MU-NLPC/Calc-aqua_rat huggingface dataset:
A, B and C invest Rs. 28000, Rs. 42000 and Rs. 56000 respectively. If C's share at the end of 1 yr is Rs. 4120, find the total profit.  Choose one.
A) Rs. 8120 B) Rs. 9270 C) Rs. 8240 D) Rs. 9150 E) None of these

Solution: Explanation:   Let ratio of capitals of A, B and C   = 28000 : 42000 : 56000   = 2 : 3 : 4   Let the total profit be Rs x.   Then, C's share = Rs. (4x/9)   But 4x/9 = 4120   => x = (4120 × 9)/4 = 9270   Hence, the total profit = Rs. 9270.   Answer: Option Rs. 9270
Answer: B
P and Q had the same number of candies. P gave Q 28 candies so that now Q has five times as many candies as P has. How many candies does Q have now?	Select
A) 65 B) 70 C) 75 D) 80 E) 85

Solution: Let P and Q be the number of candies they had at the start.   P = Q   5(P-28) = Q+28   5(Q-28) = Q+28   4Q = 168   Q = 42   Now person Q has 42+28 candies which is 70 candies.   The answer is 70.
Answer: B
Which of the following lines has x-intercept and y-intercept that are integers R?
Choose the correct choice from the following choices
A) y=3x+1  B) y=√x+1  C) y=-2/x  D) y=x^2-1  E) xy=1

Solution: Values that satisfy y=x^2-1 are (x,y)=(-1,0),(1,0),(0,-1). Hence, they are all integers R and the correct answer is y=x^2-1.
Answer: D
Each writer for the local newspaper is paid as follows: a dollars for each of the first n stories each month, and a + b dollars for each story thereafter, where a > b. How many more dollars will a writer who submits n + a stories in a month earn than a writer who submits n + b stories?
Select.
A) (a – b)( a + b + n)  B) a – b  C) a^2 – b^2  D) n( a – b)  E) an + bn – an

Solution: total earned for n+a stories =a + a(a+b)   total earned for n+b stories =a+ b(a+b)   difference = a+a(a+b) -a -b(a+b)   =(a+b)(a-b) =a^2-b^2   ANSWER:a^2 – b^2
Answer: C
A number is doubled and 6 is added. If resultant is trebled, it becomes 72. What is that number
Choose the correct choice from the following
A) 8 B) 10 C) 9 D) 14 E) 16

Solution: Explanation:   => 3(2x+6) = 72   => 2x+6 = 24   => x = 9   Option 9
Answer: C
A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late . Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late. What is the speed Y of the train. Choose one
A) a) 45  B) b) 33  C) c) 48  D) d) 55  E) e) 61

Solution: Let y be the balance distance to be covered and x be the former speed.   A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late   so, y/(3x/4) - y/x = 35/60   4y/3x - y/x = 7/12   y/x(4/3-1)=7/12   y/x*1/3=7/12   y/x=7/4   4y-7x=0 ........ 1   Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late   so, (y-24)/(3x/4) - (y-24)/x = 25/60   4(y-24)/3x - (y-24)/x = 5/12   (y-24)/x (4/3-1) = 5/12   (y-24)/x *1/3 = 5/12   (y-24)*12 = 3x*5   (y-24)*4 = 5x   4y-5x = 96 ....... 2   eq2 - eq1   2x=96   x=48=Y   Ans = c) 48
Answer: C
Sushi invested an amount of Rs. 10,000 at the rate of 15% p.a simple interest and another amount at the rate of 16% p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14% p.a. Find the total amount invested?  Pick:
A) 10900
B) 10800
C) 10500
D) 10600
E) 10580

Solution: Let the second amount be Rs. x. Then,   (10000 * 15 * 1)/100 + (x * 16 * 1)/100 = [(12000 + x) * 14 * 1] / 100   15000+ 16x= 16800 + 14x   x = 900   Total investment = 10000 + 900 = Rs. 10,900.10900nswer: 10900
Answer: A
In an office, totally there are 6400 employees and 65% of the total employees are males. 25% of the males in the office are at-least 50 years old. Find the number of males aged below 50 years?	Choose the correct choice from the following choices
A) 2882	B) 8277	C) 3120	D) 2777	E) 9112

Solution: Number of male employees = 6400 * 65/100= 
6400 * 65/100 = 4_160
4160   Required number of male employees who are less than 50 years old= 4160 * (100 - 25)%   = 4160 * 75/100= 
4160 * 75/100 = 3_120
3120.   Answer: 3120
Answer: C
The length of a rectangle is reduced by 30%. By what % would the width have to be increased to maintain the original area?  Options
A) 42.8%
B) 20%
C) 25%
D) 30%
E) 35%

