MU-NLPC/Calc-aqua_rat huggingface dataset:
Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four red stripes, four blue stripes, four white stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall?  Choose the correct choice from the following answers
A) 210	B) 350	C) 700	D) 2,520	E) 5,040

Solution: Number of ways to choose 2 colors among 3 - 3c2   Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4))   Now the order,   the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4   [Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this]   Total number of combinations - 3c2 * 2* 7c4 = 210   210
Answer: A
A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 4% of bananas were rotten. Find the percentage of fruits in good condition? Pick one:
A) 92.5%  B) 89.4%  C) 85.2%  D) 96.8%  E) 78.9%

Solution: Total number of fruits shopkeeper bought = 600 + 400= 
600 + 400 = 1_000
1000   Number of rotten oranges= 15% of 600   = 15/100 × 600   = 9000/100= 
9000/100 = 90
90   Number of rotten bananas= 4% of 400   = 16   Therefore, total number of rotten fruits = 90 + 16= 
90 + 16 = 106
106   Therefore Number of fruits in good condition= 1000 - 106= 
1000 - 106 = 894
894   Therefore Percentage of fruits in good condition= (894/1000 × 100)%   = (89400/1000)= 
(89400/1000) = 447/5 = around 89.4
89.4%   Answer:89.4%
Answer: B
Cathy and Cara begin running at the same time and they start at the same place on a straight path. Cathy runs at 10 miles per hour, and Cara runs at 5 miles per hour. After 12 minutes, Cathy stops to stretch. If it takes Cathy 24 minutes to stretch and Cara continues to run during this time, how many minutes will it take Cathy to catch up to Cara?	Choose the correct answer
A) 10
B) 12
C) 14
D) 16
E) 18

Solution: In 12 minutes, Cathy runs 2 miles.   In 36 minutes, Cara runs 3 miles.   Cathy can catch Cara at a rate of 5 miles per hour.   Since Cara is ahead by 1 mile, it will take Cathy 1 / 5 hours = 12 minutes to catch Cara.   The answer is 12.
Answer: B
Everyone shakes hands with everyone else in a room. Total number of handshakes is 91. Number of persons=?	Choose one.
A) 14  B) 12  C) 11  D) 15  E) 16

Solution: In a room of n people, the number of possible handshakes is C(n,2) or n(n-1)/2   So n(n-1)/2 = 91 OR n(n-1)=182 OR n=14   14nswer is (14)
Answer: A
Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?  Choose the correct answer:  A) 19.7  B) 19.9  C) 21  D) 21.7  E) 23

Solution: Total cost of the items he purchased = Rs.25   Given that out of this Rs.25, 30 Paise is given as tax   => Total tax incurred = 30 Paise = Rs.30/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (25−30/100−x)6/100 = 30/100   ⇒ 6(25 −0.3 −x) = 30   ⇒ (25 − 0.3 − x) = 5   ⇒ x = 25 − 0.3 − 5 = 19.7   19.7)
Answer: A
At a game of billiards, A can give B 15 points in 60 and A can give C to 20 points in 60. How many points can B give C in a game of 90?  Options
A) 22	B) 98	C) 10	D) 77	E) 28

Solution: Explanation:   A : B = 60 : 45.   A : C = 60 : 40.   \inline \fn_jvn {\color{Black}\therefore \frac{B}{C}=\left ( \frac{B}{A} \times \frac{A}{C}\right )=\left ( \frac{45}{60}\times \frac{60}{40} \right )=\frac{45}{40}=\frac{90}{80}=90:80}   B can give C 10 points in a game of 90.   Answer: 10) 10 points
Answer: C
50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 , then the rise in the water level in the tank will be:
Select:
A) 22
B) 25
C) 32
D) 99
E) 88

Solution: Explanation:   Total volume of water displaced =(4 x 50) = 200   Rise in water level = =0.25m = 25cm   Answer: 25) 25 cm
Answer: B
Ram and Shyam together can do a piece of work in 30 days. Ram having worked for 16 days, Shyam finishes the remaining work alone in 44 days. In how many days shall Shyam finish the whole work alone?	Choose one:
A) 30 days	B) 40 days	C) 60 days	D) 70 days	E) 80 days

