divelab/Sys2Bench huggingface dataset:
Question: A rectangular circuit board is designed to have a width of W inches, a length of L inches, a perimeter of P inches, and an area of D square inches. Which of the following equations must be true?
Options:
A)2W^2 + PW + 2D = 0
B)2W^2 − PW − 2D = 0
C)2W^2 − PW + 2D = 0
D)W^2 + PW + D = 0
E)W^2 − PW + 2D = 0
Rationale: P = 2(L+W)-----------------1)
A= LW------------------------2)
option A is not possible why ?? because all the terms are positive.
lets try option B , put value of P and A from 1 and 2 we have,
2W^2-2(L+W)W + 2(LW)
2W^2 - 2LW - 2W^2 + 2LW=0.
hence answer is C.
Answer: C
Question: Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%?
Options:
A)2888
B)2999
C)2799
D)1000
E)2881
Rationale: (x*5*1)/100 + [(2500 - x)*6*1]/100 = 140
X = 1000
Answer: D
Answer: D
Question: When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?
Options:
A)√10/2
B)√10
C)4
D)5
E)10
Rationale: V = pi(R^2)(H)
We have the Volume (22 cubic meters) and the Height (0.7 meters)...
22 = pi(R^2)(0.7)
pi = about 3.14
.7(pi) = about 2.2
22 = 2.2(R^2)
10 = R^2
\sqrt{10} = R
Final Answer:
B
Answer: B
Question: On a bright morning, Ashley and Cecilia decided to take out their old cars from the garage and check their speeds. Just to make things for interesting, they decided to race and find out whose car was fast. So they halted their car at the starting point and began with full throttle till the finish line.
When both the car crossed the finishing line, they realized that Ashley's car was 1.2 times faster than Cecelia. Also, Cecelia had reached the finishing line 1 minutes 30 seconds later than Ashley. Ashley's car had reached the finishing line at an average speed of 60 Km/h.
With all this data given, can you find out the total distance between the starting and the finishing lines?
Options:
A)6.5Km
B)8.5Km
C)7.4Km
D)7.5Km
E)7.7Km
Rationale: D
7.5Km
Explanation:
Denoting Ashley with A and Cecelia with C
Speed A = 60 km/hr = 1.2 x Speed C [km/hr] = 1 km/ min
Hence Speed C = 60/1.2 [km/hr] = 50 [km/hr] = 5/6 km/ min
Time C = D [km] /Speed C [km/min] = D/Speed C [min] = D/(5/6) min = 6D/5 min = 1.2 D min
Time A = D [km] /Speed A [km/min] = D/Speed A [min] = D/(1) min = D min
Since Time C � Time A = 1.5 min
Then (1.2 � 1)D min = 0.2D min = 1.5 min
Hence D = 1.5/0.2 km = 1.5*5 = 7.5 km
The total distance as calculated above is 7.5 Km.
Answer: D
Question: What is greatest positive integer n such that 2^n is a factor of 12^14?
Options:
A)a)10
B)b)12
C)c)16
D)d)20
E)e)28
Rationale: The given number is 12^14
=(2*2*3)^14
=(2^28)*(3^14)
So the greatest possible value for n such that 2^n can be factor of given number is 28.
Answer E
Answer: E
Question: On a certain plane, 2/5 of the passengers speak French and 3/4 speak Hebrew. If all of the passengers on the plane speak at least one of these languages, what is the smallest number of passengers that could be on the plane?
Options:
A)12
B)15
C)40
D)54
E)60
Rationale: Assume the total members = x
French = .4x
Hebrew = .75x
French + Hebrew = 1.15x, but this is not possible hence 15 people speak both languages.
Only French = .25x, Only Hebrew = .6x, both = .15x
Since these are all people, all of these should be whole numbers.
