mathewhe/aqua_rat huggingface dataset:
Question: Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
(A) 10
(B) 91
(C) 17
(D) 11
(E) 16
Rationale: RS = 60 -40 = 20 * 5/18 = 100/18
T = 50
D = 50 * 100/18 = 2500/9
RS = 60 + 40 = 100 * 5/18
T = 2500/9 * 18/500 = 10 sec
Answer:A
Answer: (A) 10
Question: Ratio between two numbers is 3: 4 and their sum is 420. Find the smaller number?
(A) 378
(B) 180
(C) 820
(D) 734
(E) 840
Rationale: Explanation:
3x + 4x = 420
x = 60 => 3x = 180
Answer: Option B
Answer: (B) 180
Question: Two trains of equal length are running on parallel lines in the same directions at 46km/hr. and 36km/hr. The faster trains pass the slower train in 72 seconds. The length of each train is:
(A) 82m
(B) 50m
(C) 72m
(D) 100m
(E) None of these
Rationale: Explanation:
The relative speed of train is 46-36 = 10 Km/hr = (10 X 5) / 18 = 25/9 m/s10×518=259m/s
In 72 secs the total distance traveled is 72x25/9 = 200 m.
Therefore the length of each train is = 200/2 = 100 m.
Answer D
Answer: (D) 100m
Question: The current in a river is 8 mph. A boat can travel 20 mph in still water. How far up the river can the boat travel if the round trip is to take 10 hours?
(A) 69 miles
(B) 84 miles
(C) 96 miles
(D) 100 miles
(E) 112 miles
Rationale: Upstream Speed = 20-8=12 mph
Downstream Speed = 20+8 = 28 mph
D/12 + D/28 = 10 hours
Solving for D we get D=84
Answer: B
Answer: (B) 84 miles
Question: The measures of the 2 acute angles of a triangle are in the ratio of 4 : 5. What arethe measures of the 2 angles?
(A) 20°
(B) 70°
(C) 110°
(D) 120°
(E) 50°
Rationale: If the ratio of the two angles is 4:5, then the measures of two angles can be written as 4x and 5x. Also the two acute angles of a triangle is equal to 90°. Hence
4x + 5x = 90
9x = 90
x = 10
Measures of the two acute angles are
4x = 4 × 10 = 40°
5x = 5 × 10 = 50°
E
Answer: (E) 50°
Question: What should be added to 4529 so that it may become a perfect square?
(A) 94
(B) 95
(C) 96
(D) 97
(E) 98
Rationale: 68x68=4624
4624-4529 = 95
If added to 95 get perfect square
answer =B
Answer: (B) 95
Question: A man swims downstream 45 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
(A) 2
(B) 8
(C) 9
(D) 10
(E) 10.5
Rationale: 45 --- 3 DS = 15
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (15 + 6)/2 = 10.5
Answer: E
Answer: (E) 10.5
Question: A money lender finds that due to a fall in the annual rate of interest from 8% to 7 3/4 % his yearly income diminishes by Rs. 61.50, his capital is?
(A) 24,607
(B) 24,638
(C) 24,600
(D) 24,628
(E) 24,6122
Rationale: Let the capital be Rs. x. Then,
(x * 8 * 1)/100 - (x * 31/4 * 1/100) = 61.50
32x - 31x = 6150 * 4
x = 24,600.
Answer:C
Answer: (C) 24,600
Question: Lloyd normally works 7.5 hours per day and earns $4.50 per hour. For each hour he works in excess of 7.5 hours on a given day, he is paid 2.5 times his regular rate. If Lloyd works 10.5 hours on a given day, how much does he earn for that day?
(A) $33.75
(B) $47.25
(C) $51.75
(D) $54.00
(E) $67.50
Rationale: Daily working hour*Regular Rate + Overtime*Increased Rate
7.5*4.5+ 3*4.5*2.5=67.5
Answer E
Answer: (E) $67.50
Question: In a lottery there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
(A) 1/5
(B) 2/7
(C) 2/5
(D) 1/7
(E) 3/5
Rationale: total draws = prizes+blanks= 10+25=35
probability of getting a prize = 10/35 = 2/7
correct option is B
Answer: (B) 2/7
Question: Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities.
How many mystical fruits remain after he goes through all the thirty check points?
