MU-NLPC/Calc-aqua_rat huggingface dataset:
Find the area of trapezium whose parallel sides are 20 cm and 10 cm long, and the distance between them is 10 cm.	Choose the correct choice:
A) 187 cm2 B) 185 cm2 C) 150 cm2 D) 185 cm2 E) 195 cm2

Solution: Explanation:   Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 10) * (10) = 150 cm2   Answer: Option 150 cm2
Answer: C
A cyclist covers a distance of 750 m in 2 min 30 sec. What is the speed in km/hr of the cyclist?  Choose the correct choice from the following choices:
A) 5 km/hr	B) 6 km/hr	C) 12 km/hr	D) 17 km/hr	E) 18km/hr

Solution: Speed = { 750 } m/sec =5 m/sec = { 5 * 18 } km/hr =18km/hr   Ans: 18km/hr
Answer: E
The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area?  Choose the correct choice from the following.
A) 260 cm2
B) 240 cm2
C) 280 cm2
D) 220 cm2
E) 250 cm2

Solution: 4a = 68 => a = 17   172 – 82 = 152   1/2 * 16 * 30= 
1/2 * 16 * 30 = 240
240   ANSWER:240 cm2
Answer: B
The ratio of investments of A, B and C is 5:6:7. If they share the profit in the ratio of 5:9:14, then find the ratio of their periods of investments.  Choices
A) 2:3:4	B) 3:5:6	C) 3:2:4	D) 2:4:3	E) 2:5:3

Solution: The ratio of investments of A, B and C is 5:6:7.   The ratio of shares of A, B and C is 5:9:14.   Therefore, Ratio of their periods of investments is   (5/5) : (9/6) : (14/7) = 1:3/2:2 = 2:3:4.   2:3:4NSWER:2:3:4
Answer: A
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected? Choose one:
A) 159
B) 194
C) 210
D) 209
E) 166

Solution: Out of 10 students 4 children should to be selected.   So the combination will be 10C4.   102104=10!/6!*4!=10*9*8*7*6!/6!*(4*3*2*1)   102104=210   There are 210 differect possible ways to select 4 children out of 10 students.
Answer: C
A certain meter records voltage between 0 and 10 volts inclusive. If the average value of 3 recordings on the meter was 9 volts, what was the smallest possible recording in volts?
Choose the correct choice:  A) 2  B) 3  C) 4  D) 5  E) 7

Solution: if average of 3 is 9 so sum of 3 should be 27   3 recording can be from 0-10 inclusive   to find one smallest other two should be highest   so, lets assume three var are a,b,c   say a is smallest and give b and c greatest readings say 10 and 10   so a has to be 7   7
Answer: E
At Jerri’s Pet Shop, 60 cups of bird seed are used every 5 days to feed 20 parakeets. How many cups of bird seed would be required to feed 10 parakeets for 5 days?
Select
A) 45.6  B) 20  C) 9  D) 30  E) 65

Solution: Let's go step-by-step.   60 cups are used over a 5 day period, which means 12 cups a day. This feeds 20 parakeets, which means each parakeet needs .60 of a cup every day.   For 10 parakeets, we need 10*.60= 
10*.60 = 6
6 cups a day. Over 5 days, we need 30 cups. Choice 30.
Answer: D
Which of the following must be subtracted from 2^48 so that the resulting integer will be a multiple of 3?  Pick.
A) 2	B) 1	C) 3	D) 4	E) 5

Solution: {4^1} / 3 =4/3 remainder 1   {4^2} / 3 = 16/3 remainder 1   {4^3} / 3 = 64/3 remainder 1   {4^4} / 3 = 256/3 remainder 1   Actually the same remainder keeps repeating .....   Try with a diff no, say 2   {2^1}/3 = remainder 2   {2^2}/3 = remainder 1   {2^3}/3 = remainder 2   {2^4}/3 = remainder 1   Answer : 1
Answer: B
Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get? Choose one:
A) 2400
B) 2408
C) 2487
D) 2429
E) 2123

Solution: First persons investment = x   Second persons investment = x + 1000   Third persons investments = x + 2000   x + x + 1000 + x + 2000 = 9000   3x = 6000   x = 2000   Ratio = 2000 : 3000 : 4000   2:3:4   4/9 * 54000 = 2400   2400nswer:2400
Answer: A
What is the greatest number of four digits which is divisible by 15, 25, 40 and 75 ?	Answers:  A) 9800  B) 9600  C) 9400  D) 9200  E) 9000