Checking the options:
A. 12. Only Hebrew = 12*0.6 = 7.2 We do not get the people as whole numbers. INCORRECT
B. 15. Only French = 0.25*15 Again we do not get the people as whole numbers. INCORRECT
C. 40 Only Farsi = .25*40 = 10, Only Hebrew = .6*40 = 24, both = .15*40 = 6. We have the people as whole numbers. CORRECT
D. 54
E. 60
Since we have to find the lowest number, no need to calculate for the rest of the options.
Correct Option: C
Answer: C
Question: If there are 6 seats and 3 students, in how many ways can they be seated?
Options:
A)120
B)124
C)128
D)132
E)136
Rationale: The first student has 6 choices, the second student has 5 choices, and the third student has 4 choices. The number of ways to sit is 6*5*4 = 120.
The answer is A.
Answer: A
Question: Can N and can В are both right circular cylinders. The radius of can N is twice the radius of can B, while the height of can N is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can N with the same brand of gasoline?
Options:
A) $1
B) $2
C) $4
D) $8
E) $16
Rationale: Let x be the radius of b and 2h be the height of B. Therefore, radius of N = 2x and height = h
Vol of b = 3.14*x^2*2h
Vol of a = 3.14*4x^2*h
cost to fill half of B = $4 --> cost to fill full B = $8
--> 3.14*x^2*2h = 8 --> 3.14*x^2*h = 4 --> 4*(3.14*x^2*h) = $16
Ans E
Answer: E
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 880 cm is?
Options:
A)A)15
B)B)10
C)C)14
D)D)12
E)E)11
Rationale: 2 * 22/7 * 14 * x = 880 => x = 10
ANSWER:B
Answer: B
Question: A desalination process is able to remove 2/3 of salt in each cycle. If we have 1 liter of sea water that has 5% salt (i.e. 5 g in a liter), how much salt would have been removed from the liter of water after 3 cycles of the desalination process?
Options:
A)4.15
B)4.21
C)4.52
D)4.81
E)4.93
Rationale: X is the initial quantity of salt in the water.
After a cycle of desalination the quantity of salt left would be X1=X-2/3X i.e. X1=1/3X
Same thing for X2, X3 respectively representing the quantity of salt left after 2, 3 cycles of desalination.
So we have:
X1=1/3 X
X2=1/3 X1
X3=1/3 X2
By multiplying both ends of the equations we get:
X1*X2*X3 = (1/3)^3 X*X1*X2
Simplification leaves us with:
X3 = (1/3)^3 X
X3 is the quantity of salt left after three cycles. So the cumulative quantity of salt (Q3) which has been removed after 3 cycles is: Q3= X-X3=X-(1/3)^3 X i.e. Q3 = X (1-(1/3)^3)
In this case, given X was: X=5 g
So we have Q3=5 * (1-1/27) = 5 * 26/27 = 4.814 g rounded Q3=4.81
Answer: D
Answer: D
Question: The expression pq+p is odd when the p and q are integers. Which of the following expressions must be even?
Options:
A)p
B)q
C)p + q
D)pq - p
E)p + q^2
Rationale: pq+p is odd
p and q are integers
If p were even pq+p would be even despite any value of q.
q can't be odd, so q must be even.
Ans : B
Answer: B
Question: What will be the ratio of simple interest earned by certain amount at the same rate of interest for 12 years and that for 28 years?
Options:
A)5 : 7
B)4 : 7
C)3 : 7
D)Data inadequate
E)None of these
Rationale: Let the principal be P and rate of interest be R%.
∴ Required Ratio = [(P×R×12/100) /(P×R×28/100)]=12PR/28PR=12/28=3:7
Answer C
Answer: C
Question: Two trains are moving in opposite directions with speed of 110 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds
Options:
A)26
B)48
C)47
D)36
E)25
Rationale: Explanation:
Relative speed = 110+90 = 200 km/hr (Since both trains are moving in opposite directions)
Total distance = 1.1+.9 = 2km
Time = 2/200 hr = 1/100 hr = 3600/100 = 36 seconds
Answer: Option D
Answer: D
Question: There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'P, then how many triangles can be determined with the 15 points that contain the point P?
