MU-NLPC/Calc-aqua_rat huggingface dataset:
Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat? Select the correct option.
A) 5!  B) 8!  C) 9!  D) 12!  E) 11!

Solution: Ans.(B)   Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways
Answer: B
If the tens digit of positive integer x is 2 and the tens digit of positive integer y is 2, how many possible values of the tens digit of 2(x+y) can there be? Choose the correct choice from the following choices
A) 2	B) 3	C) 4	D) 5	E) 6

Solution: We only need to consider the tens and ones digits of x and y, and the last two digits can be represented as 20 + p and 20 + q respectively.   2(20+p+20+q)= 80 + 2(p + q)   2(p+q) can range from 0 up to a maximum value of 36 when p=q=9.   Then the tens and ones digits of 2(x+y) can range from 80 up to 16.   That is, the tens digit can be 8, 9, 0, or 1.   There can be 4 possibilities for the tens digit.   The answer is 4.
Answer: C
If a + b - c = 4d, and if a - b + c = 4e, then a =	Options.
A) 2(d + e)  B) d – e  C) 3(d + e)/2  D) d-2e  E) e-d

Solution: 2(d + e)dd both equations:   a + b - c = 4d   a - b + c = 4e   a+b-c+a-b+c=4d+4e   2a=4d+4e   a=2(d+e)   2(d + e)ns:2(d + e)
Answer: A
Rose is two years older than Bruce who is twice as old as Chris. If the total of the age of Rose, B and Chris be 47 years, then how old is Bruce ?
Choose the correct choice from the following options:
A) 18 years
B) 10 years
C) 12 years
D) 13 years
E) 14 years

Solution: Let Chris's age be x years. Then, Bruce's age = 2x years.Rose's age = (2x + 2) years.   (2x + 2) + 2x + x = 47   5x = 45   x = 9   Hence, Bruce's age = 2*9= 
2*9 = 18
18 years.   18 yearsnswer : 18 years
Answer: A
First train 108 m long moving at a speed of 50 km/hr crosses a second train 112 m long coming from opposite direction in 6 seconds. Find the speed of the second train ??  Options.
A) 82 km/hr	B) 80 km/hr	C) 90 km/hr	D) 60 km/hr	E) 62 km/hr

Solution: speed of the second train consider as x   relative speed = (x+50)*5/18 m/sec   (250+5x/18) m/sec   distance = (108 + 112)= 
(108 + 112) = 220
220 m==> 220/(250+5x/18) = 6   250 + 5x = 660   =>x = 82 km/hr   82 km/hrNSWER 82 km/hr
Answer: A
445
2a3
+ 64b
+ c53
____
1892
If a and b represent positive single digits in the correctly worked computation above, what is the value of a + b + c ? Choose the correct choice from the following choices
A) 2
B) 7
C) 9
D) 11
E) 12

Solution: Adding the digits in unit's place , 5+ 3 + b + 3 = 12 (Since a and b are positive single digits )   => b = 2   Now adding the digits in ten's place , 4+a + 4 + 5 + 1= 19 (1 has been carried over from unit's place addition)   => a= 5   Now adding the digits in hundred's place , 4+ 2 + 6 +C + 1= 18 (1 has been carried over from unit's place addition)   => C= 5   a+b + C = 2+2+5   =12   Answer 12
Answer: E
Bombay Express left Delhi for Bombay at 14:30hrs travelling at a speed of 60kmph and Rajdhani Express left Delhi for Bombay on the same day at 16:30hrs travelling at a speed of 80kmph. How far away from Delhi will the two trains meet  Choose the correct answer:
A) 120km B) 360km C) 480km D) 500km E) 600km

Solution: Explanation:   Suppose they meet x hours after 14:30hrs   Then, 60x = 80(x-2) => x=8   Required distance = 60×8 = 480km   Answer: Option 480km
Answer: C
20 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 3:2. How many liters of Liquid Q must be added to make the ratio 4:3?	Choose one.
A) 1
B) 3
C) 5
D) 7
E) 9