(A) 23
(B) 24
(C) 25
(D) 26
(E) 27
Rationale: Solution:
25 Fruits
Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can.
For the first sack:
He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M,
(Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M
M = 10
Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each.
Now he must get rid of the second sack.
For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints.
(Space in First Sack) N = (Remaining fruits in second sack) 30 – N
N = 15
Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points.
Answer C
Answer: (C) 25
Question: In a basketball game, Tim scored 20 points more than Joe, but only half as many points as Ken. If the three players scored a combined total of 100 points, how many points did Tim score?
(A) 15
(B) 20
(C) 25
(D) 30
(E) 45
Rationale: Let Joe scored point = x
Then Tim Scored = x+20
Ken Scored = 2*(x+20) = 2x+40
As given, x+x+20+2x+40 = 100 points
4x+60 = 100
x = 100-60/4 = 10
So Tim Scored = x +20 i.e) 10+20 = 30
Answer : D
Answer: (D) 30
Question: If xy+z = x(y+2z), which of the following must be true?
(A) 1. x=0 and z=0
(B) 2. x=1 and y=1
(C) 3. y=1 and z=0
(D) 4. x=1 or y=0
(E) 5. x=1/2 or z=0
Rationale: xy+z=x(y+2z)
xy+z=xy+2xz
z=2xz
it means x=1/2 or z=0
Answer E
Answer: (E) 5. x=1/2 or z=0
Question: When 2/9 of the votes on a certain resolution have been counted, 3/4 of those counted are in favor of the resolution. What fraction q of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution?
(A) 11/14
(B) 13/18
(C) 4/7
(D) 3/7
(E) 3/14
Rationale: If we use variable for total votes there will be too many fractions to manipulate with, so pick some smart #: let set total # of votes is 18.
2/9 of the votes on a certain resolution have been counted--> 4 counted and 18-4=14 votes left to be counted;
3/4 of those counted are in favor of the resolution--> 3 in favor and 1 against;
Ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18*2/3=12 people who voted against, so in the remaining 14 votes there should be 12-1=11 people who voted against. Thus q=11/14 of the remaining votes must be against.
Answer: A.
Answer: (A) 11/14
Question: A train 550 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 30
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 550 * 3/55 = 30 sec.
Answer: Option E
Answer: (E) 30
Question: George does 3/5th of a piece of work in 9 days.He then calls in Paul and they finish the work in 4 days.How long would Paul take to do the work by himself?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: 9day 3/5
1 day 1/15
remaing 1-3/5=2/5
both can do 2/5 work in 4 day
one day work of both=1/10
therfor paul would take 1/10-1/15=1/30 or 30 days
ANSWER:C
Answer: (C) 30
Question: If -3/(a - 3) = 3/(a + 2), then a = ?
(A) 1/2
(B) 2/3
(C) 3/4
(D) 4/5
(E) 5/6
Rationale: Multiply all terms of the given equation by (a - 3)(a + 2), simplify and solve
(a - 3)(a + 2)[ -3/(a - 3) ] = (a - 3)(a + 2) [ 3/(a + 2) ]
- 3 (a + 2) = 3 (a - 3)
a = 1/2
correct answer A
Answer: (A) 1/2
Question: Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:
(A) 9
(B) 11
(C) 13
(D) 15
(E) 19
Rationale: Let the three integers be x, x + 2 and x + 4.
Then, 3x = 2(x + 4) + 3 x = 11.
Third integer = x + 4 = 15.
Answer: D
Answer: (D) 15
Question: Find the 5th and 7th term of the series 1, 4, 7, 10,...? And their ratio is?
(A) 11/13
(B) 17/13
(C) 19/13
(D) 21/13
(E) 17/15
Rationale: common difference = d = 4 - 1 = 3 ,, n = 5, a = first term = 1-----
By using arithmetic progression , t5 = a + (n-1)*d = 1 + (5-1)*3 = 1+12 = 13
Also 7th term , t7 = a + (n-1)*d = 1 + (7-1) * 3 = 19
Ratio = t7/t5 = 19/13 = ..... Ans - C
Answer: (C) 19/13
Question: A sum is divided among P, Q and R in such a way that for each rupee P gets, Q gets 25 paisa and R gets 15 paisa. If the share of P is RS. 70, what is the total amount?