Solution: Greatest number of four digits = 9999   LCM of 15, 25, 40 and 75 = 600   9999 ÷ 600 = 16, remainder = 399   Hence, greatest number of four digits which is divisible by 15, 25, 40 and 75   = 9999 - 399= 
9999 - 399 = 9_600
9600   Answer: Option 9600
Answer: B
If the average (arithmetic mean) of (2a+16) and (3a-8) is 69, what is the value of a?	Pick one:
A) 26
B) 30
C) 28
D) 36
E) 42

Solution: ((2a+16) + (3a-8)) / 2 = (5a+8)/2 = 69   a= 26   The answer is 26.
Answer: A
Two trains, each 100 m long, moving in opposite directions, cross other in 5 sec. If one is moving twice as fast the other, then the speed of the faster train is?
Choose the correct choice from the following choices.
A) 22	B) 96	C) 60	D) 88	E) 12

Solution: Let the speed of the slower train be x m/sec.   Then, speed of the train = 2x m/sec.   Relative speed = ( x + 2x) = 3x m/sec.   (100 + 100)/5 = 3x => x = 40/3.   So, speed of the faster train = 80/3 = 80/3 * 18/5= 
80/3 * 18/5 = 96
96 km/hr.   Answer:96
Answer: B
1, 0.2, 0.08, 0.48, 0.0384, ____ Choose the most appropriate option.
A) 0.0584
B) 0.0484
C) 0.0434
D) 0.0384
E) None

Solution: 1, 0.2, 0.08, 0.48, 0.0384, .....   1*0.2= 
1*0.2 = 0.2
0.2   0.2*0.4= 
0.2*0.4 = 0.08
0.08   0.08*0.6= 
0.08*0.6 = 0.048
0.048   0.048*0.8= 
0.048*0.8 = 0.0384
0.0384   So 0.0384*1= 
0.0384*1 = 0.0384
0.0384   ANSWER:0.0384
Answer: D
The weights of three boys are in the ratio 4 : 5 : 6. If the sum of the weights of the heaviest and the lightest boy is 45 kg more than the weight of the third boy, what is the weight of the lightest boy?  Select the correct option
A) 32 kg  B) 36 kg  C) 40 kg  D) 44 kg  E) None of these

Solution: Let the weights of the three boys be 4k, 5k and 6k respectively.   4k + 6k = 5k + 45   => 5k = 45 => k = 9   Therefore the weight of the lightest boy   = 4k = 4(9) = 36 kg.   ANSWER:36 kg
Answer: B
A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must also be in the set?
I. 1
II. -4
III. 5	Choose the correct choice from the following.
A) I only  B) II only  C) I and III only  D) II and III only  E) I, II, and III

Solution: The question is which of the following must be in the set, not could be in the set.   If -1 is in the set so must be   -1+2= 
  -1+2 = 1
1, as 1 is in the set so must be   1+2= 
  1+2 = 3
3, as 3 is in the set so must be   3+2= 
  3+2 = 5
5 and so on. So basically knowing that -1 is in the set we can say that ALL odd numbers more than -1 are also in the set.   Answer: I and III only.
Answer: C
Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is? Choose the correct answer:
A) 19 : 9	B) 19 : 1	C) 19 : 2	D) 19 : 5	E) 19 : 3

Solution: Explanation:   Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres   Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres   Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4= 
19/4 = 19/4 = around 4.75
4.75 litres   As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed= 4.75 : 1.25 = 19 : 5.   Answer:19 : 5
Answer: D
A factory has three types of machines, each of which works at its own constant rate. If 7 Machine As and 11 Machine Bs can produce 470 widgets per hour, and if 8 Machine As and 22 Machine Cs can produce 600 widgets per hour, how many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?  Choose the correct option:
A) 400  B) 475  C) 550  D) 560  E) 700

Solution: Let Machine A produce A widgets per hour. B produce B widgets per hour and C produce C widgets per hour.   7A+11B=470 ---(1)   8A+22C=600 ---(2)   560ividing (2) by 2   4A+11C=300.....(3)   Adding (1)(3)   11A+11B+11C = 770   A+B+C=70 per hour   So for eight hrs = 70*8= 
70*8 = 560
560= Answer = 560
Answer: D
The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 625 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 8 units?
Choose the correct choice from the following choices
A) 140 sq.units	B) 158 sq.units	C) 187 sq.units	D) 80 sq.units	E) 815 sq.units