Solution: Let x be the amount of liquid Q to be added.   (2/5)*20 + x = (3/7)*(20+x)   280 + 35x = 300 + 15x   20x = 20   x = 1   The answer is 1.
Answer: A
An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 3 o’clock in the afternoon?	Choose the correct choice from the following options
A) 60°
B) 90°
C) 180°
D) 210°
E) None of these

Solution: Sol.   Angle traced by the hour hand in 7 hours = [360/12 * 7= 
360/12 * 7 = 210
210°   Answer 210°
Answer: D
Dacid obtained 45, 35, 52, 47 and 55 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?	Choose the correct choice from the following answers:	A) 79	B) 99	C) 47	D) 89	E) 45

Solution: Average = (45+35+ 52+ 47+55)/5   = 234/5 = 47.   Answer:47
Answer: C
Rates for having a manuscript typed at a certain typing service are $5 per page for the first time a page is typed and $3 per page each time a page is revised. If a certain manuscript has 200 pages, of which 80 were revised only once, 20 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed?  Choose the correct option.
A) $1360	B) $1620	C) $1650	D) $680	E) $770

Solution: For 200-80-20= 
200-80-20 = 100
100 pages only cost is 5$ per page for the first time page is typed - 100*5=500$;   For 80 pages the cost is: first time 5$ + 3$ of the first revision - 80*(5+3)=640$;   For 20 pages the cost is: first time 5$ + 3$ of the first revision + 3$ of the second revision - 20(5+3+3)=220$;   Total: 500+640+220= 
500+640+220 = 1_360
1360$.   $1360nswer: $1360.
Answer: A
In Sam's hanger there are 23 boxes, 18 out of the boxes are filled with toys and the rest are filled with electrical appliances. 8 boxes are for sale, 5 of them are filled with toys. How many boxes with electrical appliances are in Sam's hanger that is not for sale?	Choose the correct choice from the following answers:
A) 1.	B) 2.	C) 3.	D) 4.	E) 5.

Solution: Total boxes = 23   Filled with toys = 18   Filled with appliance = 5   Total boxes for sale = 8   Toy boxes for sale = 5   Appliance boxes for sale = 3   Appliance boxes not for sale = 5 - 3= 
5 - 3 = 2
2   Correct Option: 2.
Answer: B
A, B and C enter into partnership. A invests 3 times as much as B invests and B invests two third of what C invests. At the end of the year, the profit earned is Rs. 8500. What is the share of B?  Select
A) 1545.45  B) 1545.48  C) 1545.42  D) 1545.46  E) 1545.43

Solution: Explanation:   Let C's capital = Rs. y. Then, B's capital = Rs. (2/3)y   A's capital = Rs. (3 × (2/3)y) = Rs. 2y   Therefore, ratio of their capitals   = 2y : (2/3)y : y   = 6 : 2 : 3   Hence, B's share = Rs. (8500 x 2/11) = Rs. 1545.45   1545.45NSWER: 1545.45
Answer: A
If @ is a binary operation defined as the difference between an integer n and the product of n and 5, then what is the largest positive integer n such that the outcome of the binary operation of n is less than 16?
Choose the correct option
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: @(n) = 5n - n   We need to find the largest positive integer such that 5n - n < 16.   Then 4n < 16 and n < 4.   The largest possible integer is n = 3.   The answer is 3.
Answer: C
Find avrg speed if a man travels at speed of 24km/hr up and 36km/hr dawn at an altitude of 200m.
Select the correct option:
A) 25.8
B) 26.8
C) 27.8
D) 28.8
E) 29.8

Solution: avg speed=2*x*y/(x+y)   =2*24*36/(24+36)= 
2*24*36/(24+36) = 144/5 = around 28.8
28.8   ANSWER:28.8
Answer: D
The cost of 16 pens and 8 pencils is Rs.352 and the cost of 4 pens and 4 pencils is Rs.96. Find the cost of each pen?
Pick one.
A) Rs.32	B) Rs.28	C) Rs.36	D) Rs.25	E) None of these

Solution: Let the cost of each pen and pencil be 'p' and 'q' respectively.   16p + 8q = 352 --- (1)   4p + 4q = 96   8p + 8q = 192 --- (2)   (1) - (2) => 8p = 160   => p = 20   ANSWNone of theseR:None of these
Answer: E
34.97 + 240.016 + 23.98 = ?	Options:	A) 298.966	B) 298.694	C) 289.496	D) 289.469	E) 298.964

