MU-NLPC/Calc-aqua_rat huggingface dataset:
The area of a square is 4761 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.
Choose the correct choice from the following answers:
A) 5:28  B) 5:19  C) 15:12  D) 5:13  E) 15:46

Solution: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.   a2 = 4761   a = 69   L = 2a and b = a - 24   b : l = a - 24 : 2a = 45 : 138   = 15:46   Answer:15:46
Answer: E
The ratio between the length and the breadth of a rectangular park is 1 : 3. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?  Choose the correct choice from the following options
A) 124545 m  B) 134561 m  C) 156787 m  D) 15450 m  E) 120000 m

Solution: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.   60   Let length = 1x metres and breadth = 3x metres.   Then, 2(1x + 3x) = 1600 or x = 200.   Length = 200 m and Breadth = 600 m.   Area = (600 x 200) m2 = 120000 m   120000 m
Answer: E
Calculate the average of first 12 even numbers is?
Choose the correct choice
A) 15 B) 14 C) 12 D) 11 E) 13

Solution: 13xplanation:   Sum of 12 even numbers = 12 * 13= 
12 * 13 = 156
156   Average= 156/12= 
156/12 = 13
13   Answer: Option 13
Answer: E
Jessica can text 75 words per minute, while Maurice can text 10 words per minute. An abridged English translation of Tolstoy’s War and Peace contains 410,400 words. Working together, how many days will it take Jessica and Maurice to text the entire abridged translation of War and Peace? Options
A) 0.3 B) 1.3 C) 3.5 D) 9 E) 11.3

Solution: Since the answer choices are reasonably spaced out, we can approximate and save time   3.5ombined words per day = 85*60*24 which should be something close to 122400 (i.e 100*25*60)   410400/122400 will be closest to only 3.5,   So, Answer should be 3.5.
Answer: C
How many positive integers less than 23 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4? Choose the correct choice from the following:
A) 17
B) 25
C) 24
D) 22
E) 20

Solution: 8 prime numbers less than 28: {2, 3, 5, 7, 11, 13, 17, 19}   2 odd multiples of 5: {5, 15}   9 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4: {6, 8, 10, 12, 14, 16, 18, 20, 22}   Notice, that 5 is in two sets, thus total # of integers satisfying the given conditions is  8+1+9-1= 
 8+1+9-1 = 17
17.   17nswer: 17.
Answer: A
At a certain high school, the senior class is three times the size of the junior class. If 1/3 of the seniors and 3/4 of the juniors study Japanese, what fraction of the students in both classes study Japanese?  Choose the correct choice from the following answers:
A) 1/2  B) 3/8  C) 5/16  D) 1/4  E) 7/16

Solution: Start by deciding on a number of students to represent the number of students in the senior class. For this example I will choose 300 students. That would make the number of students in the junior class 100. Then we can find out how many students are taking Japanese in each grade and add them together. (1/3)*300=100 and   (3/4)*100= 
  (3/4)*100 = 75
75. 100+75=175. There are a total of 400 students in the junior class and senior class combined (100+300=300), and there are 175 total students in Japanese, so 175 students in Japanese / 400 total students equals 7/16 of the students in both classes that study Japanese.   Answer: 7/16
Answer: E
A can do a piece of work n 7 days of 9 hours each and B alone can do it in 6 days of 7 hours each. How long will they take to do it working together 8 2/5 hours a day? Choose the most appropriate option.
A) 4 days  B) 3 days  C) 5 days  D) 6 days  E) 8 days

Solution: B   3 days   A can complete the work in   (7*9)= 
  (7*9) = 63
63 days   B can complete the work in   (6*7)= 
  (6*7) = 42
42 days   --> A’s one hour’s work= 1/63 and B’s one hour work = 1/42.   (A+B)’s one hour work = 1/63+1/42 = 5/126   Therefore, Both can finish the work in 126/5 hours.   Number of days of 8 2/5 hours each = (126*5/(5*42))= 
(126*5/(5*42)) = 3
3 days
Answer: B
If the ratio of apples to bananas is 5 to 2 and the ratio of bananas to cucumbers is 1 to 4, what is the ratio of apples to cucumbers? Answers:	A) 1:3	B) 2:5	C) 3:5	D) 5:8	E) 4:7

