MU-NLPC/Calc-aqua_rat huggingface dataset:
A student got 74% in math and 81% in history. To get an overall average of 75%, how much should the student get in the third subject?
Choices:
A) 66%
B) 67%
C) 68%
D) 69%
E) 70%

Solution: 74 + 81 + x = 3*75   x = 70   The answer is 70%.
Answer: E
One package of Skittles costs $6.00. There are 5 Skittles in each package. How many Skittles are in 9 packages?	Choose the correct choice from the following options:	A) 55	B) 45	C) 15	D) 35	E) 25

Solution: 5*9= 
5*9 = 45
45.Answer is 45.
Answer: B
Winners will be announced the following day at 8 AM Pacific/1 PM Eastern Time.
If A, X, Y, and Z are unique nonzero digits in the equation:
XY
*YX
____
AYZ
And Y > X, the 2-digit number XY = ?	Select.
A) 13 B) 21 C) 23 D) 24 E) 25

Solution: The reasoning is as follows:-   B) can't be answer because Y<x 23)="" 3="" 4="" a)="" answer="" be="" because="" but="" can't="" correct="" d)="" digit="" e)="" equal="" give="" is="" it="" middle="" not="" number="" number.="" the="" thus="" to="" will="" wrong="" x="" xy="" y="" y.="" yx="">xwill give 1 digit numbermiddle digit is Y   23</x>
Answer: C
A batsman makes a score of 88 runs in the 17th inning and thus increases his averages by 3.Find his average after 17th inning? Choose the correct answer:
A) 19
B) 29
C) 40
D) 49
E) 59

Solution: let the average after 17th inning =x   Then average after 16th inning=(x-3)   Therefore 16(x-3)+88=17x   Therefore x=40   ANSWER:40
Answer: C
A trader marked the price of a car 20% above the cost price and allowed the purchaser 5% discount on the marked price there by gained Rs.8400. Find the cost price of the car?
Choose the correct option
A) Rs.60000 B) Rs.60228 C) Rs.62299 D) Rs.60022 E) Rs.60298

Solution: Explanation:   Rs.60000nswer: Rs.60000
Answer: A
Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 22 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
Choose the correct option
A) 565
B) 444
C) 676
D) 456
E) 663

Solution: 1h ----- 6   ? ------ 60   12 h   RS = 16 + 22= 
16 + 22 = 38
38   T= 12   456 = 38 * 12= 
38 * 12 = 456
456   Answer: 456
Answer: D
A 100 meter long train crosses a man standing on the platform in 5 sec. What is the speed of the train? Choose the correct choice from the following options:
A) 72 kmph
B) 108 kmph
C) 176 kmph
D) 134 kmph
E) 161 kmph

Solution: S = 100/5 * 18/5= 
100/5 * 18/5 = 72
72 kmph   72 kmphnswer: 72 kmph
Answer: A
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 10 years hence?  Options:
A) 58  B) 59  C) 62  D) 70  E) 80

Solution: Explanation:   A + B = 60, A = 2B   2B + B = 60 => B = 20 then A = 40.   10 years, their ages will be 50 and 30.   Sum of their ages = 50 + 30= 
50 + 30 = 80
80.   80)
Answer: E
There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 20 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City?  Choose the correct choice from the following choices:
A) 90.
B) 80.
C) 50.
D) 40.
E) 25.

Solution: STREET-CAT 40.OMESTIC-Cat   70 130   (20gray+50other) 90gray+40other   Answer:40.
Answer: D
In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together? Choose one.
A) 8!*4!*4! Ways B) 3!*8!*4!*Ways C) 3!*4!*4! Ways D) 4!*4! Ways E) 3!*8!*4!*4! Ways

Solution: Taking all person of same nationality as one person, then we will have only three people.   These three person can be arranged themselves in 3! Ways.   8 Indians can be arranged themselves in 8! Way.   4 American can be arranged themselves in 4! Ways.   4 Englishman can be arranged themselves in 4! Ways.   Hence, required number of ways = 3!*8!*4!*4! Ways.   Ans 3!*8!*4!*4! Ways
Answer: E
What is the remainder when 81+82+83……+815 is divided by 6  Pick:	A) 0	B) 1	C) 2	D) 4	E) 5

