mathewhe/aqua_rat huggingface dataset:
Question: Two water pumps, working simultaneously at their respective constant rates, took exactly 6 hours to fill a swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Let the rate of the slow pump be x. Then the rate of the fast pump is 1.5x.
(x+1.5x)*6 = 2.5x*6 = 15x, which is the capacity of the whole pool.
Working alone:
1.5x*Time = 15x
Time = 15/1.5 = 10 hours
The answer is D.
Answer: (D) 10
Question: At a certain food stand, the price of each apple is 40¢ and the price of each orange is 60¢. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 54¢. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 48¢?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: If the average price is 54, then Mary has 7 oranges and 3 apples (a ratio of 7:3).
For the average price to be 48, the ratio should be 2:3.
Mary must put back 5 oranges.
The answer is E.
Answer: (E) 5
Question: Find large number from below question The difference of two numbers is 250. On dividing the larger number by the smaller, we get 5 as quotient and the 14 as remainder
(A) 120
(B) 135
(C) 140
(D) 309
(E) 369
Rationale: Let the smaller number be x. Then larger number = (x + 250).
x + 250= 5x + 14
4x = 236
x = 59
Large number = 59+250 = 309
D
Answer: (D) 309
Question: Entry fee in an exhibition is $1. Later this was reduced by 25% which increased the sale by 20%. The percentage increase in the number of visitors is?
(A) 20%
(B) 40%
(C) 50%
(D) 60%
(E) 100%
Rationale: Let the total original sale be $100
Then original number of visitors = 100
New number of visitors = 120/0.75 = 160
Increase % = 60%
Answer is D
Answer: (D) 60%
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 17 Kmph
(B) 26 Kmph
(C) 72 Kmph
(D) 66 Kmph
(E) 41 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer:C
Answer: (C) 72 Kmph
Question: Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate gives Danny $1. Every time the coin lands on tails, Danny gives Kate $1. After the five coin flips, what is the probability R that Kate has more than $10 but less than $15?
(A) 5/16
(B) 1/2
(C) R=12/30
(D) R=15/32
(E) R=3/8
Rationale: For 21 heads Kate will end up with < $10 and we want her to win. Therefore, only possibilities are 3 or 4 heads.
I made an educated guess and it worked fine.
Ans- 'D'
MGMAT's anagram helped here as well.
HHHHT = 5!/4!*1! = 5
HHHTT = 5!/3!*2! = 10
Total acceptable cases = 15
Total cases = 32
P = 15/32.D
Answer: (D) R=15/32
Question: An escalator moves towards the top level at the rate of 8 ft.sec and its length is 160 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.
(A) 14 sec
(B) 10 sec
(C) 16 sec
(D) 8 sec
(E) 9 sec
Rationale: Time taken to cover the entire length = tot.dist/resultant speed
= 160/ (8+2)
= 16sec
ANSWER:C
Answer: (C) 16 sec
Question: Evaluate: 10010 - 12*3*2 = ?
(A) 30002
(B) 70002
(C) 50002
(D) 90002
(E) 10002
Rationale: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
10010 - 12*3*2 = 10010 - 8 = 10002
correct answer E
Answer: (E) 10002
Question: On the xy co-ordinate plane, point C is (5,-2) and point D is (-1,1.5). The point on line segment CD that is twice as far from C as from D is:
(A) (1,-1)
(B) (1,1)
(C) (2,0.25)
(D) (3,0.5)
(E) (3,1)
Rationale: We want the point on the line that is twice as far from C as it is from D. We can examine the x and y coordinates separately since they are independent.
*It should be noted that there are two solutions to this problem, one point between C and D, and another point with D in the middle of C and the point. We can quickly look at the answer choices and see that all the points are between C and D, therefore we can search for that point using the following method:
Taking the x-coordinate first, the distance between C and D is |(x-coordinate of C) - (x-coordinate of D)|= |5 - (-1)| = 6
The x-coordinate that is twice as far from C as it is from D (and in between C and D) will be 4 units from C and 2 units from D. So the x coordinate of the point we're looking for is 5-4 = 1, or (-1)+2 = 1.
Now looking at the y-coordinate, we do the same thing. The distance between C and D is |(-2) - 2.5| = 4.5
The y-coordinate that is twice as far from C as it is from D (and in between C and D) will be 3 units from C and 1.5 units from D. So the y coordinate of the point we're looking for is (-2)+3 = 1, or 2.5-1.5 = 1.