Options:
A)91
B)105
C)182
D)210
E)455
Rationale: Fist point is P which is fixed so can be selected in 1 way
Second point can be selected in 14 ways
Third point can be selected in 13 ways
so total ways = 1x14x13 = 182
but answer is 91 which is 182/2=C
Answer: C
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 42 years now, the son's age 5 years back was?
Options:
A)12yr
B)15yr
C)14yr
D)16yr
E)20yr
Rationale: Let the son's present age be x years
Then, 42-x = x
x = 21
Son's age 5 years back = 21-5 = 16years
Answer is D
Answer: D
Question: How many odd prime numbers are there less than 50?
Options:
A)15
B)1
C)2
D)14
E)17
Rationale: Odd prime number less than 50 :3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
There is 14 the odd prime number
Answer is D
Answer: D
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?
Options:
A)100
B)80
C)70
D)20
E)40
Rationale: A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
5 years, their ages will be 45 and 25.
Sum of their ages = 45 + 25 = 70.
answer is C.
Answer: C
Question: A person crosses a 600m long street in 4 minnutes. What is his speed in km per hour?
Options:
A)5.8km/hr
B)7.2km/hr
C)9km/hr
D)2.5km/hr
E)3km/hr
Rationale: Speed = 600/4*60 = 2.5m/sec
=2.5*18/5
=9km/hr
Answer is C
Answer: C
Question: P alone can complete a job in 7 days. The work done by Q alone in one day is equal to one-sixth of the work done by P alone in one day. In how many days can the work be completed if P and Q work together?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: P's rate is 1/7
Q's rate is 1/42
The combined rate is 1/7 + 1/42 = 1/6
If they work together, the job will take 6 days.
The answer is E.
Answer: E
Question: A man rows his boat 90 km downstream and 5` km upstream, taking 3 hours each time. Find the speed of the stream?
Options:
A)7 kmph
B)5 kmph
C)2 kmph
D)8 kmph
E)1 kmph
Rationale: Speed downstream = d/t = 90/(3) = 30 kmph
Speed upstream = d/t = 51/(3) = 17 kmph
The speed of the stream = (30 - 17)/2 = 7 kmph
Answer:A
Answer: A
Question: Two persons start running simultaneously around a circular track of length 200 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
Options:
A)11
B)10
C)18
D)27
E)12
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 200 / (15 + 25)5/18 = 200* 18 / 40 * 5 = 18 seconds.
Answer: C
Answer: C
Question: If you drew a dot on the edge of a wheel and traced the path of the dot as the wheel rolled one complete revolution along a line, then the path formed would be called a cycloid, combining both forward and circular motion. What is the length of the path formed by one complete revolution? Assume the wheel has a radius of r.
Options:
A)5r
B)7r
C)4r
D)8r
E)9r
Rationale: Imagine the circle resting on coordinate (0,0) and moving east.
Also magine the point on the circle to start at (0,0).
Let t be the angle between the point on the circle and the center of the circle.
The position of the point on the circle, relative to t, is:
x = rt - r×sin(t)
y = r - r×cos(t)
Taking the derivatives:
dx/dt = r - r×cos(t)
dy/dt = r×sin(t)
The change in arc length can be defined as ( (dx/dt)2 + (dy/dt)2 ) 1/2.
So the total arc length is the integral from 0 to 2pi of ( (dx/dt)2 + (dy/dt)2 ) 1/2.
After a few steps this integral becomes:
r×21/2 × (1-cos(t))1/2.
Using the hint:
r×21/2 × 21/2 × integral of sin(t/2) dt from 0 to 2×pi
= 2×r × (-2×cos(t/w) from 2×pi to 0)
= 8r
Hint: (1-cos(t))0.5 = 20.5×sin(t/2)
Answer: D
Question: Diane find 6 and a half cans of paint are just enough to paint one third of her room. How many more cans of paint will she need to finish her room and paint a second room of the same size?