Solution: Thus odd powers will have remainder 2 ; and even powers will have remainder 4   Now, 81+82+83……+81581+82+83……+815 will have the following powers -   Odd = 1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 ( 8 odd powers ) ; Sum of remainder = 16   Even Powers = 2, 4 , 6 , 8 , 10 , 12 , 14 ( 7 even Powers ) ; Sum of remainder = 28   Total sum of remainder = 44   44/6 = Remainder 2   Hence correct answer will be (2) 2....
Answer: C
Today is Friday. The day after 59 days will be  Choose the correct choice:  A) Monday  B) Tuesday  C) Saturday  D) Sunday  E) None of these

Solution: Explanation :   59 days = 8 weeks 3 days = 3 odd days   Hence if today is Friday, After 59 days, it will be = (Friday + 3 odd days)   = Monday. Mondaynswer : Option Monday
Answer: A
Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 20 percent on food, and 30 percent on other items. If Jill paid a 5 percent tax on the clothing, no tax on the food, and an 10 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes? Choose the correct choice from the following answers.
A) 5.5% B) 3.6% C) 4.4% D) 5.2% E) 6.0%

Solution: Let amount spent by Jill = 100   Clothing=50, Food=20, others=30   Tax on clothing= 2.5   Tax on others=3   Percentage= 5.5/100=5.5%   5.5%nswer: 5.5%
Answer: A
A city had 500 migrants in the year 1998. Since then, The number of migrants in a countrythe city has doubled every 4 years. If there were 500 migrants in the country in the year 1998, What was the increase in the population of migrants during the period from 2006 to 2010?	Choose one.
A) 2000
B) 3000
C) 4000
D) 8000
E) 10000

Solution: The population will increase in the following order:   1998: 500   2002: 1000   2006: 2000   2010: 4000   Difference between 2006 and 2010 = 2000   Option 2000
Answer: A
A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit. Choose the correct choice from the following: A) Rs. 1900 B) Rs. 2660 C) Rs. 2800 D) Rs. 2840 E) Rs. 3000

Solution: Explanation:   For managing, A received = 5% of Rs. 7400 = Rs. 370.   Balance = Rs. (7400 - 370) = Rs. 7030.   Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)   = 39000 : 42000 : 30000   = 13 : 14 : 10   B's share = Rs.(7030 X 14/37)=Rs. 2660.   ANSWER IS Rs. 2660
Answer: B
Dana borrows 7500 pounds annually for her college education. If Dana gives her parents 5% of that amount back each month, how much will she still owe her parents after four years of college? Choose the correct choice from the following.
A) 8000  B) 9000  C) 10000  D) 11000  E) 12000

Solution: dana borrows 7500 and returns 5% per month.   so returns 375 per month. and 4500 per year.   so dana owes  7500-4500= 
 7500-4500 = 3_000
3000 per year.   after 4 years she will owe 12000.   Ans (12000)
Answer: E
Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 4. The numbers are  Options:
A) 12, 24, 30 B) 12, 24, 38 C) 12, 24, 362 D) 4, 8, 12 E) 12, 24, 321

Solution: Explanation:   Let the required numbers be x, 2x, 3x. Then, their H.C.F =x. so, x= 4   \inline \fn_jvn \therefore The numbers are 4, 8, 12   Answer: 4, 8, 12) 4, 8, 12
Answer: D
In the line xy plane line m has the equation y = 4x - 8, then the line m passes through which of the following points?  Choose the correct choice from the following answers
A) (3, 1)
B) (3, 4)
C) (4, 2)
D) (4, 8)
E) (6, 15)

Solution: Yes it is y=3x-8....extremely sorry for mistake....   IF that's the case then answer is (4, 8)   y=3x-8   8=3X4-8   8=16-8   8=8 (satisfied)
Answer: D
n is an integer chosen at random from the set
{5, 7, 9, 11 }
p is chosen at random from the set
{2, 6, 10, 14, 18}
What is the probability that n + p = 25 ?
Choose the correct choice from the following options: A) 0.1 B) 0.2 C) 0.05 D) 0.3 E) 0.4