Solution: Let us assume the total work to be done is 120 units.   According to the question,   Ram and Shyam finish the work in 30 days which implies 4 units of work is done by them in a single day, i.e.,   R + S = 4. ------ (1)   Also, Ram works for 16 days and the remaining work is finished by Shyam in 44 days, i.e.,   16R + 44S = 120 ------ (2)   Equating the equations (1) and (2), S = 2 units and R = 2 units.   Shyam alone finishes 2 units of work in one day.   Therefore, the number of days taken by Shyam alone to finish the whole work = 120/2= 
120/2 = 60
60 days.   ANSWER:60 days
Answer: C
A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed :
Select
A) 30 birds	B) 60 birds	C) 72 birds	D) 90 birds	E) 84 birds

Solution: Explanation:   Let the no of shots be x. Then,   Shots fired by 30 birds = 5/8x   Shots fired by B = 3/8x   Killing shots by 30 birds = 1/3 of 5/8x= 5/24x   shots missed by B =1/2 of 3/8x =3/16x   therefore, 3/16x=27=> x=144   Birds killed by 30 birds = 5/24x=(5/24)x144=30   30 birdsNSWER IS 30 birds
Answer: A
find the number, difference between number and its 3/5 is 50.
Select the correct option:  A) 120  B) 123  C) 124  D) 125  E) 359

Solution: Explanation:   Let the number = x,   Then, x-(3/5)x = 50,   => (2/5)x = 50 => 2x = 50*5,   => x = 125   Option 125
Answer: D
A cycle is bought for Rs.900 and sold for Rs.1180, find the gain percent?	Pick: A) 11 B) 31 C) 99 D) 77 E) 18

Solution: 900 ---- 280   100 ---- ? => 31%   Answer: 31
Answer: B
A can do a work in 60days and B in 12 days.Then A and B together do the work in,how many days?  Choose the correct choice from the following answers.
A) 5 days  B) 4 days  C) 10 days  D) 2 days  E) 6 days

Solution: Explanation:   A's 1day's work = 1/60   B's 1day's work = 1/12   They work together = 1/60 + 1/12 = 10 days   Answer: Option 10 days
Answer: C
An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 20-meter platform and caught it after it had traveled 52.5 meters. How many times did the ball bounce?
Choose the correct option:
A) 5 B) 6 C) 7 D) 3 E) 2

Solution: Going down = 20 m   Going Up = 10 --> Total = 30   Going down = 10 --> Total = 40   Going Up = 5 --> Total = 45   Going down = 5 --> Total = 50   Going up = 2.5 --> Total = 52.5 (Caught)   No of bouncing = 3   Answer : 3
Answer: D
The volume of a cube is 1000 cc. Find its surface. Choose the correct choice from the following answers
A) 900	B) 700	C) 600	D) 500	E) 800

Solution: a3 = 1000 => a = 106a2 = 6 * 10 * 10= 
6 * 10 * 10 = 600
600Answer: 600
Answer: C
At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 35 other employees of Company K, how many employees does Company K have?	Choose the correct option:
A) 140
B) 180
C) 190
D) 200
E) 400

Solution: Let the total number of employees in the company be x   % of secretaries = 15%   % of salespeople = 60%   % of of employees other than secretaries and salespeople = 100 - 75= 
100 - 75 = 25
25%   But this number is given as 35   so 25% of x= 35   x = 140   Therefore there a total of 140 employees in the company K   Correct answer - 140
Answer: A
The average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the last number is 13. What is the last numbers?	Choose one: A) 5 B) 7 C) 8 D) 9 E) 12

Solution: Explanation:   5 + B + C = 48   B + C + D = 45   5 + D = 13   5 – D = 3   5 + D = 13   2D = 10   D = 5   5)
Answer: A
If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true?
I. c is even
II. ab > 0
III.ab is even Select the correct option.
A) III only	B) II only	C) I and II	D) I and III	E) I, II, and III

Solution: Two ways this can happen: 1- Even/ Even= Even or 2- Even/Odd= Even   So Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above.   III only.letter III only
Answer: A
The area of a parallelogram is 72 sq m and its altitude is twice the corresponding base. Then the length of the base is?
Choose the correct option.
A) 6  B) 16  C) 8  D) 36  E) none

