 165 m.165 mnswer: Option 165 m
Answer: A
A store raised the price of an item by exactly 50 percent. Which of the following could NOT be the resulting price of the item?  Choose the correct choice from the following:
A) 150  B) 300  C) 275  D) 600  E) 225

Solution: If it raised the value by 50% then the resulting price is 1.5 times the original price. So the final answer has to be a multiple of 1.5. Check the answers.   150 - Yes   300 - Yes   275 - No   600 - Yes   225 - Yes   Answer : 275
Answer: C
The diagonal of the floor of a rectangular closet is 7 feet. The shorter side of the closet is 4 feet. What is the area of the closet in square feet? Choose one
A) 26
B) 27
C) 28
D) 29
E) 32

Solution: Other side =   15 2 - 9 2   2 2   ft   =   225 - 81   4 4   ft   =   144   4   ft   = 6 ft.   Area of closet = (6 x 4.5) sq. ft = 27 sq. ft.   27)
Answer: B
The ages of two persons differ by 16 years. 5 years ago, the elder one was 3 times as old as the younger
one. What are their present ages of the elder person Choose the correct choice from the following answers.
A) 29  B) 20  C) 25  D) 30  E) 35

Solution: Explanation:   Let's take the present age of the elder person = x   and the present age of the younger person = x � 16   (x � 5) = 3 (x-16-5)   => x � 5 = 3x � 63   => 2x = 58   => x = 58/2= 
58/2 = 29
29   29nswer: Option 29
Answer: A
a printer number the page of a book starting with 1 and uses 3189 digits in all How many pages dose the book have ?
Choose the correct choice from the following options:
A) 1000  B) 1074  C) 1075  D) 1080  E) None of these

Solution: Solution   No of digits in 1-digit page nos. = 1 * 9= 
1 * 9 = 9
9 .   No of digits in 2-digit page nos.= 2 * 90= 
2 * 90 = 180
180.   No of digits in 3-digit page nos.= 3 * 900= 
3 * 900 = 2_700
2700 .   No of digits in 4-digit page nos.= 3189 - (9 + 180 + 2700) = 3189 - 2889= 
3189 - 2889 = 300
300.   ∴ N0. of pages with 4-digit page nos.= (300/4)= 
(300/4) = 75
75   Hence, total number of pages= (999 + 75)= 
(999 + 75) = 1_074
1074 .   Answer 1074
Answer: B
A sum of money deposited at compound interest (compounded yearly) amounts to $6200 in 2 years and to $6324 in 3 years. What is the interest rate? Pick.
A) 2% B) 3% C) 4% D) 5% E) 6%

Solution: 6324 - 6200= 
6324 - 6200 = 124
124   124 / 6200= 
124 / 6200 = 1/50 = around 0.02
0.02= 2%   The answer is 2%.
Answer: A
A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water:	Choose the most appropriate option
A) 1.8h  B) 3h  C) 4h  D) 5h  E) None of these

Solution: Explanation:   Upstream speed = 3h-S   Downstream speed = 3h + s   3h - S = 15/5= 
15/5 = 3
3 km/h   Again 3h= 4S   Therefore 3h - S = 3 = 3S   => S = 1 and 3h = 4 km/h   Therefore 3h + S = 5km/h   Therefore, Time during downstream = 15/5= 
15/5 = 3
3h   Answer: 3h
Answer: B
Difference between the length &breadth of a rectangle is 18 m. If its perimeter is 206 m, then its area is?	Choose the correct choice from the following answers.
A) 2400 m^2
B) 2160 m^2
C) 2520 m^2
D) 2560 m^2
E) 2580 m^2

Solution: Solving the two equations, we get: l = 54 and b = 40.   Area = (l x b) = (54 x 40) m2 = 2160 m^2   2160 m^2
Answer: B
A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?	Choose the correct choice.
A) 79.2	B) 80	C) 82.5	D) 88.3	E) 95.3