Solution: The ratio of bananas to cucumbers is 1 to 4 which equals 2 to 8.   The ratio of apples to bananas to cucumbers is 5 to 2 to 8.   The ratio of apples to cucumbers is 5 to 8.   The answer is 5:8.
Answer: D
If s and t are integers and s^2 – t^2 is an odd integer, which of the following must be an even integer?
I. s + t + 2
II. s^2 + 2st + t^2
III. s^2 + t^2  Answers:
A) None	B) I only	C) II only	D) III only	E) I, II, and III

Solution: s^2–t^2 is an odd integer means that either s is even and t is odd or s is odd and t is even.   Check all options:   I. s + t + 2 --> even+odd+even=odd or odd+even+even=odd. Discard;   II. s^2 + 2st + t^2 --> even+even+odd=odd or odd+even+even=odd. Discard;   III. s^2 + t^2 --> even+odd=odd or odd+even=odd. Discard.   Nonenswer: None.
Answer: A
A new savings account offers 8 percent annual interest compounded every 6 months. What would be the total balance in an account after 1 year, if the initial amount in the account were $6000?	Choose the correct choice.
A) $80.00 B) $84.40 C) $360.00 D) $6,360.00 E) $6,489.60

Solution: The interest is compounded every 6 months. To calculate interest, you must take the principal and multiply it by the interest and the length of time (using the unit used in the interest, typically years). At the end of the first 6 months the interest earned is $6,000(.08) (1/2) = $240(Note: the 6 months are “1/2” in the equation since 8% is a yearly rate, not a bi-yearly one).   Since the interest is compounded, the second six months of the year are not earning interest on just the original $6,000, but on the interest as well, so they are actually earning interest on $6,240. The interest earned during the final 6 months of the year is $6,240(.08)(1/2) = $249.6. Therefore, the total balance is the original amount ($6000) + $240 + $249.60 = $6,489.60.   The correct answer is $6,489.60.
Answer: E
The cost of 200 kgs. of sugar is Rs.3000. What is the cost of3.525 kgs. of sugar?	Options:
A) Rs.54  B) Rs.48.875  C) Rs.55  D) Rs.52  E) Rs.52.875

Solution: Explanation:.   The cost of 3.525kgs. of sugar = 3000x 3.525/200= Rs.52.875   Answer: Option:Rs.52.875
Answer: E
A,B,C can do a piece of work in 11days, 20days and 55days respectively, working alone. How soon can the work be done if A is assisted by B and C on alternate days?	Pick one: A) 2 B) 4 C) 8 D) 10 E) 12

Solution: A+B 1day work = 1/11 + 1/20 +  1= 
+  1 = 1
1/11 + 1/20= 31/220   A+8 1day work = 1/11 + 1/55 = 6/55   work done in 2 days = 31/220 + 6/55 = 55/220 = 1/4   1/4 work is done by A in 2days   Whole work will be done in  2*4= 
 2*4 = 8
8days   Answer is 8
Answer: C
A grocery shop has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?	Select the correct option:  A) 4857  B) 4184  C) 4012  D) 4991  E) 5291

Solution: Let the sale in the sixth month =x   Then   (6435+6927+6855+7230+6562+x)/6 =6500   =>6435+6927+6855+7230+6562+x =6×6500   => 34009+x=39000   => x=39000−34009   =4991   ANSWER:4991
Answer: D
3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
Choose the correct choice from the following answers.
A) 45%
B) 50%
C) 57%
D) 64%
E) 78%

Solution: Total number of votes polled = (1136 + 7636 + 11628)= 
(1136 + 7636 + 11628) = 20_400
20400   So, Required percentage= 11628/20400 * 100= 
11628/20400 * 100 = 57
57%   57%
Answer: C
A is three times as old as B. C was twice-as old as A four years ago. In four years' time, A will be 31. What are the present ages of B and C ?	Choose the correct choice from the following:  A) 9, 46  B) 9, 50  C) 10, 46  D) 10, 50  E) 10, 56