Solution: 34.97   240.016   + 23.98   --------   298.966   298.966nswer is 298.966.
Answer: A
If 42.36 = k(14 + m/50), where k and m are positive integers and m < 50, then what is the value of k + m ?	Choose the correct answer:
A) 6
B) 7
C) 8
D) 9
E) 10

Solution: 42.36 = 14K + Km/50...we can rewrite the number as follows:   42+ 0.36= 14K + Km/50........Since K is integer, then 42=14K..........K=3   0.36=Km/50......36/100=3m/50......m=6   k+m=3+6= 
3+6 = 9
9   Answer: 9
Answer: D
A jar is filled of liquid which is 3 parts water and 5 parts alcohol. How much of this mixture should be drawn out and replaced such that this mixture may contain half
water and half alcohol?  Options.
A) 25%  B) 20%  C) 14.29%  D) 33.33%  E) None of these

Solution: Explanation:   Let the jar initially contain 8 litres of mixture:3 litres water and 5 litres alcohol   Let x litres of this mixture is drawn out and is replaced by x litres of water.   Amount of water now in the solution: 3-(3/8)x+x.   Amount of alcohol now in the solution: 5-(5/8)x   Desired ratio: 1/1   =>3-(3/8)x+x=5-(5/8)x   x=8/5 litres   %x=((8/5)/8)*100= 
((8/5)/8)*100 = 20
20%   ANSWER 20%
Answer: B
Siddharth wants to borrow Rs.7000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
Pick.
A) s.21.60
B) s.21.29
C) s.22.29
D) s.21.26
E) s.25.20

Solution: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.7,000   He lend the same amount for C.I at 6% p.a. for two years.   => Siddharth's income = C.I - S.I   = p[1 + r/ 100]n - p - pnr/100   = p{ [1 + r/ 100]2 - 1 - nr/100   = 7,000{ [1 + 6/100]2 - 1 - 12/100}   = 7,000 {(1.06)2- 1 - 0.12} = 7,000(1.1236 - 1 - 0.12)   = 7,000 (0.0036) = 7 * 3.6 = Rs.25.20   Answer: s.25.20
Answer: E
A merchant purchased a jacket for $60 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?
Choose the most appropriate option:
A) $0 B) $3 C) $4 D) $12 E) $15

Solution: Markup = x   x = 0.25(60 + x)   => 3x/4 = 15   => x = 20   So SP = 80   But Actual SP = 0.8 * 80= 
0.8 * 80 = 64
64   So profit= $4   Answer - $4
Answer: C
A car traveled 75% of the way from town A to town B at an average speed of 50 miles per hour. The car travels at an average speed of S miles per hour for the remaining part of the trip. The average speed for the entire trip was 60 miles per hour. What is S ?	Select:  A) 150  B) 200  C) 250  D) 300  E) 237.5

Solution: Total distance = 100 miles (easier to work with %)   75% of the distance = 75 miles   25% of the distance = 25 miles   1st part of the trip →  75/50= 
 75/50 = 3/2 = around 1.5
1.5   2nd part of the trip → 25/S= t   Total trip → (75+25)/60 = 1.5 + t » 100/60 = 1.5 + t » 2.5 = 1.5 + t » t = 0.1667   Back to 2nd part of the trip formula: 25/S = 0.1667 » S = 150   150ns 150
Answer: A
What is the year next to 1990 which will have the same calendar as that of the year 1990?  Choose the correct answer.
A) 1992
B) 2001
C) 1995
D) 1996
E) 1997