So now we have our coordinates of the point on the line that is twice as far from C as it is from D: (3,1)
Answer: E
Answer: (E) (3,1)
Question: In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been
(A) 24
(B) 144
(C) 326
(D) 292
(E) 584
Rationale: Explanation:
5 | x z = 13 x 1 + 12 = 25
--------------
9 | y - 4 y = 9 x z + 8 = 9 x 25 + 8 = 233
--------------
13| z - 8 x = 5 x y + 4 = 5 x 233 + 4 = 1169
--------------
| 1 -12
585) 1169 (1
585
---
584
---
Therefore, on dividing the number by 585, remainder = 584.
ANSWER 584
Answer: (E) 584
Question: The G.C.D. of 1.08, 0.36 and 0.9 is:
(A) 0.03
(B) 0.9
(C) 0.18
(D) 0.108
(E) 0.118
Rationale: Given numbers are 1.08, 0.36 and 0.90. H.C.F. of 108, 36 and 90 is 18,
H.C.F. of given numbers = 0.18.
Answer: Option C
Answer: (C) 0.18
Question: If r and s are positive integers, and r^2 + r/s is an odd integer, which of the following cannot be even?
(A) 3r + 2s
(B) (r-1)(s+2)
(C) r^(s+1) + s^r
(D) r^3 +3
(E) s^4 +4
Rationale: Given: r and s are positive integers, and r2r2 + r/s is an odd integer
What are some "nice" values that make this true?
How about r = 2 and s = 2. We get: 2222 + 2/2 = 4 + 1 = 5, which IS an odd integer
Great, now let's plug r = 2 and s = 2 into each answer choice.
A. 3(2) + 2(2) = 10, which is even. so ELIMINATE A
B. (2 - 1)(2 + 2) = 4, which is even. so ELIMINATE B
C. 2^(2+1) + 2^2 = 12, which is even. so ELIMINATE C
D. 23+323+3 = 11, which is odd. so KEEP D for now
E. 24+424+4 = 20, which is even. so ELIMINATE E
By the process of elimination, the answer must be D
Answer: (D) r^3 +3
Question: 117 + 1.017 + 0.117 + 1.0017 = ?
(A) 109.3657
(B) 119.7563
(C) 119.1357
(D) 119.5637
(E) 119.6753
Rationale: 117
1.017
0.117
+ 1.0017
--------
119.1357
---------
Answer is C.
Answer: (C) 119.1357
Question: A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for $75 less, he could have gained 25%. What is the cost price?
(A) 220
(B) 274
(C) 250
(D) 280
(E) 222
Rationale: C
250
$250
CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? => $250
Answer: (C) 250
Question: A cement mixture is composed of 3 elements. By weight, 1/4 of the mixture is sand, 2/5 of the mixture is water, and the remaining 14 pounds of the mixture is gravel. What is the weight of the entire mixture in pounds?
(A) 9
(B) 14
(C) 28
(D) 40
(E) 60
Rationale: Let the total weight be x.
Sand content= (1/4)x
Water content= (2/5)x
Gravel=x-(1/4)x-(2/5)x=(7/20)x=14
x=40
Then answer will be D=40
Answer: (D) 40
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?
(A) 1000
(B) 1991
(C) 2888
(D) 1777
(E) 1555
Rationale: 1120 = P [1 + (5*12/5)/100]
P= 1000
Answer:A
Answer: (A) 1000
Question: The areas of the two spheres are in the ratio 1: 4. The ratio of their volume is?
(A) 1 : 4
(B) 1 : 9
(C) 1 : 8
(D) 1 : 3
(E) 1 : 1
Rationale: 4πr12 : 4πr22 = 1 : 4
r1 : r2 = 1 : 2
4/3 πr13 : 4/3 πr23
r13 : r23 = 1 : 8
Answer: C
Answer: (C) 1 : 8
Question: A positive number x is multiplied by 10, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?
(A)  9/4
(B)  3/2
(C)  4/3
(D)  2/3
(E)  10/3
Rationale: sq rt(10x/3) = x
=> 10x/3 = x^2
=> x = 10/3
Ans - E
Answer: (E)  10/3
Question: Cost is expressed by the formula tb^4. If b is doubled, the new cost R is what percent of the original cost?