Options:
A)5
B)7 and a half
C)10
D)32 and a half
E)35
Rationale: She will need 13 cans to paint the rest of this room and 19 1/2 for the next room for a total of 32 1/2 cans.
D
Answer: D
Question: A restaurant meal cost $31.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then total amount paid must have been between:
Options:
A)$40 and $42
B)$39 and $41
C)$38 and 40
D)$37 and $39
E)$35 and $37
Rationale: let tip=t
meal cost=31.50
range of tip = from 10% of 31.5 to 15% of 35.5 = 3.55 to 5.325
hence range of amount paid= 31.5+T= 35.05 to 36.825
ANSWER:E
Answer: E
Question: A bullock cart has to cover a distance of 80km in 10hrs. If it covers half of the journey in 3/5th time. what should be its speed to cover the remaining distance in the time left.
Options:
A)8 km/h
B)10 km/h
C)12 km/h
D)14 km/h
E)16 km/h
Rationale: Time left = 10 - 3/5*10
= 4 hr 10 km/h
speed =40 km /4 hr
=10 kmph
Answer : B.
Answer: B
Question: 8, 12, 18, 27, 40.5, (...)
Options:
A)60.75
B)62
C)58
D)60.5
E)62.5
Rationale: Explanation :
8
(8×3)÷ 2 = 12
(12×3)÷ 2 = 18
(18×3)÷ 2 = 27
(27×3)÷ 2 = 40.5
(40.5×3)÷ 2 = 60.75
Answer : Option A
Answer: A
Question: Ada and Paul received their scores on three tests. On the first test, Ada's score was 10 points higher than Paul's score. On the second test, Ada's score was 4 points higher than Paul's score. If Paul's average (arithmetic mean) score on the three tests was 5 points higher than Ada's average score on the three tests, then Paul's score on the third test was how many points higher than Ada's score?
Options:
A)9
B)14
C)17
D)29
E)25
Rationale: My take is Option D (23)
I followed a simple approach (explained below):
Test 1: Ada's score = Paul's score + 10
Test 2: Ada's score = Paul's score + 4
Avg. of Paul's score = 5 points higher than Avg. of Ada's score
This implies that : Sum of Paul's score [3 Tests] = 15 points higher than Sum of Ada's score [3 Tests] (9 points higher since 3 points were given in terms of average of 3 scores)
So, Paul needs to score 29 points higher than Ada in Test 3, since Paul needs to compensate for the lower score in test 1 and Test 2 ( 29 = 10 + 4 + 15)
D
Answer: D
Question: If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 420, what is the least possible value of n?
Options:
A)5
B)7
C)9
D)11
E)12
Rationale: 420 = 2*2*3*5*7, so n must be at least 7.
The answer is B.
Answer: B
Question: How many 3 digit positive integers exist that when divided by 7 leave a remainder of 5?
Options:
A)128
B)142
C)143
D)141
E)129
Rationale: Explanatory Answer
Step 1: Find the first and last term of the series
The smallest 3-digit positive integer that leaves a remainder of 5 when divided by 7 is 103.
The largest 3-digit positive integer that leaves a remainder of 5 when divided by 7 is 999.
The series of numbers that satisfy the condition that the number should leave a remainder of 5 when divided by 7 is an A.P (arithmetic progression) with the first term being 103 and the last term being 999. The common difference of the sequence is 7.
Step 2: Compute the number of terms
In an A.P, the last term l = a + (n - 1) * d, where 'a' is the first term, 'n' is the number of terms of the series and 'd' is the common difference.
Therefore, 999 = 103 + (n - 1) * 7
Or 999 - 103 = (n - 1) * 7
Or 896 = (n - 1) * 7
So, n - 1 = 128 or n = 129
Choice E is the correct answer.
Answer: E
Question: The 7th grade French and Spanish classes each have 23 students in them, and there are seven students in the 7th grade taking both languages. If everyone in the 7th grade is in at least one of the two language classes, how many students are taking just one of the two classes?