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 8 => x = 8y   (x + 264)/20 = y   y = 22   Speed = 22 m/sec = 22 * 18/5= 
22 * 18/5 = 396/5 = around 79.2
79.2 km/hr.   79.2NSWER 79.2
Answer: A
The area of a rectangular field is equal to 50 square meters. Its perimeter is equal to 30 meters. Find the width of this rectangle. Options
A) 5 B) 10 C) 15 D) 20 E) 25

Solution: L * W = 50 : area , L is the length and W is the width.   2 L + 2 W = 30 : perimeter   L = 15 - w : solve for L   (15 - W) * W = 30 : substitute in the area equation   W = 5 and L = 10   correct answer 5
Answer: A
The sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself?	Choose the most appropriate option:
A) 7	B) 1	C) 8	D) 6	E) 9

Solution: 100 ---- 300 --- 3   900 --- 3   ----   6 years   Answer:6
Answer: D
Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:	Choose the correct option.
A) 13/109	B) 13/162	C) 13/111	D) 13/102	E) 13/112

Solution: Let S be the sample space.   Then, n(S) = \inline {\color{Black}52C_{2} }=(52 x 51)/(2 x 1) = 1326.   Let E = event of getting 1 spade and 1 heart.   n(E)= number of ways of choosing 1 spade out of 13 and 1 heart out of 13 = \inline {\color{Black}13C_{1}\times 13C_{1} } = 169.   P(E) = n(E)/n(S) = 169/1326 = 13/102.   Answer: 13/102) 13/102
Answer: D
The sides of the triangle are in the ratio 1/2:1/3:1/4 and its perimeter is 104cm. The length of the longest side is? Choose one
A) 32cm B) 48cm C) 50cm D) 28cm E) 30cm

Solution: Ratio of sides = 1/2 : 1/3 : 1/4 = 6:4:3   Largest side = 104*6/13= 
104*6/13 = 48
48cm   Answer is 48cm
Answer: B
A sells a bicycle to B and makes a profit of 25%. B sells the same bicycle to C at a profit of 50%. If the final S.P. of the bicycle was Rs. 225, find out the cost price of the bicycle for A.	Choose the correct choice:
A) 237 B) 126 C) 971 D) 611 E) 120

Solution: 120xplanation:   Let CP be 100   A sells at 25% profit so SP=125   B sells at 50% profit = 125 x (1+50/100) = 187.5   CP ---SP   100---187.5   x --- 225   CP = 225 x 100/187.5 = 120   ANSW120R: 120
Answer: E
If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?	Options
A) 8112  B) 8000  C) 8500  D) 7500  E) 6500

Solution: 8112 = 7500(26/25)2 = 8112   8112NSWER 8112
Answer: A
How many times are the hands of a clock at right angle in a day? Choose the correct choice from the following choices:
A) 22
B) 24
C) 44
D) 48
E) 55

Solution: Solution   In 12 hours, they are at right angles 22 times.   Therefore, In 24 hours, they are at right angles 44 times.   Answer 44
Answer: C
A person got Rs.35 more when he invested a certain sum at compound interest instead of simple interest for two years at 12% p.a. Find the sum?	Options: A) 7500 B) 14583 C) 15449 D) 14567 E) 2671

Solution: P = (d * 1002) / R2   => (35 * 100 * 100) / 12 * 12 = Rs.14583   Answer:14583
Answer: B
If a large pizza has a radius that is 60% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza?
Choose the correct choice from the following answers:
A) 30%
B) 60%
C) 98%
D) 120%
E) 156%

Solution: Let the radius of medium pizza be r. Then the radius of large pizza is 1.6r.   The area of the medium pizza is pi*r^2   The area of the large pizza is pi*(1.6*r)^2 = 2.56*pi*r^2, an increase of 156%.   The answer is 156%.
Answer: E
A boy is traveling from his house to school at 10km/hr and reached school 2hours late. Next day he traveled 20km/hr and reached 1hour early. Then find the distance between house and school?  Select
A) 50km  B) 45km  C) 33km  D) 60km  E) 54km

