divelab/Sys2Bench huggingface dataset:
Question: Dave can answer each problem on a certain test in 6 minutes. Michael
can answer each problem in 1 minute. Suppose Michael rests for two
hours in the middle of answering the problems but Dave works straight
through the test without stopping. Suppose further that they nish
the test at the same time. How long did it take Dave to answer all the
problems?
Options:
A)2 hours and 10 minutes
B)2 hours and 12 minutes
C)2 hours and 15 minutes
D)2 hours and 18 minutes
E)2 hours and 24 minutes
Rationale: Let n be the number of problems on the test. Then Dave took 6n minutes
to complete the test and Michael took 2 hours and n minutes (i.e., 120 + n minutes) to
complete the test. Therefore, 6n = 120 + n which implies that n = 24. Since the amount
of time to complete the test was the same for Dave and Michael, it took Dave 2 hours and
24 minutes to answer all the problems
correct answer E
Answer: E
Question: Frances can complete a job in 12 hours, and Joan can complete the same job in 9 hours. Frances starts the job at 9 a.m., and stops working at 5 p.m. If Joan starts working at 5 p.m. to complete the job, at what time is the job finished?
Options:
A)6 p.m.
B)7 p.m.
C)8 p.m.
D)10 p.m.
E)12 p.m.
Rationale: Let the total work be 24 units.
Frances can complete 2 units/hr
Joan can complete 2.67 units/hr
Work done by Frances in 8 hours is 16 units ; work left for Joan is 8 units ( 24 - 16)
Time required by Jones to complete the remaining work will be 8/2.67 => 3 hours
Given Jones starts at 5PM , so she would complete the work at 8 PM
Answer will be (C)
Answer: C
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
Options:
A)11
B)88
C)25
D)88
E)21
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75) = 25 points to C.Answer: C
Answer: C
Question: If P is a prime number greater than 100, what is the remainder when P^2 is divided by 4.
Options:
A)4
B)Cannot be determined
C)2
D)3
E)1
Rationale: take square of any prime number
remainder will be 1
Ans E
Answer: E
Question: At present the ratio between the ages of Arun and Deepak is 4:3. After 6 years Arun's age will be 26 years. What is the age of the Deepak?
Options:
A)15
B)20
C)18
D)22
E)35
Rationale: Let the present age of Arun and Deepak be 4x and 3x
4x+6 = 26
4x = 20
x = 5
Deepak's age = 3x = 15 years
Answer is A
Answer: A
Question: In what time will a train 180 meters long cross an electric pole, if its speed is 154 km/hr
Options:
A)5 seconds
B)4.3 seconds
C)3 seconds
D)2.5 seconds
E)None of these
Rationale: Explanation:
First convert speed into m/sec
Speed = 154*(5/18) = 42 m/sec
Time = Distance/speed
= 180/42 = 4.3 seconds
Option B
Answer: B
Question: If (A-B-C+D = 13) and (A+B-C-D = 9), what is the value of (B-D)^2?
Options:
A)4.
B)8.
C)12.
D)16.
E)64.
Rationale: EQ1: A - B - C + D = 13
EQ2: A + B - C - D = 9
(1) Subtract EQ1 from EQ2
A - B - C + D = 13
- A +B - C - D = 9
------------------------
-2B + 2D = 4
(2) Simplify
-B + D = 2
B - D = -2
(B-D)^2 = (-2)^2 = 4
My answer: A
Answer: A
Question: The least number which when divided by 3, 4, 5 and 6 leaves a remainder 6, but when divided by 9 leaves no remainder, is
Options:
A)117
B)126
C)252
D)336
E)None of these
Rationale: Explanation:
L.C.M of 3, 4, 5, 6 = 60
therefore Required Number is of the form 60k+6.
Least value of k for which (60k+6) is divisible by 9 is k = 2
therefore Required Number = (60 x 2+6)=126.
Answer: B
Answer: B
Question: In how many ways can the letters of the word EMULATION be arranged such that all the vowels always appear together?
Options:
A)9!