Options:
A)26
B)28
C)30
D)32
E)34
Rationale: French class + Spanish class = 46 students.
Seven students are in both classes so they were counted twice.
The number of students taking just one class is 46 - 2(7) = 32.
The answer is D.
Answer: D
Question: A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio Q of revenue from car sales in 1996 to revenue from truck sales in 1996?
Options:
A) 1:2
B) 4:5
C) 1:1
D) 3:2
E) 5:3
Rationale: A.. I have probably solved this question 3-4 times by now.. Remember the answer.. 1:2
Answer: A
Question: If p and q are prime numbers, how many divisors does the product p^3 * q^7 have?
Options:
A)25
B)30
C)32
D)35
E)40
Rationale: when a number N=a^x*b^y, where a and b are prime numbers, and x, y are positive integers, the number of divisors of N=(x+1)(y+1)
Therefore, the answer is C. 4*8=32
Answer: C
Question: The second day of a month is Friday, What will be the last day of the next month which has 31 days?
Options:
A)Friday
B)Saturday
C)Wednesday
D)Data inadequate
E)Thursday
Rationale: Explanation:
We cannot find out the answer because the number of days of the current month is not given.
Answer: Option D
Answer: D
Question: John and Peter are among the nine players a basketball coach can choose from to field a five-player team. If all five players are chosen at random, what is the probability of choosing a team that includes John and Peter?
Options:
A)1/9
B)1/6
C)2/9
D)5/18
E)1/3
Rationale: Total possible ways of selecting a 5-member team:
a combination problem, not permutation since order does not matter:
9x8x7x6x5/(5x4x3x2x1) = 126.
The ways of selecting a 5-member team including John and Peter:
It is again a combination, not permutation. Since John and Peter are already included, you don't bother about them any more. The possible ways will be the combination of the rest of the 3 players from the rest of 7 player:
7x6x5/(3x2x1) = 35.
so the probability = 35/126 = 5/18.
Answer is D: 5/18.
Answer: D
Question: In the Land of Oz only one or two-letter words are used. The local language has 64 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?
Options:
A)65
B)66
C)67
D)131
E)128
Rationale: The answer to the question is indeed E. The problem with above solutions is that they do not consider words like AA, BB, ...
The number of 1 letter words (X) that can be made from 64 letters is 64;
The number of 2 letter words (XX) that can be made from 64 letters is 64*64, since each X can take 64 values.
Total: 64+64*64.
Similarly:
The number of 1 letter words (X) that can be made from 63 letters is 63;
The number of 2 letter words (XX) that can be made from 63 letters is 63*63, since each X can take 63 values.
Total: 63+63*63.
The difference is (64+64*64)-(63+63*63)=128.
Answer: E.
Answer: E
Question: A car started running at a speed of 34 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.
Options:
A)43 km
B)76 km
C)25 km
D)15 km
E)30 km
Rationale: A
43 km
The total distance covered by the car in the first 10 hours = 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 + 50 + 52= sum of 10 terms in AP whose first term is 34 and last term is 52 = 10/2 [34 + 52] = 430 km.
Answer: A
Question: Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 70kmph, find the rate at which the train B runs.
Options:
A)40
B)60
C)120
D)105
E)100
Rationale: If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:
Sa/Sb = √(b/a)
i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.
Sa/Sb = √(4/9) = 2/3
This gives us that the ratio of the speed of A : speed of B as 2:3.
Since speed of A is 70 kmph, speed of B must be 70*(3/2) = 105 kmph
Answer D
Answer: D
Question: A monkey ascends a greased pole 6 meters high. He ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute. If this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ?
Options:
A)9th minute
B)21st minute
C)11th minute
D)22nd minute
E)13th minute
Rationale: The money is climbing 1meter in 2min. This pattern will go on till he reaches 4 meters. I mean this will continue for first 4*2=8 mins. he would have reached 4meters. After that he will climb 2meters and he will reach the pole. So total time taken = 8 + 1 = 9mins.