Solution: Let distance be x   S1 = 10km/hr   S2 = 20km/hr   T1 = x/10hr   T2 = x/20hr   60kmifference in time = 2+1= 
2+1 = 3
3hr   (x/10)-(x/20)= 3   x = 60km   Answer is 60km
Answer: D
How many seconds will a train 100 meters long take to cross a bridge 180 meters long if the speed of the train is 36 kmph?	Choose the correct answer
A) 22 sec  B) 27 sec  C) 25 sec  D) 24 sec  E) 28 sec

Solution: 28 secxplanation:   D = 100 + 180= 
100 + 180 = 280
280   S= 36 * 5/18= 
36 * 5/18 = 10
10 mps   T= 280/10= 
280/10 = 28
28 sec   Answer: Option 28 sec
Answer: E
In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 81 more candidates got selected than A. What was the number of candidates appeared from each State? Answers:
A) 7000  B) 8100  C) 6000  D) 5000  E) 4000

Solution: State A and State B had an equal number of candidates appeared.   In state A, 6% candidates got selected from the total appeared candidates   In state 8100, 7% candidates got selected from the total appeared candidates   8100ut in State 8100, 81 more candidates got selected than State A   From these, it is clear that 1% of the total appeared candidates in State 8100 = 81   => total appeared candidates in State 8100 = 81 x 100 = 8100   => total appeared candidates in State A = total appeared candidates in State 8100 = 8100
Answer: B
Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 40%?  Answers
A) 282  B) 332.5  C) 277  D) 285  E) 2812

Solution: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5   SP = CP[(100 + profit%)/100]   = 237.5 * [(100 + 40)/100] = Rs. 332.5.   Answer:332.5
Answer: B
There are 7 people and 4 chairs. In how many different ways people can occupy the chairs?  Choices
A) 840	B) 1020	C) 712	D) 516	E) 360

Solution: number of ways = 7*6*5*4= 
7*6*5*4 = 840
840   840nswer is 840
Answer: A
x is a positive integer of Z less than 500. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there?
Pick one.
A) 21 B) 22 C) 23 D) 24 E) 25

Solution: Took me more than 2 mins to solve.   That's how I did it.   x is between 1-499 included.   Smallest number that can be written as 7n+1 (7*0+1) is 1   Largest number that can be written as 7n+1 is (7*71 +1) is 498   So there are total 72 numbers that can be written as 7n+1   Because x can also be written as 3m+2, we have to see how many numbers that can be written as 7n+1 also can be written as 3m+2   7*0+1 can not be written in the form 3m+2   7*1+1 can be written in the form 3m+2   7*2+1 can not be written in the form 3m+2   7*3+1 can not be written in the form 3m+2   7*4+1 can be written in the form 3m+2   Here we see a sequence that one out of every 4 numbers can be written as 3m+1   72/4= 24 numbers can be written as 3m+1   24 is the answer
Answer: D
Two friends Simpson & Stewie decide to get together
So they start driving cars towards each other. They plan to meet halfway. Each is riding at 6 Km/hr. They live 36 kms apart. Stewie has a pet "eagle" and it starts flying the instant they start traveling. The eagle flies back and forth at 18 Km/hr between them until the two meet.
How many kms does the eagle travel ?  Choose the correct answer.
A) 54 kms	B) 44 kms	C) 34 kms	D) 24 kms	E) 14 kms

Solution: Solution:   54   It takes 3 hours for the Simpson & Stewie to meet.   so the eagle flies for 3 hours at 18 Km/hr = 54 kms   54 kmsnswer 54 kms
Answer: A
In the manufacture of a certain product, 8 percent of the units produced are defective and 5 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale? Choose the correct choice
A) 0.2%	B) 0.4%	C) 0.8%	D) 1.2%	E) 2.0%