Solution: Set N: there is 4 ways to chose a number   Set P: there is 5 ways to chose a number   so total outcome is  4*5= 
 4*5 = 20
20 which is represent 20 pairs of number   now we have 1 pairs can give us 25 which are (11,14) .   1/20= 
1/20 = 1/20 = around 0.05
0.05   Answer 0.05
Answer: C
Ram professes to sell his goods at the cost price but he made use of 800 grms instead of a kg, what is the gain percent?
Choose the most appropriate option:
A) 28%
B) 23%
C) 22%
D) 26%
E) 25%

Solution: 800 --- 200   200 --- ? =>   200/800 *100= 
200/800 *100 = 25
25%   Answer: 25%
Answer: E
three mobsters have arrived at the theater for the premiere of the film “Goodbuddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the six arrange themselves in line such that Frankie’s requirement is satisfied?  Choose the correct choice: A) 6 B) 24 C) 120 D) 360 E) 3

Solution: Arrangement of 3=3!. In half of the cases Frankie will be behind Joey and in half of the cases Joey will be behind Frankie (as probability doesn't favor any of them). So, the needed arrangement is 3!/2=3.   Answer: 3
Answer: E
Following an increase in prices, the price of a candy box was 10 pounds and the price of a can of soda was 12 pounds. If the price of a candy box was raised by 25%, and the price of a can of soda was raised by 50%. What was the price of a box of candy plus a can of soda before prices were raised?	Choose the correct answer:  A) 11.  B) 12.  C) 16.  D) 14.  E) 14.5

Solution: Price of candy before price increase= 10/1.25= 
10/1.25 = 8
8   Price of soda before price increase= 12/1.5= 
12/1.5 = 8
8   Total price= 8+8= 
8+8 = 16
16   16. is the answer
Answer: C
The length of the bridge, which a train 120 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
Pick one:
A) 230
B) 240
C) 245
D) 255
E) 260

Solution: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (120 + x)/30 = 25/2 => 2(120 + x) = 750 => x = 255 m.   Answer: Option 255
Answer: D
In the quadrilateral PQRS d=8 cm, h1=6.2 cm and
h2=3.1 cm. Find the area
Choices
A) 37.2
B) 22
C) 23
D) 24
E) 25

Solution: area of quad.=1/2*any diagonal*(sum of 2 perpendiculars which is drawn on that diagona)   so 1/2*8*(6.2+3.1)= 
1/2*8*(6.2+3.1) = 37.2
37.2   37.2NSWER:37.2
Answer: A
If small rectangular boxes, each measuring 4 inches by 7 inches by 8 inches are arranged in a rectangular box measuring 20 inches by 42 inches by 24 inches, how many smaller boxes fit into the larger box? Choose the correct choice from the following options:
A) 45 B) 90 C) 64 D) 12 E) 23

Solution: The 4 inch side should be aligned to the 20 inch side ( 5 layer)   7 inch side should be aligned to the 42 inch side. (6 layer)   and 8 inch side should be aligned to the 24 inch side.(3 layer)   Maximum number of rectangles =5*6*3= 
5*6*3 = 90
90 Answer is 90
Answer: B
If a≠b and a·b≠0, which of the following may be true? Choices.
A) a/b=−b/a B) a^2=−b^2 C) (a−b)^2<0 D) a−b=b−a E) (a+b)(a−b)=0

Solution: A and B are the same, but how are they wrong? Those equations still makes sense because we're not told whether a and b are integers only.   Consider a = \sqrt{-5} and b= \sqrt{5}   So, a^2 = -5   and b^2 = 5   Therefore, a^2 = - b^2 ;   ANSWER:a^2=−b^2
Answer: B
A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Pick one.
A) 22
B) 77
C) 36
D) 71
E) 81

Solution: Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 240 + 120= 
240 + 120 = 360
360 m.   Time taken= 360/10= 
360/10 = 36
36 sec.   Answer:36
Answer: C
Find the average marks of all the students in classes A and B, if :
classes A = 55 students (average marks of students is 85)
classes B = 48 students (average marks of students is 78) Choose the correct choice from the following answers:
A) 88.5  B) 46.3  C) 81.7  D) 78.3  E) 23.4