B)9!*4!
C)5!*4!
D)9!*5!
E)5!*5!
Rationale: The 9 letters can be grouped into 4 consonants and one set of 5 vowels.
The number of ways to arrange 5 units is 5!
Then, for each arrangement, the 5 vowels can be arranged in 5! ways.
The total number of arrangements is 5!*5!
The answer is E.
Answer: E
Question: Thurston wrote an important seven-digit phone number on a napkin, but the last three numbers got smudged. Thurston remembers only that the last three digits contained at least one zero and at least one non-zero integer. If Thurston dials 12 phone numbers by using the readable digits followed by 12 different random combinations of three digits, each with at least one zero and at least one non-zero integer, what is the probability that he will dial the original number correctly?
Options:
A)1/9
B)10/243
C)2/45
D)10/271
E)1/1000000
Rationale: If the last three digits have 1 zero (XX0), the total # of numbers possible is 9*9*3 (multiply by 3 since XX0 can be arranged in 3 ways: XX0, X0X, or 0XX).
If the last three digits have 2 zeros (X00), the total # of numbers possible is 9*3 (multiply by 3 since X00 can be arranged in 3 ways: X00, 00X, or X0X).
P = 12/(9*9*3+9*3) = 2/45.
Answer: C.
Answer: C
Question: If Sharon's weekly salary increased by 16 percent, she would earn $348 per week. If instead, her weekly salary were to increase by 25 percent, how much would she earn per week?
Options:
A) $374
B) $382
C) $385
D) $392
E) $375
Rationale: (348/116)125 =375
In this case long division does not take much time.
(348/116)=3
3*125=375(300+75)
Answer E
Answer: E
Question: If the cost price of 10 articles is equal to the selling price of 20 articles, what is the % profit or loss made by the merchant?
Options:
A)25% loss
B)25% profit
C)20% loss
D)20% profit
E)50% loss
Rationale: Let the cost price of 1 article be $1.
Therefore, cost price of 10 articles = 10 * 1 = $10
The selling price of 20 articles = cost price of 10 articles = $10.
Now, we know the selling price of 20 articles. Let us find the cost price of 20 articles.
Cost price of 20 articles = 20 * 1 = $20.
Therefore, profit made on sale of 20 articles = Selling price of 20 articles - cost price of 20 articles
= 10 - 20 = -$10.
As the profit is in the negative, the merchant has made a loss of $10.
Therefore, % loss = loss/cp * 100
% loss = -10/20 * 100 = 50% loss.
E
Answer: E
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 56 years now, the son's age 4 years back was:
Options:
A)12 years.
B)24 years.
C)17 years.
D)16 years.
E)19 years.
Rationale: Let the son's present age be x years. Then, (56 - x) = x
2x = 56.
x = 28
Son's age 4 years back (28- 4) = 24 years.
ANSWER :B
Answer: B
Question: A container holding 15 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 8 ounces of a solution that is 1 part alcohol to 3 parts water. What is the ratio of alcohol to water in the resulting solution?
Options:
A)2:5
B)3:7
C)3: 5
D)4:7
E)7:16
Rationale: Container 1 has 15 ounces in the ratio 1:2
or,
x+2x=15 gives x(alcohol)=5 and remaining water =10
container 2 has 8 ounces in the ratio 1:3
or,
x+3x=8 gives x(alcohol)=2 and remaining water =6
mixing both we have alcohol=5+2 and water =10+6
ratio thus alcohol/water =7/16
Answer E
Answer: E
Question: After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?
Options:
A)1/2
B)6/7
C)0
D)1/12
E)1/55
Rationale: Explanation :
Answer is Zero. Question is asking whether there is any chances of one letter getting inserted in an improper envelope, but there can-not be onr case as if one gets improper there is another letter who will be inserted in the improper envelope too...
Hence C is the answer.
Answer : C
Answer: C
Question: SID has 13 ten-dollar bills, 11 five-dollar bills, and 17 one-dollar bills. If SID needs to pay exactly $128, what is the least number of bills he will need to use?