Solution: 0.08*0.05= 
0.08*0.05 = 0.004
0.004= 0.4%   The answer is 0.4%.
Answer: B
How many five digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?
Choose the correct choice:
A) 360
B) 720
C) 278
D) 279
E) 274

Solution: The given digits are six.   The number of four digit numbers that can be formed using six digits is   6P5 = 6 * 5 * 4 * 3 * 2= 
6 * 5 * 4 * 3 * 2 = 720
720.   Answer: 720
Answer: B
ABCD IS A square AEGF IS A rectangle..such that the rectangle shares 25% of the area of the suare ALSO AE lies ON THE LINE AB and AG lies on segment of AD.if the square shares half the area of the rectangle what is the ratio AE:AG? Answers: A) 1:4 B) 8:1 C) 4:1 D) 3:1 E) 1:3

Solution: A------------B - - - - - -- -E   | | 50% |   G------------|- - - - - - - -F   | |   | 75% |   D -----------C   remaining Square 75% and remaining rectangle 50%   Rectangle share 25% area of Square so,   AB X AG = (AD X AB)/4   AD = 4 AG------------------(1)   Square share Half the area of Rectangle So,   AG X AB = (AE X AG)/2   AB = AE/2------------------(2)   in square all sides are equal i.e. A8:1=8:1C=CD=AD so, equation (1) and (2) both are equal   AE/2 = 4 AG   AE/AG = 8   AE : AG = 8:1   ANSWER:8:1
Answer: B
Fill in the missing number:
18 14 12 ? 10.5 10.25
Choose the correct answer.
A) 11
B) 10.4
C) 10.2
D) 10.5
E) 10.25

Solution: 11   Divide each number by 2 and then add 5 to it.   11NSWER 11
Answer: A
Six people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
Options.
A) 1/5	B) 2/7	C) 3/5	D) 4/7	E) None of them

Solution: Original share of 1 person = 1/6   New share of 1 person = 1/5   Increase = (1/5 - 1/6	= 1/30)   Therefore, Required fraction = (1/30)/(1/6)	= (1/30)x (6/1)	= 1/5   1/5nswer is 1/5.
Answer: A
A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs.6.30 less, he would have gained 30%. Find the cost of the article.
Pick
A) 30	B) 40	C) 50	D) 60	E) 70

Solution: Let C.P=100   Gain=25%   S.P=125   Supposed C.P=80   Gain=30%   S.P=(130*80)/100= 
(130*80)/100 = 104
104   Diff=(125-104)= 
(125-104) = 21
21   Diff 21 when C.P=100   then Diff 6.30 when C.P=(100*6.30)/21= 
(100*6.30)/21 = 30
30   30NSWER:30
Answer: A
A drawer contains red socks, black socks, and white socks. What is the least number of socks that must randomly be taken out of the drawer to be sure of having four pairs of socks? (A pair is two socks of the same color.)
Choose the most appropriate option:
A) 8
B) 10
C) 12
D) 14
E) 1

Solution: A good Q, which becomes easy the moment we understand the logic behind it...   4 pair of socks means there will be atleast two pairs of one colour..   since the Q uses words"to be sure", we take the worst case where we pick a different colour each time we pick..   the worst case would be we have 3 of each colour, such that the one picked up after that fulfills the condition of four pair...   3 of each colour means 1 pair +1 of each colour..   so total =3*3=9..   now the tenth we pick, irrespective of the colour picked, would make it four pairs..   so total =9+1= 
9+1 = 10
10 ..   ANS:10
Answer: B
A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
Select the correct option.
A) 480 liters
B) 600 liters
C) 720 liters
D) 800 liters
E) 820 liters

Solution: 1/x - 1/20 = -1/24   x = 120   120 * 4= 
120 * 4 = 480
480   480 litersNSWER:480 liters
Answer: A
A city council will select 2 of 9 available firefighters and 1 of 6 available police officers to serve on an advisory panel. How many different groups of 3 could serve on the panel?
Choose the correct option.
A) 36  B) 72  C) 144  D) 216  E) 432