Solution: Sum of the marks for the class of 55 students = 55 * 85= 
55 * 85 = 4_675
4675   Sum of the marks for the class of 48 students= 48 * 78= 
48 * 78 = 3_744
3744   Sum of the marks for the class of 103 students=   4675 + 3744= 
4675 + 3744 = 8_419
8419   Average marks of all the students=8419/103   = 81.7   Answer:81.7
Answer: C
The compound ratio of 7:6, 3:2 and 4:5? Pick one:
A) 7:5  B) 1:87  C) 1:6  D) 1:9  E) 1:2

Solution: 7/6 * 3/2 * 4/5 = 7/5   7:5   7:5nswer: 7:5
Answer: A
There is 60% increase in an amount in 6 years at S.I. What will be the C.I. of Rs. 12,000 after 3 years at the same rate? Select:
A) Rs. 2160 B) Rs. 3120 C) Rs. 3972 D) Rs. 6240 E) Rs. 6000

Solution: Explanation:   Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.   R = (100 * 60)/(100 * 6)= 
(100 * 60)/(100 * 6) = 10
10% p.a.   Now, P= Rs. 12000, T = 3 years and R = 10% p.a.   C.I. = [12000 * {(1 + 10/100)3 - 1}]   = 12000 * 331/1000 = Rs. 3972   ANSWER IS Rs. 3972
Answer: C
A baker charges P dollars for a birthday cake. Next week, she intends to earn 320 dollars selling cakes. If she were to reduce the price of the cake by 20 percent, she would have to sell two more cakes to earn the same amount of revenue. How many cakes does she intend to sell next week? Choose the correct choice from the following options:  A) 2  B) 4  C) 6  D) 8  E) 10

Solution: We're told that by selling cakes at P dollars/cake, a baker will make $320.   Reducing the price by 20% and selling 2 MORE cakes will also make her $320.   We're asked for the original number of cakes that the baker intends to sell.   $320 is a rather interesting number. Based on the answer choices, we're almost certainly dealing with integer values for the number of cakes AND the price per cake. As such, 6 is probably NOT going to be part of the solution (either as 4 and 6 cakes or as 6 and 8 cakes). As such, we can avoid Answers B and C....   Let's TEST ANSWER D: 8 cakes   IF....   Original cakes = 8   8(P) = $320, so P = $40/cake   20% off = $8 off = 40-8= 
40-8 = 32
$32/cake   +2 more cakes= 8+2= 
8+2 = 10
10 cakes   10(32)= $320   This is an exact MATCH for what we were told, so this MUST be the answer.   Final Answer:   8
Answer: D
present ages of A and B are in the ratio of 7:5 respectively. 5 years hence, the ratio of their ages will become 15:12 respectively . what A's present age in years?	Choose the correct choice from the following:  A) 20  B) 7/3  C) 15/4  D) 21/5  E) 20/3

Solution: A and B be 7x years and 5x years respectively   (7x+5)/(5x+5)=15/12   4(7x+5)= 5(5x+5)   x = 3/5   therefore A's present age : 7x=21/5 years   correct answer(21/5)
Answer: D
the reciprocal of the hcf and lcm of two are 1/12 and 1/312 .if one of the number is 24 then other no. is Choose the correct choice from the following answers
A) 126 B) 136 C) 146 D) 156 E) 166

Solution: reciprocal of the hcf and lcm of two are 1/12 and 1/312   so, HCF = 12 , LCM = 312   LCM * HCF = product of two numbers = a*b => b = LCM * HCF / a   so, other = 12*312 / 24= 
12*312 / 24 = 156
156   ANSWER:156
Answer: D
A polling company found that, of 300 households surveyed, 120 spent at least $100 per month on both gasoline and electricity, 60 spent at least $100 per month on gasoline but not on electricity, and for every household that did not spend at least $100 per month on gasoline or electricity, 4 spent at least $100 per month on electricity but not on gasoline. How many of the 300 households did not spend at least $100 per month on either gasoline or electricity?  Choose the correct choice from the following.
A) 24
B) 30
C) 36
D) 90
E) 96