Options:
A)16
B)121
C)45
D)456
E)57
Rationale: 128 is the total sum of money.
as we have 13 10 dollar bills so the closest we can get to 128 using the 10 dollar bills is by using 12 * 10 dollar bils
128-120 = 8
so now we need to get 8 from either 5 dollar bills or 1 dollar bills
8 - 5 (use only 1 5 dollar bill) = 3
so we can get 3 from using 3 $1 bills.
Hence 16 ( 12+1+3 )
ANSWER IS A
Answer: A
Question: A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1997. She ended on her
Options:
A)a) thumb
B)b) the index finger
C)c) the middle finger
D)d) the ring finger
E)e) the little finger
Rationale: Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number
By this patter the thumb is also at number 1993 (multiple of 8 + 1)
Hence 1997 has to be the ring finger
Answer is (D)
Answer: D
Question: How many positive integers between 1 and 400 are there such that they are multiples of 25?
Options:
A)12
B)13
C)16
D)15
E)11
Rationale: Multiples of 25 = 25,50,75,-----400
Number of multiples of 25 => 25*16= 400
Answer is C
Answer: C
Question: If A:B is 7:5, B:C is 3:4 and C is 30 then what is the value of A?
Options:
A)31.5
B)25.5
C)32.5
D)33.8
E)35.7
Rationale: A/B=7/5,
B/C=3/4,C=30
B=90/4
4A/90=7/5
A=630/20
A=31.5
ANSWER:A
Answer: A
Question: The sum of four consecutive even numbers is 140. What would be the largest number?
Options:
A)33
B)38
C)70
D)123
E)12
Rationale: Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)
Their sum = 8x - 4 = 140 => x = 18
Smallest number is: 2(x +1) = 38.
Answer: B
Answer: B
Question: Two people measure each other's height, the height of the taller person is H and the height of the other person is L. If the difference in their heights is equal to the average height, what is the Value of H/L
Options:
A)1/3.
B)3.
C)2.
D)1/2.
E)6.
Rationale: Difference = Average
H - L = (H + L)/2,
Solving for H/L gives 3. A quick check, H be 18 and L be 6, 18 - 6 = (18 + 6)/2
B
Answer: B
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is ?
Options:
A)1/26
B)1/07
C)1/22
D)1/29
E)1/21
Rationale: Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26
Answer:A
Answer: A
Question: The purchase price of an article is $48. In order to include 25% of cost for overhead and to provide $12 of net profit, the markup should be
Options:
A)50%
B)25%
C)35%
D)40%
E)45%
Rationale: Cost price of article = 48$
% of overhead cost = 25
Net profit = 12 $
We need to calculate % markup
Net profit as % of cost price = (12/48)*100 = 25%
Total markup should be = 25 + 25 = 50%
Answer A
Answer: A
Question: Two men are going along a track rail in the opposite direction. One goods train crossed the first person in 20 sec. After 10 min the train crossed the other person who is coming in opposite direction in 18 sec .After the train has passed, when the two persons will meet?
Options:
A)70 minutes
B)80 minutes
C)85 minutes
D)90 minutes
E)95 minutes
Rationale: Let us consider that speed of train , first man and second man are respectively t, f and s.
According to first given condition goods train crossed the first person moving in same direction in 20 sec.
so length of the will be 20(t-f)
similarly train crossed the second man in 18 sec.
so length of the train will be 18(t+s)
on comparing these two equations, we get 20(t-f) = 18(t+s)
or 2t = 20f + 18s
or t = 10f + 9s
now it is given that After 10 min the train crossed the other person who is coming in opposite direction so
if we consider this way of train as L then the next equation will be
L = 600t (here 600 is used for 10 minutes)
finally as asked in the question the time required to meet the two man after the train has passed will be given by
time = (L-600 f)/(f+s) {here 600f is used for the distance traveled by first man in 10 minutes}
= (600t-600f)/(f+s)
= [600(10f+9s)-600f]/(f+s)
= 600(10f+9s-f)/(f+s) = 600*9(f+s)/(f+s) = 600*9 seconds = 600*9/60 min
= 90 minutes
ANSWER:D
Answer: D
Question: If Ramola ranks 14th in a class of 26, what is her rank from the last?