Solution: Explanation:   For a year to have the same calendar with 1990 ,total odd days from 1990 should be 0.   Take the year 1992 from the given choices.   Total odd days in the period 1990-1991= 2 normal years   ≡ 2 x 1 = 2 odd days   Take the year 1995 from the given choices.   Number of odd days in the period 1990-1994 = 4 normal years + 1 leap year   ≡ 4 x 1 + 1 x 2 = 6 odd days   Take the year 1996 from the given choices.   Number of odd days in the period 1990-1995= 5 normal years + 1 leap year   ≡ 5 x 1 + 1 x 2 = 7 odd days ≡ 0 odd days   (As we can reduce multiples of 7 from odd days which will not change anything)   Though number of odd days in the period 1990-1995 is 0, there is a catch here.   1990 is not a leap year whereas 1996 is a leap year.   Hence calendar for 1990 and 1996 will never be the same.   Take the year 2001 from the given choices.   Number of odd days in the period 1990-2000= 8 normal years + 3 leap years   ≡ 8 x 1 + 3 x 2 = 14 odd days ≡ 0 odd days   Also, both 1990 and 2001 are normal years.   Hence 1990 will have the same calendar as that of 2001   Answer: Option 2001
Answer: B
A meeting has to be conducted with 5 managers. Find the number of ways in which the managers be selected from among 9 managers, if 2 managers will not attend the meeting together? Pick:	A) 35	B) 91	C) 120	D) 126	E) 150

Solution: we can either choose all 5 people from 7 manager who have no problems or choose 4 from the 7 and 1 from the 2 managers who have a problem sitting together   so 7C5 + (7C4 * 2C1)   this is 21 + 70   91 ANS:91
Answer: B
If 4 (P's Capital ) = 6 ( Q's Capital ) = 10 ( R's Capital ) , then out of the total profit of Rs 4030 , R will receive
Options.
A) 600
B) 780
C) 800
D) 900
E) None of these

Solution: Explanation :   Let P's capital = p, Q's capital = q and R's capital = r   Then   4p = 6q = 10r   => 2p = 3q = 5r   =>q = 2p/3   r = 2p/5   P : Q : R = p : 2p/3 : 2p/5   = 15 : 10 : 6   R's share = 4030 * (6/31) = 130*6= 
130*6 = 780
780. Answer : Option 780
Answer: B
How many positive integers will divide evenly into 370?
Choose the correct choice from the following answers:
A) 4 B) 6 C) 8 D) 12 E) 16

Solution: The question is asking how many factors 370 has.   370 = 2*5*37   The number of factors is 2^3 = 8   The answer is 8.
Answer: C
A composer’s guild is planning its spring concert, and eleven pieces have been submitted for consideration. The director of the guild knows that they will only have time to present three of them. If the pieces can be played in any order, how many combinations of pieces are possible?
Choices:
A) 402
B) 165
C) 154
D) 512
E) 126

Solution: Combination question..   11C3 = 165..   IMO option 165 is correct..
Answer: B
The cash difference between the selling prices of an article at a profit of 8% and 6% is Rs 3. The ratio of two selling prices is  Choose one:
A) 51:52
B) 52:53
C) 53:54
D) 54:53
E) None of these

Solution: Explanation:   Let the Cost price of article is Rs. x   Required ratio = (108% of x) / (106% of x)   =108/106   =54/53 = 54:53.   Answer: 54:53
Answer: D
A car travels from point A to point B. The average speed of the car is 60 km/hr and it travels the first half of the trip at a speed of 48 km/hr. What is the speed of the car in the second half of the trip?
Choose the correct choice
A) 72  B) 75  C) 80  D) 84  E) 90

Solution: Let D be the distance and let V be the speed in the second half.   The total time = T1 + T2   D/60 = D/96 + (D/2) / V   8D/480 - 5D/480 = (D/2) / V   D/160 = D/2V and so V = 80 km/hr   The answer is 80.
Answer: C
A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 6 years ago?  Pick
A) 8 B) 10 C) 12 D) 14 E) 16

Solution: Let's say   Age of Richard isR   Age of David isD   Age of Scott isS   Now   Richard is 6 years older than David,   i.e. R = D +6   David is 8 years older than Scott   i.e. D = S +8   If in 8 years, Richard will be twice as old as Scott   i.e. R+8 = 2x(S+8)   i.e. R+8 = 2S + 16   i.e. R = 2S+8   But R = D+6 = (S+8)+6 = S+14   therefore, 2S + 8 = S +14   i.e. S = 6   i.e. R = 20   i.e. D = 14   Now,   how old was David 6 years ago?   i.e. D-6 = 14-6= 
14-6 = 8
8 years   8nswer: Option   8
Answer: A
The length of a train and that of a platform are equal. If with a speed of 126 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?  Choose the most appropriate option
A) 227  B) 299  C) 1050  D) 750  E) 211