Solution: 120 spend $100 on gas & electricity   60 spend $100 on gas but not on electricity   For every one that spent <$100 on both there are 4 that spent $100 on electricity not gas   Let the ones that spent on neither be x   The ones that spent on just electricity will be 4x   Total households = Those who spend >$100 on both + Those who spend >$100 on just one + Those who spend <$100 on both = 120 + 60 + 4x + x   300 = 180 + 5x implies x=24   24nswer is (24)
Answer: A
How many tow-digit integers exist such that all their digits are even?	Choose the correct choice from the following answers:
A) 20
B) 100
C) 120
D) 125
E) 135

Solution: 0 is also an even integer   so last digit can be filled in 5 ways- 0,2,4,6,8   for both second and third digit there are 5 possibilities-   5 X 5 = 25   _______________   The first digit can be any of the four: 2, 4, 6, or 8. For both seconddigits, there are 5 possibilities. The answer is 4∗5=20.   The correct answer is 20
Answer: A
In Orange County, one ninth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?	Choices:
A) 212  B) 235  C) 240  D) 252  E) 275

Solution: The number must be a multiple of both 9 and 7 so the answer is 252.   The answer is 252.
Answer: D
Sandy purchased 20 dozen toys at the rate of $360 per dozen. Sandy sold each toy at the rate of $30.60. What was the percentage profit?  Choose the correct choice
A) 1%  B) 2%  C) 3%  D) 4%  E) 5%

Solution: A dozen toys cost $360, so each toy cost $30.   selling price / cost price = 30.60 / 30= 
30.60 / 30 = 1.02
1.02   The percentage profit is 2%.   The answer is 2%.
Answer: B
The greatest possible length which can be used to measure exactly the length 5m, 4m 45m, 10 m 45 cm is
Choose the correct choice:
A) 15 cm
B) 25 cm
C) 5 cm
D) 42 cm
E) 43 cm

Solution: Explanation:   Required Length = H.C.F of 500 cm, 445 cm and 1045 c   = 5 cm. Answer: 5 cm
Answer: C
Smithtown High School is holding a lottery to raise money. The tickets are assigned numbers from 1 to 200. Tickets with numbers divisible by 2 win t-shirts, tickets with numbers divisible by 3 win gift certificates, and tickets with numbers divisible by 7 win movie passes. How many tickets win none of the prizes?	Options:	A) 6	B) 52	C) 58	D) 142	E) 194

Solution: Total numbers divisible by:   3->200/3=66.66; Ignore the decimal part=66   2->200/2=100;   7->200/7=28.Something; Ignore decimal part=28   3*2->200/6=33   3*7->200/21=9   2*7->200/14=14   3*2*7->200/42=4   Thus, total numbers that can win prize= 66+100+28-33-9-14+4= 
66+100+28-33-9-14+4 = 142
142 [:Note Used the same formula as we do for overlapping sets A∪B∪58=n(A)+n(B)+n(58)−n(A∩B)−n(A∩58)−n(B∩58)+n(A∩B∩58)   Non-winnable numbers=200-142= 
200-142 = 58
58   Ans: "58"
Answer: C
Machine M, N, O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 2/7 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?	Choose the correct choice from the following answers.
A) 1/2	B) 7/13	C) 4/13	D) 8/29	E) 6/33

Solution: Now ultimately the speed of every machine is given with respect to Mach O.   So lets assume the speed of O, say 12 hrs to make x units (assuming 6 because we can see we will need to divide by 3 and 4   Mach O makes x units in 12 hrs   So, Mach N = 2/7 of O = 2/7*12 = 24/7 hrs to make x units   and Mach M = 3/4 of N = 3/4*24/7 = 1/6hrs to make x units   No they are running simultaneously. Lets see how much each mach makes in 1 hr   Mach O = x/12 units   Mach N = 7/24 units   Mach M = x/6 units   In 1 hr, together they make - x/12+7/24+x/6 = 13/24   So what ratio of this has Mach N made?   (7/24) / (13/24) = 7/13   Ans:7/13=7/13
Answer: B
Three rugs have a combined area of 204 square meters. By overlapping the rugs to cover floor area of 140 square meters, the area that is covered by exactly two layers of rug is 24 square meters. What is the area that is covered with three layers of rug ?  Select the correct option.
A) 18 square meters  B) 20 square meters  C) 24 square meters  D) 28 square meters  E) 30 square meters