Solution: Explanation:   We have : A = 3B ...(i) and   C - 4 = 2 (A - 4) ...(ii)   Also, A + 4 = 31 or A= 31-4= 
31-4 = 27
27.   Putting A= 27 in (i), we get: B = 9.   Putting A = 27 in (ii), we get C = 50.   Answer: 9, 50
Answer: B
Two numbers are in the ratio 3 : 4. If their L.C.M. is 96. what is sum of the numbers?	Choose the most appropriate option:	A) 48	B) 56	C) 76	D) 84	E) 85

Solution: Explanation:   Let the numbers be 3x and 4x   LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x)   Given that LCM of 3x and 4x is 96   => 12x = 96   => x = 96/12= 
96/12 = 8
8   Sum of the numbers= 3x + 4x   = 7x   3  + 4= 
3  + 4 = 7
7x= 7 x 8 = 56   Answer: Option 56
Answer: B
A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 19 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix? Select: A) 1/10 B) 3/10 C) 1/2 D) 7/10 E) 29/100

Solution: C+M+B-CM-MB-CB-2CMB = 100   C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.   the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.   50 + 40 + B-CB-MB-19 -2CMB = 100   B-CB-MB-2CMB = 29   hence the probability = 29/100.   29/100
Answer: E
If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is? Choose the correct option:
A) 1/8
B) 1/2
C) 1/9
D) 11/1
E) 1/12

Solution: The number of exhaustive outcomes is 36.   Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2   P(E) = 1 - 1/2   = 1/2.   Answer:1/2
Answer: B
Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.
Year	Item of Expenditure
Salary	Fuel and Transport	Bonus	Interest on Loans	Taxes
1998	288	98	3.00	23.4	83
1999	342	112	2.52	32.5	108
2000	324	101	3.84	41.6	74
2001	336	133	3.68	36.4	88
2002	420	142	3.96	49.4	98
The total expenditure of the company over these items during the year 2000 is?
Choose the correct option.
A) Rs. 544.44 lakhs B) Rs. 544.54 lakhs C) Rs. 544.79 lakhs D) Rs. 545 lakhs E) Rs. 546 lakhs

Solution: Total expenditure of the Company during 2000   = Rs. (324 + 101 + 3.84 + 41.6 + 74) lakhs   = Rs. 544.44 lakhs.   Rs. 544.44 lakhs)
Answer: A
3/5 of all married couples have more than one child. 2/5 of all married couples have more than 3 children. What fraction of all married couples have 2 or 3 children?  Select the correct option: A) 1/5 B) 1/4 C) 7/20 D) 3/5 E) It cannot be determined from the given information.

Solution: Plug in simple numbers. Take 100 couples for example.   3/5 of 100 couples have more than one child = 60 couples.   2/5 of 100 couples have more than 3 kids = 40 couples.   This implies that 40 couples are a subset of 60 couples and the complement of 60 couples within those 100 couples, which equals 20 couples have either one or no kids at all.   We need to find couples that have 2 or 3 kids, so essentially, it is  60 - 40= 
 60 - 40 = 20
20. Fraction will be 20/100= 1/5.   Option 1/5
Answer: A
The owner of a furniture shop charges his customer 25% more than the cost price. If a customer paid Rs. 8340 for a computer table, then what was the cost price of the computer table? Choose one:
A) Rs.6672
B) Rs.6727
C) Rs.6908
D) Rs.6725
E) Rs.6728

Solution: CP = SP * (100/(100 + profit%))   = 8340(100/125) = Rs.6672.   Rs.6672nswer: Rs.6672
Answer: A
What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 18%? Pick.
A) 20%  B) 26%  C) 42%  D) 27%  E) 23%

Solution: SP2 = 2/3 SP1   CP = 100   SP2 = 82   2/3 SP1 = 82   SP1 = 123   100 --- 23 => 23%   Answer: 23%
Answer: E
If k is the sum of the digits of integer m, and m=16n, where n is an integer, which of the following must be true?
Choose the correct option.
A) k is not divisible by 9  B) The sum of the digits of k is 9  C) m is a multiple of 2k  D) k is a multiple of 9  E) k is a multiple of 6

Solution: m= 16n i.e n =1,2,3 ,4 etc or -1,-2.-3 ,-4 then m 16,32,48,64 or -16 ,-32 ,-48 ,-64 then k 7,5 12,10 or -(1+6) , -(3+2) , -(4+8) ,-(6+4)   ans k is not divisible by 9
Answer: A
Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered? Pick:
A) 17603
B) 17608
C) 17628
D) 17600
E) 176023