(A) 48
(B) 84
(C) 74
(D) 47
(E) 64
Rationale: p:q:r = 100:25:15
20:5:3
20 --- 70
28 --- ? => 84
Answer:B
Answer: (B) 84
Question: The maximum number of student amoung them 1020 pens and 860 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
(A) 20
(B) 40
(C) 60
(D) 80
(E) None of these
Rationale: Solution
Required number of student = H.C.F of 1020 and 860 = 20. Answer A
Answer: (A) 20
Question: Angela has 15 pairs of matched socks. If she loses 5 individual socks, which of the following is NOT a possible number of matched pairs she has left?
(A) 8
(B) 9
(C) 13
(D) 11
(E) 12
Rationale: I think if Angela loses 5 individual socks,then she is bound to have lost minimum of 2 pairs and 1 individual sock,in this way she is left with only 12 pairs of socks (15-(2+1)).
Hence,13 cannot be the answer as maximum is 12.
Hence, option (C)
Answer: (C) 13
Question: The sum of a number and the two numbers preceding it is equal to 30. Find the number:
(A) 10
(B) 11
(C) 9
(D) 8
(E) 7
Rationale: Number is 9, AS 9 +10+11=30
Answer: C
Answer: (C) 9
Question: Shop Offered 20% offer for every Shirt, Smith bought a shirt at Rs. 780. and What was the shop's original selling Price?
(A) 500
(B) 550
(C) 600
(D) 700
(E) 975
Rationale: SP* (80/100) = 780
SP= 9.75 * 100 => CP = 975
Answer:E
Answer: (E) 975
Question: A car traveled 281 miles in 4 hours 41 minutes. What was the average speed of the car in miles per hour?
(A) 60 miles / hour
(B) 50 miles / hour
(C) 80 miles / hour
(D) 90 miles / hour
(E) 40 miles / hour
Rationale: We first convert the time of 4 hours 41 minutes in minutes
4 hours 41 minutes = 4 ? 60 + 41 = 281 minutes
Average speed S is given by distance / time. Hence
S = 281 miles / 281 minutes = 1 mile / minute
= 60 miles / hour
correct answer A
Answer: (A) 60 miles / hour
Question: Three numbers are in the ratio 1.5:2:3.5 and their H.C.F is 18. The numbers are:
(A) 22,36, 63
(B) 27,45, 63
(C) 27,54, 63
(D) 54, 45, 36
(E) 27,36, 63
Rationale: Let the required numbers be 1.5x, 2x and 3.5x. Then, their H.C.F = x. So, x = 18.
The numbers are 27,36, 63.
ANSWER:E
Answer: (E) 27,36, 63
Question: An inspector rejects 15% of the meters as defective. How many will he examine to reject 10?
(A) A)100
(B) B)66.7
(C) C)250
(D) D)200
(E) E)160
Rationale: Then, 10% of x= 15
(15/100)x = 10
x = (10*100*)/15= 66.7
Answer is B
Answer: (B) B)66.7
Question: If the price of a certain computer increased 30 percent from y dollars to 351 dollars, then 2y =
(A) 540
(B) 570
(C) 619
(D) 649
(E) 700
Rationale: Before Price increase Price = y
After 30% Price increase Price = y+(30/100)*y= 1.3y = 351 (Given)
i.e. y= 351/1.3 = $270
i.e. 2y = 2*270 = 540
Answer: option A
Answer: (A) 540
Question: Cars P and Q are approaching each other on the same highway. Car P is moving at 48 mph northbound and Car Q is moving at 52 mph southbound. At 2:00 pm, they are approaching each other and 190 miles apart. Eventually they pass each other. At what clock time are they moving away from each other and 35 miles apart?
(A)  3:30 pm
(B)  3:45 pm
(C)  4:00 pm
(D)  4:15 pm
(E)  4:30 pm
Rationale: Total distance, which should be covered by both cars is 190+35=225 miles.
Let t be the time so the equation will be 48t+52t=225 thus,
t=2.25 hours
Answer: D
Answer: (D)  4:15 pm
Question: Aarti can do a piece of work in 3 days. In how many days will she complete four time of work of same type?