Solution: 2x * x = 72 => x   = 6   6nswer:6
Answer: A
A person spends 1/3rd of the money with him on clothes, 1/5th of the remaining on food and 1/4th of the remaining on travel. Now, he is left with Rs 400. How much did he have with him in the beginning?
Choose one.
A) s 200  B) s 1000  C) s 300  D) s 450  E) s 550

Solution: Suppose the amount in the beginning was Rs ’x’   Money spent on clothes = Rs 1x/3 s 1000alance = Rs 2x/3   Money spent on food = 1/5 of 2x/3 = Rs 2x/15   s 1000alance = 2x/3 - 2x/15 = Rs 8x/15   Money spent on travel = 1/4 of 8x/15 = Rs 2x/15 = 8x/15 - 2x/15 = 6x/15 = Rs2x/5   Therefore 2x/5 = 400 = 1000   ANSWER:s 1000
Answer: B
If p is the product of the integers from 1 to 34, inclusive, what is the greatest integer k for which 3^k is a factor of p?	Choose the correct choice from the following answers.
A) 11
B) 13
C) 15
D) 17
E) 19

Solution: 34! has 3, 6, 9,....30, 33 as factors, which are 11 multiples of 3.   We need to add 4 more to these 11 because of 9, 18, and 27.   The greatest integer of k is 15.   The answer is 15.
Answer: C
In Mr. Mehta's family, there are one grandfather, two fathers, two mothers, one father-in-law, one mother-in-law, one brother, two sisters, two sons, two daughters, etc. You have to give the minimal number of members
Choose the most appropriate option:
A) 4 B) 5 C) 6 D) 7 E) 8

Solution: one grandfather and his wife.   grandfather's first son and his wife.   grandfather's second son alone.   2 daughters from first son.   total minimal no =7.   ANSWER:7
Answer: D
If P(A) = 5/7 and P (B) = 2/5, find P (A n B) if A and B are independent events.  Choices:
A) 7/25
B) 3/25
C) 8/25
D) 2/7
E) 3/17

Solution: P (A n B) = P(A) . P(B)   P (A n B) = 5/7 . 2/5   P (A n B) = 2/7.   2/7
Answer: D
A is three times as fast as B. If B alone can do a piece of work in 12 days, in what time can A and B together complete the work?  Choose the correct choice from the following answers:
A) 5	B) 8	C) 3	D) 2	E) 12

Solution: A can do the work in 12/3 i.e., 4 days.   A and B's one day's work = 1/4 + 1/12 = (3+ 1)/12 = 1/3   So A and B together can do the work in 3 days.   Answer:3
Answer: C
. A car covers a distance of 495 km in 5 hours. Find its speed? Choose the correct choice from the following answers:  A) 99  B) 100  C) 102  D) 288  E) 2761

Solution: 495/5= 
495/5 = 99
99 kmph   99nswer: 99
Answer: A
1/2 is what percent of 1/3
Choose the correct choice:
A) 150% B) 200% C) 250% D) 300% E) 400%

Solution: Explanation:   1/2/1/3 * 100 = 1/2 * 3/1 * 100= 
1/2 * 3/1 * 100 = 150
150 %   150%nswer: Option 150%
Answer: A
4 friends want to buy a company from the $150 000 cost. However, they have only $20 000 to be put in the company. How much partner will they have to fetch in more and which will be the equal value for every partner (The value should not contain of decimals) ?
Choose the correct choice from the following
A) 2	B) 3	C) 4	D) 5	E) 6

Solution: 4 friends * $ 20 000 = $ 100 000 total   $150 000 - $ 100 000 = $ 50 000 / $ 20 000 = 2.5 partners (impossible and not equal)   1+5+0+0+0+0= 
1+5+0+0+0+0 = 6
6 (even) so the answer have to be even (2 partners, 4 partners, 6 partners)   $150 000/ (4 actuals partners + 2 new partners)= $25 000 but they can only afford $ 20 000. The option is reject   $150 000/ (4 actuals partners + 4 new partners) = $ 18 750   We don't need to go further because $18 750 is the close number to $20 000. Answer is 4, 4 more partners   4orrect option: 4) 4 partners
Answer: C
A man took a loan from a bank at the rate of 13% p.a. simple interest.After 3 years he had to pay Rs. 5400 interest only for the period.The principal amount borrowed by him was : Choose the correct choice from the following options
A) Rs. 12,000.15 B) Rs. 13846.15 C) Rs. 15,000.15 D) Rs. 20,000.15 E) None