Solution: Given that the area of the square = 625 sq.units   => Side of square = √625 = 25 units   The radius of the circle = side of the square =25 units   Length of the rectangle = 2/5 * 25= 
2/5 * 25 = 10
10 units   Given that breadth= 8 units   Area of the rectangle = lb = 10 * 8= 
10 * 8 = 80
80 sq.units   Answer: 80 sq.units
Answer: D
If the a radio is sold for rs 490 and sold for rs 465.50.find loss%.	Choose the correct choice.
A) 2  B) 4  C) 3  D) 5  E) 6

Solution: sol. cp=rs490,sp= 465.50.   loss=rs(490-465.50)=rs 24.50.   loss%=[(24.50/490)*100= 
(24.50/490)*100 = 5
5%   Option 5
Answer: D
120 liters of a mixture contains milk and water in the ratio 4:2. If 10 liters of this mixture be replaced by 10 liters of milk, the ratio of milk to water in the new mixture would be? Choose the correct option
A) 8:6  B) 9:3  C) 9:4  D) 9:6  E) 8:2

Solution: Quantity of milk in 120 liters if mix = 120*4/6= 
120*4/6 = 80
80 liters   Quantity of milk in 130 liters of new mix= 80+10= 
80+10 = 90
90liters   Quantity of water in it= 130-90= 
130-90 = 40
40 liters   Ratio of milk and water in new mix= 90:40 = 9:4   Answer is 9:4
Answer: C
What is the sum of 80 consecutive integers from -39 inclusive, in a increasing order?	Choose the correct choice: A) -29 B) 39 C) -30 D) 40 E) 60

Solution: From -39 to -1 --> 39 nos.   zero --> 1 number   from +1 to +39 --> 39 nos.   When we add up nos. from -39 to +39 sum will be zero. Total 79 nos will be added.   80th number will be 40.   Sum of these 80 nos. = 40.   40 is the answer.
Answer: D
Out of 15 students studying in a class, 7 are from Maharashtra, 5 are from Karnataka and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka? Choose the correct option.
A) 12⁄13
B) 11⁄13
C) 10⁄15
D) 1⁄15
E) None of these

Solution: Total possible ways of selecting 4 students out of 15 students = 15C4 = 15×14×13×12 /1×2×3×4=1365   The no. of ways of selecting 4 students in which no student belongs to Karnataka = 10C4   ∴ Hence no. of ways of selecting at least one student from Karnataka = 15C4 – 10C4 = 1155   ∴ Probability = 1155⁄1365 = 77⁄91 = 11⁄13   Answer 11⁄13
Answer: B
In a series of six consecutive even numbers, the sum of the third and sixth numbers is 30. What are the third and sixth number respectively?	Choose the correct option
A) 10,16  B) 8,14  C) 16,22  D) 14,20  E) 12, 18

Solution: Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10.   Given (x + 4) + (x + 10) = 30   => 2x + 14 = 30 => x = 8   The third number = x + 4 = 8 + 4= 
8 + 4 = 12
12.   The sixth number= x + 10 = 8 + 10= 
8 + 10 = 18
18.   Answer: 12, 18
Answer: E
Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?  Select
A) 12,7 B) 12,9 C) 10,5 D) 11,6 E) 15,4

Solution: x â€“ y = 5   4x â€“ 6y = 6   x = 12 y = 7   12,7NSWER 12,7
Answer: A
In a box, there are 5 blue, 8 white and 3 yellow bulbs. One bulb is picked up randomly. What is the probability that it is neither white nor blue?  Choose one:
A) 3/16  B) 5/16  C) 8/32  D) 2/32  E) 9/32

Solution: Total number of bulbs = (5 + 8 + 3)= 
(5 + 8 + 3) = 16
16.   Let E= event that the bulb drawn is neither white nor blue = event that the bulb drawn is yellow.   Therefore, P(E)=3/16   3/16NSWER:3/16
Answer: A
Find compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually  Choose the correct choice:
A) 2109	B) 3109	C) 4109	D) 6109	E) 1109

Solution: Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.   Amount = Rs'. [8000 X (1+(15/100))^2 X (1+((1/3)*15)/100)]   =Rs. [8000 * (23/20) * (23/20) * (21/20)]   = Rs. 11109. .   :. C.I. = Rs. (11109 - 8000) = Rs. 3109. Answer: 3109
Answer: B
If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x=2^i∗3^k∗5^m∗7^p, then i + k + m + p =  Answers
A) 4 B) 7 C) 8 D) 11 E) 12