Solution: Ways to select 2 firefighters out of 9 is C29=36;   Ways to select 1 police officer out of 6 is C16=6;   Total ways to select 2 firefighters out of 9 and 1 police officer out of 6 is  36*6= 
 36*6 = 216
216.   It's called Principle of Multiplication: if one event can occur in m ways and a second can occur independently of the first in n ways, then the two events can occur in m*n ways.   Answer: 216.
Answer: D
Of two mixers and one T.V cost Rs.7000, while two T.Vs and one mixer cost Rs.9800, the value of one T.V is :
Choose the correct choice from the following answers:
A) Rs.2800  B) Rs.2100  C) Rs.4200  D) Rs.8400  E) None

Solution: Explanation:   2x+y = 7000 ............ (i)   x+2y= 9800 ..............(ii)   Solving (i) and (ii), we get y = 4200   Rs.4200orrect Option : Rs.4200
Answer: C
Jake remembers only the last three letters of his four-letter Klingon name. If he is sure that the first letter is neither "N" nor "Z", and assuming that there are only 10 letters in the Klingon alphabet, what is the probability that he will give the correct name when asked for it by the space attendant?	Options:
A) 8/100 B) 9/100 C) 1/8 D) 4/5 E) 9/10

Solution: Total letters 10, out of which the first letter is anything of 10 but N or X...   So there are 8 possible letters for first place..   And only one of them is correct..   So 1/8..   Answer: 1/8
Answer: C
A, B and C rents a pasture for Rs.957. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
Pick:
A) 270
B) 289
C) 297
D) 255
E) 552

Solution: 12*8 :16*9 = 18*6   8: 12: 9   9/29 * 957= 
9/29 * 957 = 297
297   Answer: 297
Answer: C
A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m? Pick one:  A) 675, Rs.1350  B) 575, Rs.1350  C) 1350, Rs.675  D) 1450, Rs.675  E) None

Solution: 675, Rs.1350rea = (l + b +2d) 2d   = (75 + 55 +2.5 * 2) 2*2.5 => 675   675 * 2 = Rs.1350   675, Rs.1350NSWER:675, Rs.1350
Answer: A
The least number which when increased by 5 each divisible by each one of 24, 32, 36 and 54 is :  Choose the correct choice from the following answers
A) 427
B) 859
C) 869
D) 4320
E) None of these

Solution: Solution   Required number = (L.C.M. of 24, 32, 36, 54) - 5 = 864 - 5= 
864 - 5 = 859
859. Answer 859
Answer: B
The length of the bridge, which a train 170 meters long and travelling at 45 km/hr can cross in 30 seconds, is?  Choose the correct choice from the following answers:
A) 766 m
B) 205 m
C) 245 m
D) 156 m
E) 156 m

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time   = 30 sec. Let the length of bridge be x meters. Then, (170 + X)/30 = 25/2   ==> 2(170 + X) = 750 ==> X   = 205 m.   Answer: 205 m
Answer: B
Let a be a positive integer. If t is divisible by 2^a and t is also divisible by 3^(2a), then it is possible that t is NOT divisible by  Select:
A) 6  B) 3 × 2^a  C) 2 × 3^(2a)  D) 6^a  E) 6^(2a)

Solution: Since, t is divisible by 2^a and 3^(2a), it must be divisible by 6. As least value of a = 1   Only for 6^(2a), 6^(2a) doesn't satisfy, if a = 1 and t=18, it is not divisible by 6^2 (i.e 36)   Hence answer is 6^(2a)
Answer: E
Two pipes can fill a tank in 10 and 12 hours, while third pipe will make the tank empty in 20 hours. If all three pipes operate simultaneously. In how many hours the tank will be filled ? Choose the correct choice from the following answers
A) 5.5 Hours
B) 7.5 Hours
C) 8.5 Hours
D) 9.5 Hours
E) 6.5 Hours