Solution: Speed = [126 * 5/18] m/sec = 35 m/sec; Time = 1 min. = 60 sec.   Let the length of the train and that of the platform be x meters.   Then, 2x/60 = 35 è x = 35 * 60 / 2= 
35 * 60 / 2 = 1_050
1050   Answer: 1050
Answer: C
which of the following is a prime number ?
Choose the correct choice
A) 17	B) 18	C) 15	D) 20	E) 25

Solution: Clearly, 17 is a prime number.   Option 17
Answer: A
A man's regular pay is $3 per hour up to 40 hours. Overtime is twice the payment for regular time. If he was paid $180, how many hours overtime did he work? Choose the correct choice from the following:
A) 8 B) 5 C) 9 D) 6 E) 10

Solution: At $3 per hour up to 40 hours, regular pay = $3 x 40 = $120 If total pay = $168, overtime pay = $180 - $120 = $60 Overtime rate (twice regular) 180 -  120= 
180 -  120 = 60
$60 Overtime rate (twice regular)= 2 x $3 = $6 per hour => number of overtime hours = $60/$6 =10   Ans is 1060/ 6= 
60/ 6 = 10
10   Ans is 10
Answer: E
A man takes 3 hours 45 minutes to row a boat 25 km downstream of a river and 2 hours 30 minutes to cover a distance of 15 km upstream. Find the speed of the current.
Choose the correct choice from the following
A) 1 km/hr
B) 2/3 km/hr
C) 1/3 km/hr
D) 4 km/hr
E) None of these

Solution: Explanation:   First of all, we know that   speed of current = 1/2(speed downstream - speed upstream) [important]   So we need to calculate speed downstream and speed upstream first.   Speed = Distance / Time [important]   Speed upstream =(25/3 3/4)km/hr   =20/3km/hr   Speed Downstream = (15/2 1/2)km/hr   =6km/hr   So speed of current = 1/2(20/3−6)   =1/3 km/hr   Option 1/3 km/hr
Answer: C
An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?  Choose the correct choice from the following answers:
A) 144°	B) 150°	C) 168°	D) 180°	E) none

Solution: Solution   Angle traced by hour hand in   5 hrs 10 min.	= (360/12 x 6)°   = 180°.   Answer 180°
Answer: D
Mr. Wayne bungee jumps from the top of a building straight to the ground at a constant speed. 3 seconds after he starts plummeting he passes the 20th floor. 15 seconds after he starts plummeting he passes the 5th floor. Each floor is 4 meters high. What is Mr. Wayne's speed in meters per second?	Select the correct option.
A) 3 B) 3.75 C) 4 D) 4.25 E) 5

Solution: IMO: 5   15 Floors * 4 Meter/Floor = 60 Meters   Time= 12 sec   Rate * 12 = 60   Rate= 60/12= 
60/12 = 5
5   Answer 5
Answer: E
A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 12m/h. what is the speedof the person while he was going to his office? Select
A) 8km/h  B) 10km/h  C) 12km/h  D) 13km/h  E) 14km/h

Solution: u = k , v= 3k   \inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=12   \inline \Rightarrow 1.5k = 12   \inline \Rightarrow k=8km/h   8km/h
Answer: A
A marketing firm determined that, of 200 households surveyed, 80 used neither Brand R nor Brand B soap, 60 used only Brand R soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?	Pick.
A) 15  B) 20  C) 30  D) 40  E) 45

Solution: SOLUTION FOR SOAP R AN40 SOAP B   (40) 40
Answer: D
David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 14 family members in a row for the picture?  Choices
A) 12!	B) 13×12!	C) 12×13!	D) 14!/2!	E) 14!