Solution: Price at which the TV set is bought = Rs. 12,500   Discount offered = 20%   Marked Price = 12500 * 100/80 = Rs. 15625   The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375   = Rs. 16000   The price at which the TV should be sold to get a profit of 10% if no discount was offered = 16000 * 110/100   = Rs. 17600   Answer: 17600
Answer: D
A train covers a distance of 12 km in 10 min. If it takes 9 sec to pass a telegraph post, then the length of the train is?  Select:
A) 298	B) 288	C) 120	D) 776	E) 180

Solution: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.   Length of the train = 20 * 9= 
20 * 9 = 180
180 m.   Answer:180
Answer: E
HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 48, then the other number is?  Choices.
A) 99 B) 66 C) 132 D) 264 E) 364

Solution: 12 * 396 = 48 * x   x = 99   99NSWER:99
Answer: A
The length of a room is 5 m and width is 4.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 900 per sq. metre.	Choose the correct choice from the following answers.
A) 21375
B) 25750
C) 26550
D) 26750
E) 25725

Solution: Area = 5 × 4.75 sq. metre.   Cost for 1 sq. metre. = Rs. 900   Hence total cost = 5 × 4.75 × 900   = 5 × 4275 = Rs. 21375   21375nswer is 21375.
Answer: A
A circular rim 28 inches in a diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes B revilutions per second, how many revilutions per minute does the larger rim makes in terms of B?  Choose the correct option.
A) a) 48pi/B B) b) 75m C) c) 48B D) d) 24B E) e) B/75

Solution: distance covered by a circular wheel per sec* = 2*pi* r * n   where n is number of revolution   So we know the smaller rim makes B rev per sec so the inches coverd SR per sec = 28 * pi* B   the problem the say SR rotates the same number of inches as the LR.   The inches covered by the LR per sec = 35 * pi*Y   So equate both u will get Y = 4/5 B   Theis is in sec we need the answer in min so 48B   answer is c) 48B
Answer: C
for every correct answer 4 is awarded but for a wrong answer 2 is deducted. If there are a total of 150 questions and sukanya scores 480 how many answers of sukanya were correct? Pick one: A) 110 B) 120 C) 130 D) 140 E) 150

Solution: If x questions are correct, then   4x-2(150-x) = 480   6x= 780   x=130   so 130 questions are correct.   ANSWER:130
Answer: C
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 75 sq.cm. What is the length of the rectangle
Choose the correct choice:
A) 18 cm  B) 16 cm  C) 40 cm  D) 20cm  E) 28 cm

Solution: Explanation:   Let breadth =x cm   Then, length =2x cm   Area =x×2x=2x^2 sq.cm.   New length =(2x−5) cm   New breadth =(x+5) cm   New area =(2x−5)(x+5) sq.cm.   Given that, new area = initial area +75 sq.cm.   ⇒(2x−5)(x+5)=2x^2+75   ⇒2x^2+10x−5x−25=2x^2+75   ⇒5x−25=75   ⇒5x=75+25= 
75+25 = 100
100   ⇒x=1005=20 cm   Length =2x=2×20=40 cm   Answer: Option 40 cm
Answer: C
Two vessels A and B contain milk and water mixed in the ratio 4:3 and 2:3 in what ratio must these mixtures be mixed to form new mixture containing half milk and half water? Choose the most appropriate option
A) 7:6 B) 7:1 C) 7:5 D) 7:2 E) 7:8

Solution: Answer with Explanation: Step (i): Let C.P. of 1 liter milk be Re.1 Ratio of mixture in A = 4:3  Milk in 1 litre mixture in A = 4/7 lit,  C.P of 1 litre mix of A = Rs. 4/7 Ratio of mix in B = 2:3  Milk in 1 litre mixture in B = 2/5 lit,  C.P of 1 litre mix of B = Rs. 2/5 Ratio of new mixture = 1:1  Milk in 1 litre mixture = 1/2 lit,  C.P of 1 litre mix = Rs. ½ (Mean price = re. ½ ) Step (ii) By the rule of alligation C.P. of 1 lit mix. In A (d) C.P. of 1 lit mix. In B (c) 4/7 2/5   Mean Price (m)   m-c (1/2 – 2/5) = 1/10 1/2 d-m (4/7 – 1/2) = 1/14   Required Ratio = 1/14 : 1/10 = 7 : 5   Answer:7:5
Answer: C
In how many ways can three consonants and two vowels be selected from the letters of the word "TRIANGLE"? Choose the correct choice from the following answers:
A) 28 ways B) 35 ways C) 67 ways D) 23 ways E) 30 ways