(A) 12 days
(B) 18 days
(C) 21 days
(D) 3 days
(E) 13 days
Rationale: We have the important relation, More work, More time (days)
A piece of work can be done in 3 days.
Four times of work of same type can be done in 3 x 4
= 12 days
Answer A
Answer: (A) 12 days
Question: A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17thinnings?
(A) 27
(B) 22
(C) 25
(D) 37
(E) 29
Rationale: 16x + 85 = 17(x + 3)
x = 34 + 3 = 37
Answer:D
Answer: (D) 37
Question: One day Eesha started 30 min late from home and reached her office 50 min late while driving 25% slower than her usual speed. How much time in min does eesha usually take to reach her office from home?
(A) 22
(B) 60
(C) 88
(D) 26
(E) 18
Rationale: We know that Speed is inversely proportional to time
While she drives 25% slower means she drove at 3434(S)
We know that D = S x T
When speed became 3434(S) then Time taken should be 4343(T)
i.e, She has taken 4343(T) - T extra to cover the distance.
Extra Time = T3T3 = 20 min (as 20 min late due to slow driving)
Actual time T = 60 Minutes
Answer:B
Answer: (B) 60
Question: 8, 27, 64, 100, 125, 216, 343
(A) 64
(B) 100
(C) 125
(D) 216
(E) 343
Rationale: The pattern is 2 cube, 3 cube, 4 cube, 5 cube, 6 cube, 7 cube. But, 100 is not a perfect cube.
answer : B
Answer: (B) 100
Question: Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest?
(A) 635.5
(B) 613.5
(C) 975.5
(D) 653.5
(E) 670.3
Rationale: 4000
200 ---- I
200
10 ---- II
---------------
4410
2210
--------
2000
110 ---- III
110
5.50 ---- IV
-----------
2425.50
2210
-----------
4635.50
4000
----------
635.50
ANSWER A
Answer: (A) 635.5
Question: Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 48 white marbles. How many red marbles could be in bag A?
(A) 1
(B) 3
(C) 4
(D) 10
(E) 12
Rationale: 6 is the answer.
Bag A-
R:W:B = 2:6:9
Let W in bag A be 6K
Bab B -
R:W = 1:4
Let W in bag B be 4P
W = 48 = 6K+4P
=> K =6, P=3
Total Red's in bag A will be 2K = 12
E
Answer: (E) 12
Question: The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 75% of the required amount. What is the net difference in the expenditure on that product?
(A) A)12.5%
(B) B)13%
(C) C)13.15%
(D) D)14%
(E) E)93.75%
Rationale: Quantity X Rate = Price
1 x 1 = 1
0.75 x 1.25 = 0.9375
Decrease in price = ( 0.125/1) × 100 =12.5%
A)
Answer: (A) A)12.5%
Question: A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each of which is to have either 60 feet or 100 feet of lake frontage. If 1/9 of the lots are to have 60 feet of frontage each and the remaining 40 lots are to have 100 feet of frontage each, what is the value of x ?
(A) 400
(B) 4,300
(C) 3,700
(D) 4,400
(E) 4,760
Rationale: Total number of plots,be T
Plots with 60ft is (1/9)th of total plots.
Plots with 100ft frontage = (8/9) X total number of plots
i.e 8/9 X T = 40 T = 45
Total lake frontage = 40X100 + 5X60 = 4300
Answer : B
Answer: (B) 4,300
Question: What is the ratio of y to x if (x + 3y) / ( x - y) = 3/5?
(A) -1/9
(B) -5/3
(C) -1/15
(D) 3/5
(E) 15/1
Rationale: Solving for y/x gives, -1/9 (A)
Answer: (A) -1/9
Question: The number 7490xy is divisible by 90. Find out (x+y).
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 10×9=90 where 10 and 9 are co-prime numbers. Hence, if
7490xy is divisible by 9 and 10, it will also be divisible by 90
7490xy is divisible by 10. We know that a number is divisible by 10 if the last digit is 0.
Hence
Thus we have the number
7490x0. If this is divisible by 9,
7+4+9+0+x+0 is divisible by 9
20+x is divisible by 9 (where
x
x is a digit)
x=7
Hence,
(x+y)=(7+0)=7
Answer : D
Answer: (D) 7
Question: A man was employed on the promise that he will be paid the highest wages per day. The contract money to be paid was Rs. 1189. Finally he was paid only Rs. 1073. For how many days did he actually work?