Solution: In 1 hour it fill 1/10 + 1/12 - 1/20 = 8/60   So fill tank fillup in   60/8= 
  60/8 = 15/2 = around 7.5
7.5 Hours   ANSWER:7.5 Hours
Answer: B
A rectangular table seats 7 people on each of two sides, with every person directly facing another person across the table. If fourteen people choose their seats at random, what is probability that any two of them directly face other?  Pick one: A) 1/13 B) 1/8 C) 1/7 D) 15/56 E) 4/7

Solution: A B C D E F G   ------------   | TABLE |   ------------   H I J K L M N   A to N are 14 people.   Prob to select any 1 person = 1   Prob to select the person opposite to the chosen person = 1/13   For ex. If we select A as the person than prob of choosing N is 1/13.   Hence, answer will be 1/13.
Answer: A
By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?  Options.
A) 38008 B) 38000 C) 27888 D) 27799 E) 27761

Solution: CP + CP/8 = 45000   CP = 40000   SP = 40000*(95/100)= 
40000*(95/100) = 38_000
38000   Answer:38000
Answer: B
Last year’s receipts from the sale of greeting cards during the week before Mother’s Day totaled $175 million, which represented 10 percent of total greeting card sales for the year. Total greeting card sales for the year totaled how many million dollars? Choices
A) 17,010
B) 2,100
C) 1,890
D) 1,701
E) 1,750

Solution: 10% ---- 175 millions   for 100% => ( 175 * 100% )/10% = 1750.   Option 1,750.( 175 * 100  )/10= 
( 175 * 100  )/10 = 1_750
1750.   Option 1,750.
Answer: E
A shopkeeper sold an book offering a discount of 5% and earned a profit of 42.5%. What would have been the percentage of profit earned if no discount was offered?  Pick.
A) 140	B) 120	C) 130	D) 110	E) 150

Solution: Let C.P. be $100.   Then, S.P. = $142.50   Let marked price be $x. Then, 95/100 x = 142.5   x = 14250/95= 
14250/95 = 150
$150   Now, S.P.= $150, C.P. = $100   Profit % = 50%.   150
Answer: E
If the cost price of 20 articles is equal to the selling price of 25 articles, what is the % profit or % loss made by the merchant?
Choose the correct choice from the following choices:
A) 25% loss B) 25% profit C) 20% loss D) 20% profit E) 5% profit

Solution: Explanatory Answer   Approach: Assume a value for cost price. Compute cost price and selling price for the same number of articles   Let the cost price of 1 article be $1.   Therefore, cost price of 20 articles = 20 * 1= 
20 * 1 = 20
$20   The selling price of 25 articles= cost price of 20 articles = $20.   Let us find the cost price of 25 articles.   Cost price of 25 articles = 25 * 1= 
25 * 1 = 25
$25.   Therefore, profit made on sale of 25 articles= Selling price of 25 articles - cost price of 25 articles   = 20 - 25 = -$5.   Because the profit is in the negative, the merchant has made a loss of $5.   Therefore, % loss = Loss/Cost Price∗100   % loss = 5/25∗100 = 20% loss.   20% losshoice 20% loss
Answer: C
A seller has 1000kg of rice part of which he sells at 8% profit and the rest at 18% profit. He gains 14%. The quantity sold at 18% profit is? Pick one:
A) 200 kg  B) 300 kg  C) 400 kg  D) 600 kg  E) 800 kg

Solution: By rule of alligation,   Profit% by selling 1st part Profit% by selling 2nd part   8 18   Net % profit   14   18-14= 
18-14 = 4
4 14-8=6   => Quantity of part1 : Quantity of part2 = 4 : 6 = 2 : 3   Total quantity is given as 1000 kg. So quantity of part2 (quantity sold at 18% profit)   =1000×35   = 600 kg   600 kg
Answer: D