Solution: Here the idea is to go expressing each factor from one to eight, decomposed into its primes:   1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 = 1 * 2 * 3 *(2*2) * 5 +(2*3) * 7 *(2*2*2) = 2 ^ 7 * 3 ^ 2 * 5 ^ 1 * 7 ^ 1   Then   i = 7   k = 2   m = 1   p = 1   i + k + m + p = 11   Correct answer 11
Answer: D
There are 14 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 14 points that contain the point A?
Pick one:  A) 78  B) 105  C) 182  D) 210  E) 455

Solution: Any 2 points out 13 points will create triangle with third point A, so the answer is 13C2=78.   78nswer: 78.
Answer: A
Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?  Answers:	A) 7.18	B) 7.12	C) 7.16	D) 7.15	E) 7.11

Solution: T = (121 + 165)/ (80 + 65) * 18/5   T = 7.15   Answer:7.15
Answer: D
The ratio between the present ages of A and B is 4.5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago? Select:
A) 3:4 B) 3:0 C) 3:1 D) 7:3 E) 3:7

Solution: Let the present ages of A and B be 4.5x and 3x years respectively.   Then, (4.5x - 4)/(3x + 4) = 1/1   1.5x = 8 => x = 5.33   Required ratio = (5x + 4):(3x - 4) = 28:12 = 7:3.Answer: 7:3
Answer: D
The area of a square is 4225 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
A) 5:28  B) 5:19  C) 5:12  D) 5:13  E) 41:130

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 = 4225   a = 65   L = 2a and b = a - 24   b : l = a - 24 : 2a = 41 : 130   Answer:41:130
Answer: E
In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed? Options.
A) 83.37%  B) 83.93%  C) 83.38%  D) 83.23%  E) 83.33%

Solution: Percentage of milk in the mixture formed   = [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100%   = 5/6 * 100% = 83.33%.   Answer:83.33%
Answer: E
The average of 10 numbers is zero. Of them, How many of them may be greater than zero, at the most?	Choose the correct answer.
A) 6 B) 7 C) 10 D) 8 E) 9

Solution: Average of 10 numbers = 0   => Sum of 10 numbers/10=0   => Sum of 10 numbers = 0   Hence at the most, there can be 9 positive numbers.   (Such that if the sum of these 9 positive numbers is x, 10th number will be -x)   ANSW9R:9
Answer: E
By selling an article at Rs.500, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?	Answers.
A) s.600 B) s.480 C) s.300 D) s.450 E) s.550

Solution: SP = 500   Profit = 25%   s.300P = (SP)*[100/(100+P)]   = 500 * [100/125]   = 400   Loss 500 *  100/125= 
500 *  100/125 = 400
400   Loss= 25% = 25% of 400 = Rs.100   SP = s.300P - Loss = 400 - 100 = Rs.300   ANSWER:s.300
Answer: C
What percent is 50 gm of 1 kg?  Select the correct option
A) 1.5 % B) 0.5 % C) 2.5 % D) 3.5 % E) 5 %

Solution: 1 kg = 1000 gm   50/1000 × 100 = 5000/1000= 
5000/1000 = 5
5/1= 
5/1 = 5
5 %   5 %)
Answer: E
A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $920 in total compensation, how many total hours did he work that week?	Choose the correct choice from the following options:  A) 36  B) 40  C) 44  D) 50  E) 52

Solution: For 40 hrs = 40*16= 
40*16 = 640
640   Excess= 920-640= 
920-640 = 280
280   For extra hours=.75(16)=12+16= 
12+16 = 28
28   Number of extra hrs=280/28=70/7= 
70/7 = 10
10   Total hrs=40+10= 
40+10 = 50
50   Answer 50 50
Answer: D
A and B started a business investing Rs. 90,000 and Rs 30,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively? Choose one:
A) 9:2
B) 3:1
C) 18:20
D) 18:4
E) 17:4

Solution: A: 3:1 = 90000 : 30000   = 9 : 3   = 3 : 1   ANSWER:3:1
Answer: B
x varies inversely as square of y. Given that y=3 for x=1. The value of x for y = 4 will be equal to:  Choose the most appropriate option:
A) 3
B) 6
C) 1/9
D) 1/3
E) 9/16