Options:
A)11th
B)13th
C)12th
D)14th
E)15th
Rationale: when considered from last, 12 (i.e 26-14) students are ranked before her. so she is 13th rank from last.
ANSWER:B
Answer: B
Question: In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?
Options:
A)2/3
B)8/21
C)3/7
D)9/22
E)10/21
Rationale: Explanation:
Total number of balls = (8 + 7 + 6) = 21
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 8/21.
Answer: Option B
Answer: B
Question: In a contest, a bowl contains 18 keys, only one of which will open a treasure chest. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If Anna is allowed to draw two keys, simultaneously and at random, from the bowl as the first contestant, what is the probability that she wins the prize?
Options:
A)1/18
B)1/9
C)5/36
D)1/4
E)3/71
Rationale: P(not winning) = 17/18*16/17 = 8/9
P(winning) = 1 - 8/9 = 1/9
The answer is B.
Answer: B
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 7.2 kilometer long bridge, at the same speed?
Options:
A)4 min
B)2 min
C)8 min
D)9 min
E)3 min
Rationale: S = 600/40 = 15 mps
S =7200/15 =480 sec =8 min.Answer:C
Answer: C
Question: A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound. She mixes peanuts worth $1.50 a pound with cashews worth $5.00 a pound. How many pounds of cashews must she use?
Options:
A)40
B)45
C)50
D)55
E)60
Rationale: From the question stem we know that we need a mixture of 100 pounds of peanuts and cashews. If we represent peanuts as x and cashews as y, we get x + y = 100. Since the wholesaler wants to sell the mixture of 100 pounds @ $2.50, we can write this as: $2.5 * (x + y) = $1.5x + $4y
From the equation x + y = 100, we can rewrite y as y = 100 - x and substitute this into our equation to get:
$2.5 * (x + 100 - x) = $1.5x + $4(100 - x)
If you solve for x, you will get x = 60, and therefore y = 40. So the wholesaler must use 40 pounds of cashews.
You can substitute into the original equation to see that: $250 = $1.5(60) + $4(40)
Answer is B
Answer: B
Question: The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 50 kms. what was the total distance traveled in 12 hours?
Options:
A)252 kms
B)152 kms
C)732 kms
D)752 kms
E)152 kms
Rationale: Explanation:
Total distance travelled in 12 hours =(50+52+54+.....upto 12 terms)
This is an A.P with first term, a=50, number of terms,
n= 12,d=2.
Required distance = 12/2[2 x 50+{12-1) x 2]
=6(122)
= 732 kms.
Answer: C
Answer: C
Question: workers decided to raise Rs.3 lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.15 lacs . How many workers were they?
Options:
A)300
B)230
C)500
D)560
E)590
Rationale: N * 50 = (315000 - 300000) = 15000
N = 15000 / 50
= 300
A
Answer: A
Question: Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 60. He was allowed to drop his lowest score. After doing so, his average test score improved to 65. What is the lowest test score that was dropped?
Options:
A)20
B)25
C)45
D)65
E)80
Rationale: The arithmetic mean of 4 equally weighted tests was 60. So what we can assume is that we have 4 test scores, each 60.
He dropped his lowest score and the avg went to 65. This means that the lowest score was not 60 and other three scores had given the lowest score 5 each to make it up to 60 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was 3 *5 = 15 less than 60.
So the lowest score = 60 - 15 = 45
Answer (C)
Answer: C
Question: Dhoni bought a 1-year, $40,000 certificate of deposit that paid interest at an annual rate of 6 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?
Options:
A)$2456
B)$2436
C)$2446
D)$2466
E)$2426
Rationale: 6 percent compounded semiannually --> 3% in 6 moths.