Solution: Total = Rug1 + Rug2 + Rug3 - {overlap of exactly 2 rugs} - 2*{overlap of exactly 3 rugs}   140 = 204 - 24 - 2*{overlap of exactly 2 rugs} --> {overlap of exactly 3 rugs} = 20.   Answer: 20 square meters.
Answer: B
38 68 22 70 31 47 13 82
Which of the following numbers is greater than three fourths of the numbers but less than one fourth of the numbers in the list above?
Select.
A) 56 B) 68 C) 69 D) 71 E) 73

Solution: Arrange the numbers in ascending order:   13, 22, 31, 38, 47, 68, 70, 82 (Just cross check the count to ensure that you didn't miss anything)   How many numbers do we see?   8, alright.   What's (1/4)8?   2.   What's (3/4)8?   6.   We're asked to find a number that are greater than 6 numbers in the list AND smaller than the remaining two.   13, 22, 31, 38, 47, 68,70, 82   13, 22, 31, 38, 47, 68: Find a number greater than any of these numbers.   70, 82: Find a number smaller than any of these numbers.   Only 69 fits the description.   Ans:69
Answer: C
A man saves Rs. 200 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years?	Choose the correct answer:
A) Rs.662.22	B) Rs.662.20	C) Rs.662.02	D) Rs.662.12	E) Rs.662.09

Solution: Amount = [200(1 + 5/100)3 + 200(1 + 5/100)2 + 200(1 + 5/100)]   = [200 * 21/20(21/20 * 21/20 + 21/20 + 1)]   = Rs.662.02   Answer: Rs.662.02
Answer: C
Teacher took exam for English, average for the entire class was 80 marks. If we say that 10% of the students scored 95 marks and 20% scored 90 marks then calcualte average marks of the remaining students of the class. Pick: A) 60 B) 70 C) 65 D) 75 E) 80

Solution: Lets assume that total number of students in class is 100 and required average be x.   Then from the given statement we can calculate :   (10 * 95) + (20 * 90) + (70 * x) = (100 * 80)   70x = 8000 - (950 + 1800)= 
8000 - (950 + 1800) = 5_250
5250 ANSWER : 75   x= 75.
Answer: D
Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction? Choose the correct option:
A) 10	B) 12	C) 14	D) 15	E) 20

Solution: Speed of the first train =(120/10) m/sec = 12 m/sec   Speed of the second train =(120/15) m/sec = 8 m/sec   Relative speed = (12 + 8)= 
(12 + 8) = 20
20 m/sec.   Required time= (120+120)/20= 
(120+120)/20 = 12
12 sec   answer :12
Answer: B
The sum of the digits of a two-digit number is 9 less than the number. Which of the following digits is at unit’s place of the number?
Options:
A) 1
B) 2
C) 4
D) Data inadequate
E) None of these

Solution: Solution   Let the ten's digit be x and unit's digit be y. Then, (10x + y) - (x + y) = 9 or x = 1.   From this data, we cannot find y, the unit's digit. So the data is inadequate.   Answer Data inadequate
Answer: D
A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?  Choose the correct choice from the following options
A) 10% B) 12% C) 100% D) 18% E) 80%

Solution: MP = 100   100%P = 75   SP = 150   ------   75 ---- 75   100 ---- ? => 100%   Answer:100%
Answer: C
The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4 ?	Choose the most appropriate option
A) 76  B) 79  C) 85  D) 87  E) 89

Solution: Explanation:   Average = total runs / no.of innings = 32   So, total = Average x no.of innings = 32 x 10 = 320.   Now increase in avg = 4runs. So, new avg = 32+4= 
32+4 = 36
36runs   Total runs= new avg x new no. of innings = 36 x 11 = 396   Runs made in the 11th inning = 396 - 320= 
396 - 320 = 76
76 76nswer: 76
Answer: A
if A and B can do a piece of work in 10 days and A alone can do it in 15 days, how long will B take to do it?  Choose the correct choice.
A) 20	B) 30	C) 35	D) 40	E) 45

Solution: 1/10-1/15=1/30   30 days   ANSWER:30
Answer: B