Solution: Explanation :   Solution: Given x = k/y^2, where k is constant. Now, y=3 and x =1 gives k = 9.   .'. x = 9/y^2   => x =9 /4^2 = 9/16   Answer : 9/16
Answer: E
The true discount on a bill due 9 months hence at 16% per annum is Rs. 198.The amount of the bill is  Options.
A) Rs. 1386 B) Rs. 1764 C) Rs. 1650 D) Rs. 2268 E) None of these

Solution: Solution   32.5   Let P.W. be Rs. x.Then,S.I. on Rs.x at 16% for 9 months =Rs.198.   ∴ x 16 x9/ 12x 1/100}= 198 or x = 1650.   ∴ P.W. = Rs. 1650.   Answer Rs. 1650
Answer: C
What is the next number in the sequence : 14,19,29,40,44,52,59,73 __?	Choose the correct answer:
A) 90
B) 85
C) 81
D) 85
E) 83

Solution: next no. = previous + (sum of digits)   14 + (1+4)= 
14 + (1+4) = 19
19   19 + (1+9)= 
19 + (1+9) = 29
29   29 + (2+9)= 
29 + (2+9) = 40
40   40 + (4+0)= 
40 + (4+0) = 44
44   44 + (4+4)= 
44 + (4+4) = 52
52   52 + (5+2)= 
52 + (5+2) = 59
59   59 +(5+9)= 
59 +(5+9) = 73
73   73 + (7+3)= 
73 + (7+3) = 83
83   ANSW83R:83
Answer: E
A person starts writing all 4 digit numbers .How many times had he written the digit 3? Choose the correct choice from the following options
A) 3700 B) 3800 C) 3900 D) 4000 E) 4100

Solution: _ _ _ 3 = 9*10*10   _ _ 3 _ = 9*10*10   _ 3 _ _ = 9*10*10   3 _ _ _ = 10*10*10   900+900+900+1000= 
900+900+900+1000 = 3_700
3700   3700NSWER:3700
Answer: A
The salaries of A, B and C are in the ratio 1:3:4. If the salaries are increased by 5%, 10% and 15% respectively, then the increased salaries will be in the ratio  Choose the correct answer:
A) 20:66:95
B) 21:66:96
C) 21:66:92
D) 19:66:92
E) None

Solution: Solution: Let A's Salary = Rs. 100   Then, B's Salary = Rs. 300   And, C's Salary = Rs 400   Salary has given in 1:3:4 ratio.   Now,   5% increase in A's Salary,   A's new Salary = (100 + 5% of 100) = Rs. 105.   B's Salary increases by 10%, Then,   B's new Salary = (300 + 10% of 200) = Rs. 330.   C's Salary increases by 15%,   C's new Salary = (400 + 15% of 400) = Rs. 460.   Then, ratio of increased Salary,   A:B:C = 105:330:460 = 21:66:92.   Alternative   100(A's salary)===5%↑===> 105(A's increased salary);   300 (B's salary)===10%↑===>330 (B's increased salary);   400 (C's salary)===15%↑===> 460 (C's increased salary).   Ratio of their increased salary = 105:330:480 = 21:66:92   Answer: Option 21:66:92
Answer: C
If the average (arithmetic mean) of a and b is 45 and the average of b and c is 50, what is the value of c âˆ’ a?	Choices: A) 25 B) 10 C) 90 D) 14 E) It cannot be determined from the information given

Solution: the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1   similarly for b+c=100 --2   subtracting 1 from 2 we have   c-a=10;   ANSWER:10
Answer: B
A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?	Select:
A) 1:2 B) 1:8 C) 1:1 D) 1:6 E) 1:3

Solution: T = 192/32= 
192/32 = 6
6 h   T= 6 - 3= 
6 - 3 = 3
3   Time Ratio= 6:3 = 2:1   Speed Ratio = 1:2   1:2nswer: 1:2
Answer: A
Find the least value of 'a' so that 365a16 is divisible by 8. Choose the correct choice from the following choices
A) 9  B) 8  C) 0.  D) 2  E) 1

Solution: Explanation:   Given, number is divisible by 8 only if 'a16' is divisible by 8.   .: Least value of a is '0'.   Answer: Option 0.
Answer: C
A mixture contains milk and water in the ratio 5:2. On adding 10 liters of water, the ratio of milk to water becomes 5:3. The quantity of milk in the original mixture is?
Choose the correct answer:
A) 30	B) 40	C) 50	D) 60	E) 70