(A) 39
(B) 40
(C) 37
(D) 35
(E) 45
Rationale: HCF of 1189, 1073 = 29
1073/29 = 37
ANSWER:C
Answer: (C) 37
Question: Ross has 160 shirts, 3/4 of the shirts are green and 1/10 is without buttons. Therefore Ross has between ___ and ___ shirts with buttons that are not green.
(A) 24 ; 40.
(B) 23 ; 40.
(C) 22 ; 40.
(D) 21 ; 40.
(E) 20 ; 40.
Rationale: Total shirts = 160
Green shirts = 3/4*160 = 120, Non green shirts = 40
Shirts without button = 1/10*160 = 16, shirts with button = 144
Required: Range of shirts with buttons that are not green.
Maximum non green shirts with buttons = number of non green shirts = 40
Minimum non green shirts with buttons (All without button shirts are non green) = Non green shirts - shirts without button = 40 - 16 = 24
Hence the range would be (24, 40)
Correct Option: A
Answer: (A) 24 ; 40.
Question: What is the sum of the numbers between 1 and 5, inclusive?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: Sol. add numbers between 1 and 5.
Answer = C, 15.
Answer: (C) 15
Question: Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 3x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 3x boxes?
(A) 3 minutes
(B) 4 minutes
(C) 4.2 minutes
(D) 6 minutes
(E) 12 minutes
Rationale: Rate = Work / Time
Given Rate of Machine A = X / 10 min
Machine B Produces 3x boxes in 5 min hence , Machine B produces 4x boxes in 10 min .
Rate of Machine B = 6x / 10
we need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates
let's first find the combined Rate of Machine A and B
Rate of Machine A = X / 10 min + Rate of Machine B = 6x / 10 = 7X/10
Now combine Time = combine work needs to be done / Combine Rate = 3x/7x * 10 = 4.2 Min
Ans: C
Answer: (C) 4.2 minutes
Question: if the ratio of age of x and y is 5:7.and the sum of the ages are 48.calculate the age of X.
(A) 20
(B) 25
(C) 30
(D) 28
(E) 26
Rationale: 5x+7x=48
12x=48,x=4.
age of X=5x=20.
answer A
Answer: (A) 20
Question: A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
(A) 2
(B) 5
(C) 6
(D) 7
(E) 1
Rationale: C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.
S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.
Gain ={\color{Black} \left ( \frac{80}{1600} \times 100\right ) }% = 5%
Answer: B
Answer: (B) 5
Question: Someone on a skateboard is traveling 10 miles per hour. How many feet does she travel in 20 seconds? (1 mile = 5280 feet)
(A) 292 ft
(B) 293.4 ft
(C) 295 ft
(D) 296 ft
(E) 297 ft
Rationale: per second => 10*5280 ft/60*60 =14.67 ft
20 seconds => 14.67 * 20 = 293.4 ft
Answer : B
Answer: (B) 293.4 ft
Question: The present ages of three persons in proportions 2 : 4 : 6. Eight years ago, the sum of their ages was 36. Find their present ages (in years).
(A) 10, 20, 30
(B) 16, 28, 36
(C) 20, 35, 45
(D) 18, 24, 32
(E) None of these
Rationale: Explanation:
Let their present ages be 2x, 4x and 6x years respectively.
Then, (2x - 8) + (4x - 8) + (6x - 8) = 36
12x = 60
x = 5
Their present ages are 2x = 10 years, 4x = 20 years and 6x = 30 years respectively.
Answer: A
Answer: (A) 10, 20, 30
Question: From 2000 onwards, till 2003 the price of computers increased every year by 10%. After that due to government subsidy the price of computers decreases every year by 10%. The price of a computer in 2006 will be approx. how much per cent less than the price in 2000 if the same pattern of price is continued :
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Solution:
Year	Value
2000	100 (Let)
2001	110
2002	121
2003	133.1
2004	119.79
2005	107.811
2006	97.0299
Now,
[(100-97.0299)*100]/100 ≈ 3
Answer: Option B
Answer: (B) 3
Question: x, y, and z are all unique numbers. If x is chosen randomly from the set {8, 9, 10, 11} and y and z are chosen randomly from the set {20, 21, 22, 23}, what is the probability that x and y are prime and z is not?