Solution: Solution   Principal = Rs.(100x5400/13x3)= Rs. 13846.15.   Answer Rs. 13846.15
Answer: B
A peacock of flying speed 5 km/h is sitiing on a top of a wooden pole of height 10m. There is a hole in the pole downwards and a snake is approaching that hole which is 21m away from the snake.How much time it will take for the peacock to catch the snake before it enters the hole.
Choose the most appropriate option:
A) 14.73 seconds B) 16.73 seconds C) 15.73 seconds D) 17.73 seconds E) 18.73 seconds

Solution: Speed of the peacock = 5 km/h(given)   Distance of the pole = 10m(given)   Distance between the pole hole and snake = 21m(given)   Therefore, we have to first find the distance between the peacock and the snake.   This can be done by using Pythagora's Theorem,   Therefore, 21^2 + 10^2 = 23.26 metre(approx)   Speed of the peacock = 5 km/h or 1.39 metre/sec(approx)   Now, we know can find the time for peacock to catch the snake by,   Time = Distance/Speed   = 23.26/1.39   = 16.73 seconds(approx)   Therefore, the required time for peacock to catch the snake before it enters the hole of the pole is 16.73 seconds.   ANSWER:16.73 seconds
Answer: B
Machine Y takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine Y to make 40 widgets?	Pick one
A) 5 B) 6 C) 8 D) 10 E) 12

Solution: i approached this one by plugging in numbers...started with C.   if 40 are made in 8 hours, then 20 are made in 4 hours. so time of Y is 4, and time of B is 2.   rate together: 20/4 + 20/2 = 5+10= 
5+10 = 15
15. so in 1 hour, together make 15 widgets. in 3 hours= 45. way too much. we can eliminate right away C, B, and A - because B and Y reduces the time - the total # of widgets made will be even higher.   now between D and E -> try only one ..if it doesn't work, then the other one is the answer.   i picked E:   12h to make 40 widgets, and 6 hours to make 20. this is the time of Y. time of B=4 hours.   20/6 + 20/4 = 10/3 + 20/4   find LCM of 3 and 4 = 12. multiply first by 4, and second by 3:   40+60/12 = 100/12   divide by 4:   25/3   so this is the rate given.   12 is the correct answer
Answer: E
One-quarter of one-seventh of a land is sold for Rs. 30,000. What is the value of an eight thirty-fifth of load?	Choose one:
A) Rs. 1,92,2300. B) Rs. 1,92,2450. C) Rs. 1,92,2400. D) Rs. 1,92,2000. E) none of these

Solution: One-quarter of one-seventh = 1/4 x 1/7   = 1/28   Now, 1/28 of a land costs = Rs. 30,000   Thus, 8/35 of the land will cost = 30,000 x 28 x 8/35   = Rs. 1,92,2000.   ANSWER:Rs. 1,92,2000.
Answer: D
A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is? Choose the correct option:	A) 33.9	B) 33.6	C) 33.3	D) 33.1	E) 33.2

Solution: Let B = 100   A = 50   33.3 * (150/100) = 50   333.3 = 100   33.3 = 33.3 then '33.3' 33.3heapest   Answer: 33.3
Answer: C
From the below series find the remainder? 1201 × 1203 ×1205 × 1207 is divided by 6 Choose the most appropriate option
A) 3
B) 4
C) 6
D) 7
E) 8

Solution: If you don't know the above rule, this problem is really calculation intensive.   But by applying the above rule, when 1201, 1201, 1203, 1204 divided by 6, leaves remainders 1, 3, 5, 1. The product of these remainders = 15.   When 15 is divided by 6, Remainder is 3   3
Answer: A
An book was sold after a discount of 20% and there was a gain of 20%. If the profit made on it was $6 less than the discount offered on it, find its selling price?  Choose the correct answer.
A) $66  B) $38  C) $77  D) $72  E) $63