Solution: milk:water = 5:2   5x : 2x + 10 = 5 : 3   3[5x] = 5[2x + 10]   15x = 10x + 50   15x - 10x = 50   x = 10   The quantity of milk in the original mixture is = 5 : 2 = 5 + 2= 
5 + 2 = 7
7   7x= 70   Short cut method:   milk:water = 5 :2   after adding 10 liters of water   milk:water = 5 :3   milk is same but water increse 10liters then the water ratio is increse 1 parts   1 part -----> 10 liters   The quantity of milk in the original mixture is = 5 : 2 = 5 + 2= 
5 + 2 = 7
7   7 parts -----> 70 liters (Answer is= 70)   Short cut method - 2 : for Only milk problems   milk : water   5 : 2   5 : 3   milk ratio same but water ratio 1 part incress per 10 liters   1 part of ratio -------> 10 liters   7 part of ratio -------> 70 liters   50)
Answer: C
If x,y ,and z are positive real numbers such that x(y+z) = 132, y(z+x) =152 , and z(x+y) = 180, then xyz is Pick one.
A) 40
B) 60
C) 160
D) 100
E) 120

Solution: xy+xz = 132 --------------------------------------1)   yz+yx = 152---------------------------------------2)   xz+zy = 180---------------------------------------3)   Re-writing equation 3 as follows:   xz+zy = 152 + 28   xz+zy = yz+yx + 28   xz = yx + 28 ............... (4)   Adding (1)(4)   2xz = 160   xz = 80   xyz has to be multiple of 80,only 160 fits in   Answer = 160
Answer: C
One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 2,00,000 as total savings, how much has he saved in Public Provident Fund ?  Options
A) Rs. 30,000
B) Rs. 50,000
C) Rs. 80,000
D) Rs. 90,000
E) None

Solution: EXPLANATION   Let savings in N.S.C and P.P.F. be Rs. x and Rs. (200000 – x) respectively. Then,   1/3x=1/2(200000-x)   => x/3 + x/2 = 100000   => 5x/6 = 100000   => x= 100000 x 6 /5= 120000   Savings in Public Provident Fund = Rs. (200000 – 120000) = Rs. 80000   Answer Rs. 80,000
Answer: C
A shop sells floor tiles at Rs 48 per square meter. A building contractor employs a machine that polishes the tiles that damages 10% of the total number of tiles which cannot be used any more. Calculate the amount that needs to be paid by contractor to tile shop owner, if the hall is of a square shape and has a perimeter of 400 meters?	Choose the correct choice from the following options:  A) Rs 4,00,000  B) Rs 5,00,000  C) Rs 5,28,000  D) Rs 3,65,000  E) Rs 3,75,000

Solution: 4 sides of a square then 400/4= 
400/4 = 100
100   area of the hall   100*100= 
  100*100 = 10_000
10000   10% damaged so  10000*110/100= 
 10000*110/100 = 11_000
11000   48 per square meter then   48*11000= 
  48*11000 = 528_000
528000   ANSWER:Rs 5,28,000
Answer: C
In what ratio must the rice at Rs.3.20/kg be combined with rice at Rs.2.90/kg so that the combination becomes of worth Rs.3.08/kg ?  Choose one:  A) 3:2  B) 5:3  C) 7:3  D) 7:5  E) 8:5

Solution: Explanation :   Given   i. C.P of a kg quantity of I kind (p) = 3.20   ii. C.P of a kg quantity of II kind (p) = 2.90   iii. Mean rice price (p) = 3.08   iv. d – m = 3.08 – 2.90 = 0.18   v. m – c = 3.20 – 3.08 = 0.12   Therefore, Needed ratio = 0.18 : 0.12 = 3 : 2   3:2nswer : 3:2
Answer: A
1/3th of the passengers got down at first stop and 30 people got into the bus, 1/4th of the passengers got down at second stop and 12 people got into the bus.In last stop 84 people got down from the bus. What is the initial capacity of the bus?	Select the correct option:
A) 98  B) 99  C) 97  D) 96  E) 95

Solution: Let x be the no of initial passenger   no of passengr left in 1st stop (2x/3)+30   no of passenger in the 2nd stop 3/4((2x/3)+30) + 12   which is equal to 84 (passngr on last stop)   so final eqn....3/4((2x/3)+30) + 12 = 84   Ans x = 99   ANSWER:99
Answer: B