Solution: The number of ways to arrange 14 people is 14!   We need to subtract the arrangement when these two people are together.   Let's think of these two people as a single unit so there are 13 units.   The number of ways to arrange 13 units is 13!   We need to multiply this by 2 since these two people could switch places.   The total number of valid arrangements is 14! - 2*13! = 13!*(14-2) = 12x13!   The answer is 12×13!.
Answer: C
What is the units digit of 33^2 * 17^3 * 39^2?	Pick:
A) 1 B) 3 C) 5 D) 7 E) 9

Solution: The units digit of 33^2 is the units digit of   3*3= 
  3*3 = 9
9 which is 9.   The units digit of 17^3 is the units digit of   7*7*7= 
  7*7*7 = 343
343 which is 3.   The units digit of 39^2 is the units digit of   9*9= 
  9*9 = 81
81 which is 1.   The units digit of  9*3*1= 
 9*3*1 = 27
27 is 7.   The answer is 7.
Answer: D
A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
Choose the most appropriate option
A) 22	B) 99	C) 40	D) 28	E) 23

Solution: 800*(25/100)= 
800*(25/100) = 200
200 ---- 5   ? ---- 1=> Rs.40   Answer: 40
Answer: C
Saskia needs to catch the 3.15pm train in order to get to her Mixed Martial Arts fight on time. It is 2.55 pm and Saskia is 2 miles from the train station. Saskia can run at an average speed of 10 miles per hour. However Saskia is carrying a sack of bricks which slows her down by 20%. If she runs to the station how many minutes early or late will she be for the train?	Select:
A) 10 minutes early	B) 5 minutes early	C) 0 minutes early	D) 5 minutes late	E) 10 minutes late

Solution: Saskia can run at an average speed of 10 miles per hour however she is slowed down by 20% by the sack of bricks and so can only run at 8 miles per hour. (0.2 x 10 = 2; 10 - 2 = 8)   At a speed of 8 miles per hour, Saskia can run 2 miles in 15 minutes. (8 miles / 2 miles = 4; 60 minutes/4 = 15 minutes)   Saskia has 20 minutes until her train but can run the distance in 15 minutes therefore she will be 5 minutes early (20 - 15 = 5 minutes).   ANSWER: 5 minutes early
Answer: B
The H.C.F of two numbers is 15 and their L.C.M is 3300. If one of the numbers is 225, then the other is?
Choose the correct choice from the following answers:  A) 200  B) 210  C) 220  D) 230  E) 240

Solution: Other number = (15 * 3300)/225= 
(15 * 3300)/225 = 220
220.   Answer: 220
Answer: C
A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance Q between the two cities?
Choose one
A) 48 B) 72 C) 96 D) 120 E) 192

Solution: Hmmm I did this question a while ago and got it wrong so trying again   Rate x time = distance.   For the initial trip lets the distance Q to the midpoint be represented by P.   EQN1: R x 2 = P   For the second trip we know one bus left late and one left early. Together this is just a tricky way of saying one bus left an hour after the other. We know the total trip takes 4 hours (since getting to P is 2 hours). The second trip can be represented by:   Since the trip takes 4 hours if a bus leaves one hour early, the reminaining 3 hours are split between the two buses, ie. 1 + 3/2 = 2.5   EQN2: R x 2.5 = P + 24   EQN2-EQN1 : 0.5R=24   R=48   So the distance is rate x time = 48 x 4 = 192.   ANS = 192
Answer: E
The slant height of a cone is 12 cm and radius of the base is 4cm, find the curved surface of the cone? Choose the correct choice from the following options:
A) 26
B) 28
C) 48
D) 26
E) 28

Solution: π * 12 * 4   = 48   Answer:48
Answer: C
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 4 years hence?  Select the correct option.
A) 50  B) 60  C) 68  D) 80  E) 90

Solution: A + B = 60, A = 2B   2B + B = 60 => B = 20 then A = 40.   5 years, their ages will be 44 and 24.   Sum of their ages = 44 + 24= 
44 + 24 = 68
68.   ANSWER:68
Answer: C
What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58? Choose the correct choice from the following options:  A) 3944  B) 2287  C) 2977  D) 2668  E) 1298

Solution: Let the side of the square plot be a ft.   a2 = 289 => a = 17   Length of the fence = Perimeter of the plot = 4a = 68 ft.   Cost of building the fence = 68 * 58 = Rs. 3944.   3944nswer:3944
Answer: A