For the first 6 moths interest was 3% of $40,000, so $1200
For the next 6 moths interest was 3% of $41,200, so $1236
Total interest for 1 year was $1200+$1236=$2436
Answer : B
Answer: B
Question: A and B finish the job in 15 days.while A,B and C can finish it in 12 days . C alone will finish the job in
Options:
A)40 days
B)30 days
C)60 days
D)70 days
E)50 days
Rationale: Explanation:
12 = (15 * x)/(15 + x)
180+12x=15x
3x=180
X=60
Answer: Option C
Answer: C
Question: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
Options:
A)6 days
B)7 days
C)8 days
D)9 days
E)10 days
Rationale: Explanation:
1 woman's 1 day's work = 1/70
1 Child's 1 day's work = 1/140
5 Women and 10 children 1 day work =
(5/70+10/140)=1/7
So 5 women and 10 children will finish the work in 7 days
Option B
Answer: B
Question: Adding two non multiples of R always results in a multiple of R; which of the following must be the value of R ?
Options:
A)[A] two
B)[B] three
C)[C] five
D)[D] ten
E)[E] hundred
Rationale: NON- multiples of 2 would always be ODD and sum of two odd would be EVEN.
so irrespective of value of non-multiples, sum of two them would always be even and thus multiple of 2..
A
Answer: A
Question: Ashish and Rahul started walking from same point E. Ashish walked at the speed of 15 kmph to the east, and Rahul walked 25 kmph to south, at what time they meet 10 miles apart?
Options:
A)15 min
B)16 min
C)17 min
D)18 min
E)19 min
Rationale: Consider 1 mile = 1.6 km
so 10 miles = 16 km
both are walking in at an angle 90 from same point so pythagorous theorem can be apply hence
(15x)^2 + (25x)^2 = 16^2
by solving and x hours are converted into min we got
approximate 18 min
ANSWER:D
Answer: D
Question: Find the fourth proportional to 0.2,0.12 and 0.3?
Options:
A)0.18
B)0.21
C)0.22
D)0.34
E)0.45
Rationale: Formula = Fourth propotional = (b × c)/a
A = 0.2 , B = 0.12 and C = 0.3
(0.12 × 0.3)/0.2
0.036/0.2 = 0.18
A
Answer: A
Question: Bottle R contains 100 capsules and costs $6.30. Bottle T contains 130 capsules and costs $2.99. What is the difference between the cost per capsule for bottle R and the cost per capsule for bottle T?
Options:
A) $0.04
B) $0.12
C) $0.05
D) $0.03
E) $0.002
Rationale: Cost per capsule in R is 6.30/100=0.063
Cost per capsule in T is 2.99/130=0.023
The difference is 0.004
The answer is A
Answer: A
Question: Using all the letters of the word "NOKA", how many words can be formed, which begin with N and end with A?
Options:
A)8
B)2
C)9
D)3
E)1
Rationale: There are five letters in the given word.
Consider 4 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 2! ways.
The number of words = 2! = 2.
Answer:B
Answer: B
Question: The average age of 20 men in the class is 15.6 years. Five new men join and the new average becomes 16.56 years. What was the average age of five new men?
Options:
A)15.5
B)15.4
C)15.25
D)20.4
E)15.6
Rationale: Total age of 20 men = 15.6 x 20 = 312
Now, total age of 25 men = 141.
Total age of five men added later = 414 - 312 = 202.
Hence, the total average of five men = 102/5 = 20.4
ANSWER:D
Answer: D
Question: If f(1, 1) = 5 and f(1, 5) = 26, what is the value of f(1, 10)?
Options:
A)107
B)101
C)147
D)None of these
E)Cannot be determined
Rationale: Solution:
The function f(a, b) = a3 + b2
f(1, 2) therefore is = 1^3 + 2^2 = 1 + 4 = 5 and
f(1, 5) = 1^3 + 5^2 = 1 + 25 = 26
Therefore, f(1, 10) = 1^3 + 10^2 = 1 + 100 = 101
Answer B
Answer: B
Question: In a survey about potential presidential candidates A and B, 30% of the public likes A and 50% liked B.If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that liked neither.