Solution: The word contains five consonants. Three vowels, three consonants can be selected from five consonants in ⁵C₃ ways, two vowels can be selected from three vowels in ³C₂ ways.   3 consonants and 2 vowels can be selected in ⁵C₂ . ³C₂ ways i.e., 10 * 3   =30 ways.   Answer:30 ways
Answer: E
A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs.14.70 less, he would have gained 30%. Find the cost of the article. Choose the correct choice.
A) 30
B) 40
C) 50
D) 60
E) 70

Solution: Let C.P=100   Gain=25%   S.P=125   Supposed C.P=80   Gain=30%   S.P=(130*80)/100= 
(130*80)/100 = 104
104   Diff=(125-104)= 
(125-104) = 21
21   Diff 21 when C.P=100   then Diff 14.70 when C.P=(100*14.70)/21= 
(100*14.70)/21 = 70
70   ANSW70R:70
Answer: E
In how many ways Chief Minister and Minister be elected from a team of 14 members?
Choose the correct choice from the following answers.
A) 162 ways
B) 192 ways
C) 182 ways
D) 172 ways
E) 152 ways

Solution: To do this, if captain is elected first, then we have 14 ways of doing this.   For election of vice-captain, we have only 13 ways left, Bcoz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)   So, the ans is 14*13= 
14*13 = 182
182 ways.   182 ways
Answer: C
y selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%? Choices.
A) 8
B) 9
C) 7
D) 5
E) 4

Solution: 80% --- 12   120% --- ?     80/120 * 12= 
  80/120 * 12 = 8
8   8nswer: 8
Answer: A
The sum of the ages of 5 children born at the intervals of 4 years each is 50 years. what is the age of the eldest child ?  Choose the correct choice:
A) 15
B) 8
C) 18
D) None of these
E) Cannot be determined

Solution: Explanation:   Let x = the youngest child. Each of the other four children will then be x+4, x+8, x+12, x+16.   We know that the sum of their ages is 50 .   so, x+(x+4)+(x+8)+(x+12)+(x+16) = 50   x= 2   The youngest child is 2 years old.   Age of eldest child is = 2+16= 
2+16 = 18
18   Answer: 18
Answer: C
(64 - 12)2 + 4 x 64 x 12 = ?  Options:
A) 5246	B) 4406	C) 5126	D) 5776	E) None of these

Solution: Explanation :   Here, the given statement is like (a - b)2 + 4ab where a= 64 and b = 12   (a - b)2 + 4ab = (a2 - 2ab + b2) + 4ab = a2 + 2ab + b2 = (a + b)2   Hence (64 - 12)2 + 4 x 64 x 12 = (64 + 12)2 = 762 = 5776. Answer : Option 5776
Answer: D
The forth proportional to 10,8,15 is?  Pick: A) 15 B) 12 C) 18 D) 20 E) 24

Solution: Let the fourth proportional to 10,8,15 be x   then 10:8::15:x   10x = 8*15   x = 12   Answer is 12
Answer: B
In an examination a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination? Options:
A) 176  B) 9  C) 87  D) 11  E) 16

Solution: Let the number of papers be x. Then,   63x + 20 + 2 = 65x   = 2x = 22   = x = 11.   Answer:11
Answer: D
Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 48 seconds. Find the length of the faster train?	Select the correct option.
A) 270
B) 288
C) 266
D) 299
E) 480

Solution: Relative speed = (72 - 36) * 5/18 = 2 * 5= 
2 * 5 = 10
10 mps.   Distance covered in 27 sec= 48 * 10= 
48 * 10 = 480
480 m.   The length of the faster train= 480 m.   Answer: 480
Answer: E
A person bought 110 glass bowls at a rate of Rs. 10 per bowl. He sold 100 of them at Rs. 14 and the remaining broke. What is the percentage gain for A?
Choose the correct choice
A) 40  B) 300/11  C) 243/7  D) 279/11  E) 279/8