(A) R=200
(B) R=600
(C) R=800
(D) R=1600
(E) R=50
Rationale: Original Cost C1=t1*b1^4
New Cost C2= t2*b2^4....only b is doubled so t2=t1 and b2=2b1
C2=t2*(2b1)^4
=16(t1*b1^4)
=16C1
16 times C1=>1600% of C1
Ans D=1600
Answer: (D) R=1600
Question: In what ratio must a grocer mix two varieties of pulses costing Rs.15 and Rs.20 per kg respectively so as to get a mixture worth Rs.16.50 per Kg?
(A) 3 : 7
(B) 5 : 7
(C) 7 : 3
(D) 7 : 5
(E) None
Rationale: Solution
Required ratio = 3.50 : 1.50 = 35 : 15 = 7 : 3.
Answer C
Answer: (C) 7 : 3
Question: Anup was asked to find the value of 7/12 of a sum of money R. Instead of multiplying the same by 7/12,he divided it by 7/12 and his answer exceeded the correct answer by 95. The correct answer is:
(A)  48
(B)  89
(C)  84
(D)  69
(E)  49
Rationale: R=12/7*x-7/12*x=95 --> x=84 --> 7/12*x=49.
So if bythe correct answerquestion means 7/12 of the amount then the answer should be E.
Answer: (E)  49
Question: A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?
(A) 2 hours
(B) 7 hours
(C) 5 hours
(D) 9 hours
(E) 3 hours
Rationale: |-----------20--------------------|
50 40
D = 20
RS = 50 – 40 = 10
T = 20/10 = 2 hours
Answer: A
Answer: (A) 2 hours
Question: A man walks at a rate of 10 mph. After every ten miles, he rests for 6 minutes. How much time does he take to walk 40 miles?
(A)  258
(B)  318
(C)  322
(D)  324
(E)  330
Rationale: To cover 40 miles the man needs (time) = (distance)/(rate) = 40/10 = 4 hours = 240 minutes. He will also rest 3 times (after 10, 20, and 30 miles), so total resting time = 3*6 = 18 minutes.
Total time = 240 + 18 = 258 minutes.
Answer: A.
Answer: (A)  258
Question: What is the difference between the CI on Rs. 5000 for 1 years at 4% per annum CI yearly and half yearly?
(A) Rs. 2.04
(B) Rs. 3
(C) Rs. 4.50
(D) Rs. 5
(E) Rs. 6.50
Rationale: C.I. when interest
compounded yearly
= Rs. 5000 x 1 + 4 x 1 + x 4
100 100
= Rs. 5000 x 26 x 51
25 50
= Rs. 5304.
C.I. when interest is
compounded half-yearly
= Rs. 5000 x 1 + 2 3
100
= Rs. 5000 x 51 x 51 x 51
50 50 50
= Rs. 5306.04
Difference = Rs. (5306.04 - 5304) = Rs. 2.04
A
Answer: (A) Rs. 2.04
Question: Of the female students at Barkely University, 1/6 are on the honor roll. Of the male students, 2/5 are on the honor roll. If 3/5 of the students are female, what is ratio of male to female students on honor roll?
(A) 8/5
(B) 3/15
(C) 23/30
(D) 43/60
(E) 53/90
Rationale: let the total students be 100
given 3/5 of the students are females = 60
then males = 2/5 = 40
1/6 of the females are on honor roll = 10
males on the honor roll = 2/5= 16
ratio of M:F students on honor roll = 16/10 = 8/5
A
Answer: (A) 8/5
Question: A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?
(A) 33 days
(B) 27 days
(C) 24 days
(D) 18 days
(E) 17 days
Rationale: 2c = 1/4 + 1/6 – 1/3 = 1/12
c = 1/24 => 24 days
Answer: C
Answer: (C) 24 days
Question: If 4 men can colour 48 m long cloth in 2 days, then 5 men can colour 36 m long cloth in
(A) 1.2 day
(B) 2.0 days
(C) 3 days
(D) 4.2 days
(E) 5 days
Rationale: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 5 = 1.2 day.
A
Answer: (A) 1.2 day
Question: If s=1 and (s-b)/c = 1 which of the following is NOT a possible value of b?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: Equation is:
(s-b)/c = 1 where s = 1
so plug in 1 for s and look at it again
(1-b)/c = 1
now C can be anything we want, so if b = -2 we can plug it in and make it work
(1-(-2))/c = 1
3/c = 1
c = 3 and it works
HOWEVER, if we have a 0 in the numerator there isn't a number on earth that makes 0/C = 1
(1-1)/c = 1
0/c = 1
there aren't any matches for C to make this true
B cannot be 1.