Solution: $72   $72   Let CP = $100x   SP = $120x   MP = 120x/80 * 100 = $150x   $72 120 /80 * 100= 
120 /80 * 100 = 150
$150x   $72= $150x - $120x = $30x   $72 - P 150  -  120= 
150  -  120 = 30
$30x   $72 - P= 30x - 20x = $6, 10x = $6   120x = 120/10 * 6= 
120/10 * 6 = 72
$72
Answer: D
Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?	Choose the correct choice from the following options.
A) 3:7	B) 9:31	C) 7:21	D) 9:25	E) 7:6

Solution: 1/4 : 3/4 = (1:3)5 = 5:15   1/5 : 4/5 = (1:4)4 = 4:16 = > 9:31   ANSWER 9:31
Answer: B
Twelve kilograms of oranges contained 98% of water. If the next day the concentration of water decreased by 2%, what was the new weight of the oranges, in kilograms? Answers
A) 6
B) 4.8
C) 2.5
D) 2
E) 1

Solution: Twelve kilograms of oranges contained 98% of water. If the next day the concentration of water decreased by 2%, what was the new weight of the oranges, in kilograms?   (A) 6   (B) 4.8   (C) 2.5   (D) 2   (E) 1   If A is the answer, then the question means that the concentration of water the newt day became 96%.   Out of 12 kilograms 98%, or 11.76 kilograms was water and 0.24 kilograms was non-water.   The next day, after some water evaporated, oranges became 96% water and 4% of non-water, so the next day 0.24 kilograms of non-water composed 4% of oranges, which means that the new weight of the oranges was x*0.04=0.24 --> x=6 kilograms.   6nswer: 6.
Answer: A
The greatest number of four digits which is divisible by 21, 25, 40 and 75 is:  Choose the correct choice from the following.
A) 9000  B) 8400  C) 9600  D) 9800  E) 9200

Solution: Greatest number of 4-digits is 9999.   L.C.M. of 21, 25, 40 and 75 is 4200.   On dividing 9999 by 4200, the remainder is 1599.   Required number  (9999 - 1599)= 
 (9999 - 1599) = 8_400
8400.   Answer: Option 8400
Answer: B
On a certain test, Bill scored 20 more points than John, but half as many points as Sue. If the sum of the scores of the three students was 220 points, how many points did Bill receive?
Options: A) 30 B) 40 C) 50 D) 60 E) 100

Solution: consider john's points as x   so bill's points are x +20   So sue's points are 2x +40   total of all three students is 4x +60, but this total is given as 220   x = 40   so bill's points = 40 +20= 
40 +20 = 60
60   correct answer option 60
Answer: D
In how many ways can a cricket eleven be chosen out of a batch
of 15 players. Choose the correct choice from the following answers:	A) 1255	B) 1355	C) 1340	D) 1365	E) 1300

Solution: Required number of ways   = 15C 11 = 15C (15-11)   = 15 C 4   15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1   = 1365   ANSWER 1365
Answer: D
Joe had an average of 95 on his first 5 tests. He had an average score of 90 on his first 6 tests. What did he score on the 6th test?	Pick one.
A) 95	B) 85	C) 65	D) 45	E) 30

Solution: The sum of Joe's first 5 tests is 95 * 5 and the sum of his first 6 tests is 90*6, so he received 90*6 - 95*5 on his 6th test. You can do the arithmetic and the correct answer is 65.
Answer: C
Rory and Roxy, both house cats, love to hunt and chase insects. Since Rory only has three paws, Roxy is able to catch approximately 2.5 times more insects than Rory in one day.
After 3 days of hunting, Roxy was able to catch 23 insects. Assuming that both cats had an equal amount of hunting time, how many total insects can the two of them catch after 18 days of hunting?
Please round to the nearest whole number.  Select:	A) 143	B) 193	C) 111	D) 194	E) 138