Options:
A)70%
B)55%
C)60%
D)65%
E)50%
Rationale: T=100
A=30
B=50
Both=x
A only=30-x
B only=50-x
N=Neither
Given:
A only+B only=2*Both
30-x+50-x=2x
80=4x
x=20
T=A only+B only+Both+Neither
100=30-20+20-20+20+N
100=30+N
N=100-30=70
Ans:A
Answer: A
Question: 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?
Options:
A)14299
B)27888
C)26687
D)14000
E)62912
Rationale: 25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000 .Answer: D
Answer: D
Question: The no of revolutions a wheel of diameter 40cm makes in traveling a distance of 176m is
Options:
A)338
B)140
C)287
D)277
E)136
Rationale: Explanation:
distance covered in 1 revolution = {\color{Blue} 2\Pi r} = 2 *(22/7) *20 = 880/7 cm
required no of revolutions = 17600 *(7/880) = 140
Answer: B) 140
Answer: B
Question: The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 65 sq. cm. Find the length of the rectangle.
Options:
A)12cm
B)14cm
C)16cm
D)18cm
E)20cm
Rationale: Explanation:
Let breadth = x. Then, length = 2x. Then,
(2x - 5) (x + 5) - 2x * x = 65 => 5x - 25 = 65 => x = 16.
Length of the rectangle = 16 cm.
Answer: Option C
Answer: C
Question: The base of pyramid P is an isosceles right triangle whose leg is 3. If the height of P is 4, what is the volume of P?
Options:
A)36
B)18
C)12
D)8
E)6
Rationale: Volume of a pyramid is given by
V=1/3Ah, where A is the area of the triangular base and h is the height of the pyramid.
Area of triangular base = 1/2 * 3*3 = 9/2
So, V = 1/3 * 9/2 *4 = 6
Option E
Answer: E
Question: Suppose you want to buy three loaves of bread that cost $1.00 each
and a jar of peanut butter that costs $5. A jar of jelly is $2.75, but you
donâ€™t need any jelly. You have $16. How much money will you have left
over?
Options:
A)$1.50
B)$6
C)$8
D)$7
E)$5.50
Rationale: The jelly is extra information. 16.00 â€“ 3 x 1 â€“ 5.00 =
16.00 â€“ 3 â€“ 5.00 = 8
You have $8 left.
correct answer C
Answer: C
Question: 30% people of a village in Sri Lanka died by bombardment, 25% of the remainder left the village on account of fear. If now the population is reduced to 6695, how much was it in the beginning?
Options:
A)7000
B)6700
C)6695
D)7645
E)6575
Rationale: X * (70/100) * (75/100) = 3515
X = 6695
Answer: C
Answer: C
Question: A’s speed is 17/14 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?
Options:
A)1/14
B)1/17
C)3/14
D)3/17
E)1/31
Rationale: Let x be the fraction of the distance that B runs.
Let v be the speed at which B runs.
The time should be the same for both runners.
Time = D / (17v/14) = xD/v
(14/17)*D/v = x*D/v
x = 14/17
B should have a head start of 3/17 of the full distance.
The answer is D.
Answer: D
Question: Anu can do a work in 6 days and Binu alone in 9 days. Anu and Binu undertook to do it for Rs.5700. With help of Minu, they completed the work in 3 days. How much is to be paid to Minu and Anu?
Options:
A)s.750, Rs.2250
B)s.2000, Rs.750
C)s.750, Rs.2000
D)s.850, Rs.2250
E)s.950, Rs.2850
Rationale: Minuâ€™s one dayâ€™s work = 1/3 - 1/6 + 1/9= 1/3 - 5/18 = 1/18
Anuâ€™s wages: Binuâ€™s wages: Minuâ€™s wages = 1/6 : 1/9 : 1/18 = 6: 4: 2
Minuâ€™s share = Rs.5700* 2/12 = Rs.950
Anuâ€™s share = Rs.5700* 6 /12 = Rs.2850
ANSWER:E
Answer: E