Answer is D
Answer: (D) 1
Question: A certain factory employed 600 men and 400 women and the average wager was Rs. 25.50 per day, If a woman got Rs. 5 less than a man, then what are their daily wages ?
(A) m:25.50 w:27.50
(B) m:27.50 w:22.50
(C) m:26.50 w:27.50
(D) m: 24.50 w:26.50
(E) None of these
Rationale: Explanation:
Let the daily wage of a man be Rs. x.
Then, daily wage of a woman = Rs. (x - 5).
Now, 600x + 400 (x - 5) = 25.50 * (600 + 400) <=> 1000x = 27500 <=> x = 27.50.
Man's daily wages = Rs. 27.50; Woman's daily wages = (x - 5) = Rs. 22.50. Answer: B
Answer: (B) m:27.50 w:22.50
Question: What is the sum of all remainders obtained when the first 100 natural numbers are divided by 7?
(A) 397
(B) 401
(C) 403
(D) 405
(E) 364
Rationale: A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0.
1 divided by 9 gives the remainder of 1;
2 divided by 9 gives the remainder of 2;
...
8 divided by 9 gives the remainder of 8;
9 divided by 9 gives the remainder of 0.
We'll have 11 such blocks, since 99/9=11. The last will be:
91 divided by 9 gives the remainder of 1;
92 divided by 9 gives the remainder of 2;
...
98 divided by 9 gives the remainder of 8;
99 divided by 9 gives the remainder of 0.
The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be:
11(1+2+3+4+5+6+7+8+0)+1=364.
Answer: E.
Answer: (E) 364
Question: If the equation x^2−6x=2k has at least one solution, which of the following must be true?
(A) k > 9
(B) k < −9
(C) k = 9
(D) k ≤ 9
(E) k ≥ −9/2
Rationale: x^2−6x=2k
=> x^2−6x - 2k = 0
For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative.
b^2-4ac ≥0
=> 36 - 4*1*(-2k) ≥0
=> 36 + 8k ≥0
=> k ≥ -9/2
Answer E
Answer: (E) k ≥ −9/2
Question: Find the greatest number which divides 83, 125 and 209 leaving the same remainder in each case.
(A) 19
(B) 17
(C) 42
(D) 23
(E) 32
Rationale: The greatest number which divides three dividends p, q and r leaving the same remainder in each case is given by H.C.F(any two of (q - p), (r - p) and (r - q)).
For the given problem, p = 83, q = 125 and r = 209.
Hence the greatest number which divides these three leaving the same remainder in each case is H.C.F(any two of (125 - 83, 209 - 83, 209 - 125) = 42.
ANSWER:C
Answer: (C) 42
Question: A student multiplied a number by 3/5 instead of 5/3. What is the percentage error.
(A) 64%
(B) 65%
(C) 66%
(D) 67%
(E) 68%
Rationale: Explanation:
Let the number be x,
then,
5/3−3/5=16/15x
Error% =
(16/15x∗3/5∗100)
Answer: Option A
Answer: (A) 64%
Question: A and B both work for the same company. A goes to work Monday through Thursday, and B goes to work Tuesday thru Thursday. A takes 2 weeks of vacation per year, and B only takes 1 week. They do not take their vacations during the same week. What percent of the year can they carpool to work together, assuming they both have the same schedule? 1 year = 52 weeks = 364 days
(A) 42.9%
(B) 56.4%
(C) 45.6%
(D) 27.2%
(E) 40.4%
Rationale: A works M T W Th and B works T W Th
A and B work the same days on T W TH or 3/7
They don't work the same schedule for 3 weeks out of 52.
For 49 of the 52 weeks (i.e. 49/52=94.2%) they can carpool 3 days each week (i.e. 3/7=42.9%)
In a year, they can carpool 49/52 x 3/7 = 147/364 or 40.4% of the year.
Answer is E
Answer: (E) 40.4%
Question: 9 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?
(A) 12/9 days
(B) 15/2 days
(C) 82/8 days
(D) 22/76 days
(E) 22/2 days
Rationale: 9M = 6W ---- 20 days
12M + 8W -----?