Solution: 18 (total days) is divisible by 3 (initial data given days) 6 times,   therefore we can easily find Roxy's total for the 18 day period is 23 x 6 = 138 insects   Taking Roxy's total, we can then find Rory's total by dividing 138 by 2.5 = 55.2 insects   To find the pair's total, we add   138 + 55.2= 
  138 + 55.2 = 193.2
193.2   This number rounded to nearest whole number is 193, answer B.   You could also divide 23 by 2.5 to get 9.2, which would be Rory's total for the first 3 days.   You could then multiply again, (23x6) + (9.2x6)= 138 + 55.2= 
138 + 55.2 = 193.2
193.2
Answer: B
An escalator moves towards the top level at the rate of 7 ft.sec and its length is 180 feet. If a person walks on the moving escalator at the rate of 2 feet per second towards the top level, how much time does he take to cover the entire length. Choose the most appropriate option: A) 5sec B) 25sec C) 20sec D) 15sec E) 10sec

Solution: Explanation :   Time taken to cover the entire length = tot.dist/resultant speed = 180/ (7+2)= 
180/ (7+2) = 20
20sec   Answer : 20sec
Answer: C
In a cricket team, the average of eleven players is 28 years. Out of these, the average ages of three groups of three players each are 25 years, 28 years and 38 years respectively. If in these groups, the captain and the youngest player are not included, and the captain is eleven years older than the youngest player, what is the age of the captain ?	Choose the correct choice from the following answers:
A) 23 years
B) 34 years
C) 35 years
D) 36 years
E) 37 years

Solution: Explanation :   Let the age of youngest player be x.   Then, age of the captain = (x + 11).   => 3*25 + 3*28 + 3*38 + x + x + 11= 
+ 11 = 11
11*28.=> 75+84+114+2x+11=308   so 2x = 24   so x = 12.   Age of the captain = (x+11)   = 23 years.   23 yearsnswer : 23 years
Answer: A
Bobby bought 2 shares, and which he sold for $96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares Bobby had...  Choose the correct choice from the following options
A) a profit of 10 B) a profit of 8 C) a loss of 8 D) a loss of 10 E) neither a profit nor a loss

Solution: a loss of 8ost of the first stock: 96/1.2= 
96/1.2 = 80
80, so profit from it  96-80= 
 96-80 = 16
16   a loss of 8ost of the second stock:  96/0.8= 
 96/0.8 = 120
120, so loss from it 96-120=-24   Overall loss 16-24=-8   Answer: a loss of 8.
Answer: C
In a school of 850 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities? Choose the most appropriate option:  A) 176  B) 179  C) 153  D) 167  E) 107

Solution: 44 + 28 + 10= 
44 + 28 + 10 = 82
82%   100 – 82= 18%    850 * 18/100= 
 850 * 18/100 = 153
153   Answer: 153
Answer: C
A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.	Choose the most appropriate option:
A) 24 kmph
B) 34 kmph
C) 44 kmph
D) 14 kmph
E) 22 kmph

Solution: 24 kmph   24 kmph   Total time taken = x/40 + 2x/20 hours   = 5x/40 = x/8 hours   24 kmphverage speed = 3x/(x/8) = 24 kmph
Answer: A
Linda and Angela contract to paint a neighbor's house. Even though Linda
spends 10% more time painting the house than Angela, each receives a payment
of m dollars when the work is completed. If Angela decides to pay Linda n
dollars so that they would have received the same compensation per hour
worked, what is n in terms of m? Choose the correct choice from the following
A) A)(1/21)m	B) B)(1/3)m	C) C)(1/4)m	D) D)(1/5)m	E) E)(1/6)m

Solution: let angela work for 10hrs and get 1100 rs. (m =1050)   According to question, linda works 10% more time and gets the same amount. so let linda work 11hrs and get 1050 rs.   so they do a total of  10 +11= 
 10 +11 = 21
21 hrs of work and get 2100 rs together . The question basically asks to equalise their payment. so a total of 2100 rs is received by them and they do 21 hrs work together. average rate will be  2100/21= 
 2100/21 = 100
100 rs per hr. so linda should get 11*100= 
11*100 = 1_100
1100 rs. But she got only 1050. so angela should give 50 rs to linda. answer= 50/1050 =1/21   answer (1/21)m
Answer: A