Solution: CP=110*10= 
110*10 = 1_100
1100 and SP=100*14= 
100*14 = 1_400
1400   Gain %= 100*(1400-1100)/1100= 300/11   ANSWER:300/11
Answer: B
A, B and C started a shop by investing Rs. 27,000, Rs. 72,000 and Rs. 81,000 respectively. At the end of the year, the profits were distributed among them. If C’s share of profit be Rs. 36,000, then the total profit was :	Choices:
A) 30,000  B) 60,000  C) 80,000  D) 120,000  E) None

Solution: Sol.   A : B : C = 27000 : 72000 : 81000 = 3: 8 : 9. so, C’s share : Total Profit = 9 : 20.   Let the total profit be Rs. x. Then, 9/20 = 36000/x or x   = 36000 * 20 / 9= 
36000 * 20 / 9 = 80_000
80000.   Answer 80,000
Answer: C
The jogging track in a sports complex is 1040 m in circumference. Kapil and his wife start from the same point and walk in opposite directions at 7.5 km/hr and 3.7 km/hr respectively. They will meet for the first time in?	Choose the correct choice from the following:
A) 3.12 min B) 3.74 min C) 4.25 min D) 4.90 min E) 5.57 min

Solution: Clearly, the two will meet when they are1040 m apart.   To be (7.5 + 3.7)= 
(7.5 + 3.7) = 11.2
11.2 km apart, they take 1 hour. THat is 60 minutes.   To be 1040m apart, they take= (1040/11200 * 60) min   = 5.57 min.   Answer: 5.57 min
Answer: E
A shopkeeper sells three items P, Q and R and incurs a loss of 21, 11 and 10respectively. The overall loss percentage on selling P and Q items is 14.33 and that of Qand R items is 10.4. Find the overall loss percentage on selling the three items?  Options.
A) 15%  B) 12.16%  C) 13.4%  D) 20.2%  E) None of these

Solution: Explanation :   Let the costs of the items P, Q and R are Rs p, Rs q and Rs r respectively.   And, S.P pf the items P, Q and R are 0.79p, 0.89p and 0.9r respectively.   Overall loss percentage of the 1st two items = 14.33%   =>(0.21p+0.11q)/(p+q)=0.1433   =>p/q=1/2.   Overall loss percentage of the 2nd and 3rd item =10.4%   =>(0.11q+0.1r)/(q+r)=0.104.   =>q/r=2/3.   Therefore, the overall loss percentage is :   =>(0.21p+0.11q+0.1r)x100/(p+q+r).   =>(1(0.21)+2(0.11)+3(0.1))x100/(1+2+3).   =>0.1216×100.   =>12.16%.   Answer : 12.16%
Answer: B
Three hundred multiples of seven are chosen at random, and 450 multiples of eight are chosen at random. Approximately what percentage of the 750 selected numbers are odd?
Pick one:
A) 20%  B) 25%  C) 40%  D) 50%  E) 80%

Solution: About half the multiples of seven will be odd while all the multiples of eight are even.   The percentage of odd numbers is about (1/2)(300) / 750 = 20%   The answer is 20%.
Answer: A
mixture contains alcohol and water in the ratio 4 : 3. If 6 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture. Pick:
A) 10 B) 6.8 C) 27 D) 22 E) 29

Solution: Let the quantity of alcohol and water be 4x litres and 3x litres respectively   24x = 4(3x+5)   12x = 20   x = 1.7   Quantity of alcohol = (4 x 1.7) litres = 6.8 litres.   Answer: 6.8
Answer: B
Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?  Choices: A) 14 sec B) 87 sec C) 48 sec D) 17 sec E) 16 sec

Solution: Relative speed = 45 + 30= 
45 + 30 = 75
75 km/hr.   75 * 5/18= 125/6 m/sec.   Distance covered = 500 + 500= 
500 + 500 = 1_000
1000 m.   Required time= 1000 * 6/125= 
1000 * 6/125 = 48
48 sec.   Answer:48 sec
Answer: C