8W + 8 W = 16W ---?
6W ---- 20 16 -----?
6 * 20 = 16 * x => x = 15/2 days
Answer:B
Answer: (B) 15/2 days
Question: The average of temperatures at noontime from Monday to Friday is 60; the lowest one is 50, what is the possible maximum range of the temperatures?
(A) 50
(B) 25
(C) 40
(D) 45
(E) 75
Rationale: Average=60, Sum of temperatures=60*5=300
As the min temperature is 50, max would be 300-4*50=100 --> The range=100(max)-50(min)=50
Answer: A
Answer: (A) 50
Question: Two friends A and B apply for a job in the same company. The chances of A getting selected is 2/5 and that of B is 4/7. What is the probability that both of them get selected?
(A) 8/35
(B) 34/35
(C) 27/35
(D) 21/32
(E) 33/35
Rationale: Solution:
P(A) = 2/5
P(B) = 4/7
E = {A and B both get selected}
P(E) = P(A)*P(B)
= 2/5 * 4/7
= 8/35
ANSWER IS A
Answer: (A) 8/35
Question: A certain no. when divided by 50 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
(A) 2
(B) 4
(C) 5
(D) 8
(E) 9
Rationale: Explanation:
50 + 25 = 75/15 = 5 (Remainder)
C
Answer: (C) 5
Question: Pandiyan buys an old scooter for Rs. 6000 and spends Rs. 600 on its repairs. If he sells the scooter for Rs. 7200, his gain percent is :
(A) 20%
(B) 12%
(C) 9.09%
(D) 5%
(E) None of these
Rationale: Explanation :
Solution: C.P. =Rs. (6000+600) =Rs. 6600; S.P. = Rs. 7200.
Gain% = 7200-6600/6600*100 = 9.09%
Answer : C
Answer: (C) 9.09%
Question: 500 x (200 + 4) Ã— (3 + 2) = ?
(A) 55000
(B) 450000
(C) 250000
(D) 410000
(E) 510000
Rationale: 500 x204 x 5 =510000 Answer : E
Answer: (E) 510000
Question: Two tains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
(A) 12
(B) 24
(C) 36
(D) 48
(E) 38
Rationale: Sol.
Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 ⇔ 2x = 20 ⇔ x = 10.
∴ Speed of each train = 10 m/sec = [10 * 18/5] km/hr = 36 km/hr.
Answer C
Answer: (C) 36
Question: If a certain sample of data has a mean of 25.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?
(A) 12.0
(B) 13.5
(C) 17.0
(D) 23.5
(E) 26.5
Rationale: Value ismore than 2.5SDfrom the mean means that the distance between the mean and the value must be more than 2.5*SD=7.5. So the value must be either less than 25-7.5=17.5.5or more than 25+7.5=32.5.
Answer: C.
Answer: (C) 17.0
Question: The number 0.650 is how much greater than 1/8 ?
(A) ½
(B) 21/40
(C) 1/50
(D) 1/500
(E) 2/500
Rationale: let x be the difference
then
.65-1/8=x
65/100-1/8=x
x=21/40
ans B
Answer: (B) 21/40
Question: Which of the following multipliers will cause a number to be increased by 29.7%?
(A) 1.297
(B) 12.97
(C) 129.7
(D) 1297
(E) None
Rationale: Solution
Let the number be 100 and required multiplier be y.
Then, 100y = 129.7
y = 129.7 / 100
= 1.297
Answer D
Answer: (D) 1297
Question: How many diagonals does a polygon with 17 sides have, if one of its vertices does not connect to any diagonal?
(A) 102
(B) 104
(C) 110
(D) 90
(E) 84
Rationale: If I calculate it using the formulae, #diagonals = n (n-3)/2Each vertex sends of n-3 diagonals
n= 17-1 then 16*(16-3)/2 = 104
Correct Option:	B
Answer: (B) 104
Question: For any real number x, the operatoris defined as:
(x) = x(6 − x)
If p + 1 =(p + 1), then p =
(A) −2
(B) 0
(C) 1
(D) 2
(E) 5
Rationale: (x) = x(6 − x)
(p + 1) = (p + 1)(6 - p - 1) = (5-p)(p+1)
We are given that p + 1 =(p + 1)
Therefore (5-p)(p+1) = (p + 1)
Or (p + 1) + (5-p)(p+1) = 0
(p + 1)(p-5) = 0
p = -1,p=5
Option E
Answer: (E) 5
Question: Diane find 6 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?