So, asnwer will be A
Answer: A
Question: A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the probability T that the 2 apples selected will include the spoiled one?
Options:
A)a. 1/5
B)b. 3/10
C)c. 2/5
D)d. 1/2
E)e. 3/5
Rationale: there can be two ways in which one can select a spoiled apple and a good apple.
1. you pick the spoiled one first and the good one later..
Prob of picking bad one = 1/5 (one bad apple)
Prob of picking a good one from the remaining 4 good apples (4/4 =1)
therefore the total prob for case 1 = i/5 * 1 = 1/5
Total prob T= porb1 + prob2 = 1/5+1/5 = 2/5.C
Answer: C
Question: A Prototype fuel-efficient car (P-Car) is estimated to get 87% more miles per gallon of gasoline
than does a traditional fuel-efficient car (T-Car). However, the P-Car requires a special type
of gasoline that costs 27% more per gallon than does the gasoline used by a T-Car. If the two
cars are driven the same distance, what percent less than the money spent on gasoline for the
T-Car is the money spent on gasoline for the P-Car?
Options:
A)16 2/3%
B)32 %
C)50%
D)60%
E)66 2/3 %
Rationale: Assumption
Miles/Gallon
T = 100
P = 187 ( 87% more)
$/gallon
T = 100
P = 127 (27% more)
Miles
100 for both
Cost = (Miles X $/ Gallon)/ M/gallon
T = 100
P = 67.9
Hence 100 - 67.9 = 32%
Ans B
Answer: B
Question: Raja's Bank's saving amount is decreased 40% due to loan payment and current balance is Rs.30000. Find the actual balance before deduction?
Options:
A)8000
B)8500
C)50000
D)9500
E)10000
Rationale: 40% decreased
60% Balance = 30000
100% = 30000/60*100 = 50000
Answer : C
Answer: C
Question: If each side of a square is increased by 325% in length, find the percentage change in its area?
Options:
A)54%
B)957%
C)956.25%
D)958.25%
E)959.50%
Rationale: let each side of the square be a , then area = a x a
New side = 325a / 100 = 13a / 4
New area =(13a x 13a) / (4 x 4) = (25a²/16)
increased area== (169a²/16) - a²
Increase %= [(153a²/16 ) x (1/a² ) x 100]% = 956.25%
answer :C
Answer: C
Question: The present population of a town is 220. Population increase rate is 10% p.a. Find the population of town after 1 years?
Options:
A)100
B)120
C)200
D)242
E)250
Rationale: P = 220
R = 10%
Required population of town = P*(1 + R/100)^T
= 220*(1 + 10/100)
= 220*(11/10)
= 242
Answer is D
Answer: D
Question: The average age of a group of 10 friends is 15 yr. If one friend leaves the group, the average becomes 16 yr. Find the age of the friend who left the group.
Options:
A)5 yr
B)4 yr
C)6 yr
D)None of these
E)Cannot be determined
Rationale: Answer
Age of friend left = Previous average of the age - Number of persons present x Increase in average age
= 15 - ( 10-1 ) x ( 16-15 )
= 15- 9 x 1
= 15 - 9 = 6yr
Correct Option: C
Answer: C
Question: The prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 10% and that of tea dropped by 20%. if in july , a mixture containing equal quantities of tea and coffee costs 50/kg. how much did a kg of coffee cost in june ?
Options:
A)50
B)45
C)52.63
D)40
E)35
Rationale: Let the price of tea and coffee be x per kg in June.
Price of tea in July = 1.1x
Price of coffee in July = 0.8x .
In July the price of 1/2 kg (500gm) of tea and 1/2 kg (500gm) of coffee (equal quantities) = 50
1.1x(1/2) + 0.8x(1/2) = 50
=> x =52.63
C
Answer: C
Question: P and Q started a business investing Rs. 85,000 and Rs. 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
Options:
A)17:6
B)17:0
C)17:4
D)17:2
E)17:3
Rationale: P:Q = 85000 : 15000
= 17:3.
Answer: E
Answer: E