(A) 1/16
(B) 3/11
(C) 13/20
(D) 3/10
(E) 1/10
Rationale: P(x is prime) = 1/4
P(y is prime) = 1/4
If y is prime, then z is not prime since y and z are unique.
Then the probability is 1/4*1/4 = 1/16
The answer is A.
Answer: (A) 1/16
Question: In a covering a certain distance, the speeds of A and B are in the ratio of 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is?
(A) 1 hrs
(B) 8 hrs
(C) 2 hrs
(D) 6 hrs
(E) 9 hrs
Rationale: Ratio of speeds = 3:4
Ratio of times taken = 4:3
Suppose A takes 4x hrs and B takes 3x hrs to reach the destination.
Then, 4x - 3x = 30/60 => x = 1/2
Time taken by A = 4x hrs = 4 * 1/2 = 2 hrs.
Answer:C
Answer: (C) 2 hrs
Question: The H.C.F. of two numbers is 12 and their L.C.M. is 600. If one of the number is 120, find the other?
(A) 100
(B) 60
(C) 120
(D) 200
(E) 150
Rationale: Other number = 12*600/120= 60
Answer is B
Answer: (B) 60
Question: Two brother X and Y appeared for an exam. The probability of selection of X is 1/3 and that of B is 2/5. Find the probability that both of them are selected.
(A) 2/69
(B) 2/15
(C) 2/63
(D) 2/29
(E) 2/10
Rationale: Explanation:
Let A be the event that X is selected and B is the event that Y is selected.
P(A) = 1/3, P(B) = 2/5.
Let C be the event that both are selected.
P(C) = P(A) Ã— P(B) as A and B are independent events:
= (1/3) Ã— (2/5) = 2/15
Answer: B) 2/15
Answer: (B) 2/15
Question: Nandesh sold half of his cloth at 10% profit, half of the remaining at 10% loss and the rest was sold at the cost price. In the transaction, his gain or loss will be :
(A) 2.5% gain
(B) 5% gain
(C) 2.5% loss
(D) 5% loss
(E) None of these
Rationale: Explanation :
Solution: Let C.P. of whole be Rs. X. C.P. of 1/2 stock = Rs. x/2, C.P. of 1/4 stock = Rs. x/4.
Total S.P. = Rs.[(110% of x/2)+(90% of x/4)+x/4] = Rs. (11x/20 + 9x/40 + x/4)
= Rs. 41x/40.
Gain = Rs. (41x/40 - x) = Rs. x/40.
.'. Gain% = (x/40 * 1/x * 100)% = 2.5%
Answer : A
Answer: (A) 2.5% gain
Question: A person buys an article at Rs.575. At what price should he sell the article so as to make a profit of 15%?
(A) 600
(B) 277
(C) 269
(D) 661.25
(E) 281
Rationale: Cost price = Rs.575
profit = 15% of 575= Rs.86.25
Selling price = Cost price + Profit
= 575 + 86.25 = 661.25
Answer: D
Answer: (D) 661.25
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
(A) 379
(B) 375
(C) 268
(D) 269
(E) 297
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
75 ----- ? => 375
Answer:B
Answer: (B) 375
Question: How many halves are there in seven-fourth?
(A) 8
(B) 12
(C) 3.5
(D) 7
(E) 3.2
Rationale: divide 7/4 by 1/2
=7/4÷1/2
=7/4*2/1
=14/4
=3.5.
Answer is C.
Answer: (C) 3.5
Question: (1^2+2^2+3^2+.....+8^2)=?
(A) 330
(B) 345
(C) 204
(D) 385
(E) None of them
Rationale: formula is (1^2+2^2+3^2+....+n^2=1/6 n(n+1)(2n+1)
n=8
=(1/6x8x9x17)
=204
Answer is C.
Answer: (C) 204
Question: Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 18000, then find his savings?
(A) Rs.3600
(B) Rs.3603
(C) Rs.3639
(D) Rs.3632
(E) Rs.3602
Rationale: Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively.
Income, 5x = 18000 => x = 3600
Savings = Income - expenditure = 5x - 4x = x
So, savings = Rs.3600.
Answer:A
Answer: (A) Rs.3600