(A) 5
(B) 7 and a half
(C) 10
(D) 12 and a half
(E) 30
Rationale: She will need 12 cans to paint the rest of this room and 18 for the next room for a total of 30 cans.
E
Answer: (E) 30
Question: A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 15 minutes. How long will it take to go 5 km in stationary water?
(A) 40 minutes
(B) 1 hour
(C) 1 hour 15 min
(D) 1 hour 30 min
(E) 1 hour 40 min
Rationale: speed (upstream) =2/1 = 2 kmhr
speed (downstream)=1/(15/60)= 4 kmhr
speed in still water = 1/2 (2+4) = 3 kmhr
time taken in stationary = 5/3 = 1 hrs 40 min
ANSWER:E
Answer: (E) 1 hour 40 min
Question: The average wages of a worker during a fortnight comprising 15 consecutive working days was $90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was $91 per day. What was his wage on the 8th day?
(A) $83
(B) $90
(C) $92
(D) $97
(E) $104
Rationale: Average daily wage of a worker for 15 consecutive working days = 90$
During the first 7 days , the daily average daily wage = 87$
During the last 7 days , the daily average daily wage = 91$
Wage on 8th day = 90*15 -( 87*7 + 91 *7)
= 1350 - (609 + 637)
=1350 - 1246
= 104
Answer E
Answer: (E) $104
Question: If two numbers are in the ratio 2:3. If 5 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
(A) A)10
(B) B)20
(C) C)25
(D) D)30
(E) E)35
Rationale: 2:3
2x + 10 : 3x + 10 = 3 : 4
4[2x + 5] = 3[3x + 5]
8x + 20 = 9x + 15
9x - 8x = 20 - 15
x = 5
Then smallest number is = 2
2x = 10
Correct Option A
Answer: (A) A)10
Question: A thief is spotted by a policeman from a distance of 300metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 16km/hr and that of the policeman 20km/hr, how far the thief will have run before he is overtaken ?
(A) A)1km
(B) B)500m
(C) C)650m
(D) D)750m
(E) E)1200m
Rationale: Relative speed of the policeman = 20-16 = 4 km/hr
time taken by policeman to cover 300m = (300/1000)*(1/4) = 3/40 hr
In 3/40 hr the thief covers a distance of 48/40 km = 6/5 km = 1200m
Answer is E
Answer: (E) E)1200m
Question: √(14)^2
(A) 7
(B) 14
(C) 49
(D) 21
(E) None of these
Rationale: explanation
√(14)^2 =?
or, ? = 14
Answer B
Answer: (B) 14
Question: 12 men work 8 hours per day to complete the work in 10 days. To complete the same work in 8 days, working 15 hours a day, the number of men required?
(A) 8 days
(B) 9 days
(C) 11 days
(D) 13 days
(E) 15 days
Rationale: That is, 1 work done = 12 × 8 × 10
Then, 12 8 × 10 = ? × 15 × 8
? (i.e. No. of men required) = 12 × 8 × 10/15× 10 = 8 days.
A)
Answer: (A) 8 days
Question: The sale price sarees listed for Rs.400 after successive discount is 15% and 5% is?
(A) 297
(B) 879
(C) 323
(D) 762
(E) 269
Rationale: 400*(85/100)*(95/100)
= 323
Answer: C
Answer: (C) 323
Question: Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 9180, how much money did he borrow?
(A) 9000
(B) 80288
(C) 2668
(D) 2600
(E) 2781
Rationale: Let the sum be Rs. x. Then,
[(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 9180
18x + 45x + 39x = (9180 * 100)
102x = 918000 => x = 9000.
Answer:A
Answer: (A) 9000
Question: If a trader sold two cars each at Rs. 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is?
(A) 1.44
(B) 1.42
(C) 1.49
(D) 1.42
(E) 1.43
Rationale: SP of each car is Rs. 325475, he gains 12% on first car and losses 12% on second car.
In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (12)(12)/100 % = 1.44%
Answer:A
Answer: (A) 1.44
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 2 years hence?
(A) 58
(B) 59
(C) 64
(D) 70
(E) 74
Rationale: Explanation:
A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
2 years, their ages will be 42 and 22.
Sum of their ages = 42 + 22 = 64.
C)
Answer: (C) 64