Solution: Sol. Required change = (30*100)/(100-30)=42.8%   42.8%
Answer: A
The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?	Choose one: A) 432 B) 376 C) 299 D) 276 E) 111

Solution: 2(3x + x) = 96   l = 36 b = 12   lb = 36 * 12= 
36 * 12 = 432
432   432
Answer: A
Pipe A can fill a tank in 12 hours. Due to a leak at the bottom it takes 20 hours to fill the tank. In what time the leak alone can empty the full tank?	Pick
A) 18 hours
B) 23 hours
C) 28 hours
D) 30 hours
E) 40 hours

Solution: Let leak can empty the full tank in x hours.   1/12- 1/X = 1/20   => 1/12 – 1/20 = 1/X   1/X =5-3 /60= 1/30   x= 30 hours   ANSWER:30 hours
Answer: D
From a pack of 52 cards, one card is drawn. What is the probability that the card is a color of red? Select the correct option.
A) 1/6 B) 2/2 C) 1/2 D) 8/2 E) 3/6

Solution: Let S be the sample space. Then,   n(S) = 52C1	= 52.   Let E = event of getting 1 face card.   n(E) = number of ways of choosing 1 face card out of 26   =26C1 = 26   P(E) = n(E) / n(S)	= 26 / 52   = 1/2.   Answer 1/2
Answer: C
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was: Choose the correct choice from the following answers:
A) 14 years
B) 19 years
C) 33 years
D) 38 years
E) 40 years

Solution: Explanation:   Let the son's present age be x years. Then, (38 - x) = x   2x = 38.   x = 19.   Son's age 5 years back (19 - 5)= 
(19 - 5) = 14
14 years.   14 yearsnswer: 14 years
Answer: A
Which of the following is a prime number ?  Choose the correct choice:	A) 33	B) 81	C) 93	D) 97	E) 32

Solution: Explanation:   Clearly, 97 is a prime number. Because it is not divisible by other numbers.   ANSWER IS 97
Answer: D
John found that the average of 15 numbers is 40. If 10 is added to each number then the mean of number is?
Choose one
A) 50 B) 65 C) 70 D) 75 E) 80

Solution: (x+x1+...x14)/15 = 40   50   Option 50
Answer: A
A train is 300 meter long is running at a speed of 54 km/hour. In what time will it pass a tunnel of 1200 meter length?  Choose the correct choice from the following answers:
A) 90 seconds	B) 85seconds	C) 40 seconds	D) 100 seconds	E) 120 seconds

Solution: Speed = 54 Km/hr = 54*(5/18) m/sec = 15 m/sec   Total distance = 300+1200= 
300+1200 = 1_500
1500 meter   Time= 100 secondsistance/speed   = 1500 * (15) = 100 seconds   Answer: 100 seconds
Answer: D
A train has a length of 150 meters . it is passing a man who is moving at 2 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train.	Pick one
A) 182 km/hr	B) 180 km/hr	C) 152 km/hr	D) 169 km/hr	E) 179 km/hr

Solution: Explanation:   Length of the train, l = 150m   Speed of the man , Vm= 2 km/hr   Relative speed, Vr = total distance/time = (150/3) m/s = (150/3) × (18/5) = 180 km/hr   Relative Speed = Speed of train, Vt - Speed of man (182 km/hrs both are moving in the same direction)   => 180 = Vt - 2   => Vt = 180 + 2= 
180 + 2 = 182
182 km/hr   182 km/hrnswer: Option 182 km/hr
Answer: A
Four barrels of water have an average capacity of 8 gallons. What is the maximum possible capacity of the smallest barrel E if the median is 10 gallons?  Answers
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: Suppose 4 barrels are B1, B2, B3, B4 in ascending capacity.   (B1+B2+B3+B4)/4 = 8   B1+B2+B3+B4=32   median is 10 ....... as the no. of terms are even i.e 4, median = (22+23)/2   ==> 22+23 = 20   now we have 21+24 = 32-20= 
32-20 = 12
12   Only the following possible cases can be there :   1,9,11,11   1,10,10,11   2,10,10,10   Max value of smallest barrel E= 2=2
Answer: B
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.	Choose the correct choice from the following answers:
A) 150	B) 88	C) 2767	D) 288	E) 712

Solution: Speed = 60*(5/18) m/sec = 50/3 m/sec   Length of Train (Distance) = Speed * Time     (50/3) * 9= 
  (50/3) * 9 = 150
150 meter   150nswer: 150
Answer: A
How many 3x3x3 cubes could fit in a 10x24x16 box?  Choose the correct choice.
A) 150 B) 145 C) 138 D) 142 E) 175

Solution: The answer is D) 142. The 10x24x16 box has an area of 3840. If you divide it by 27 (the total of the 3x3x3 smaller cube) you get 142.2. This means you could fit 142 whole cubes in the larger box.
Answer: D
An bus covers a certain distance at a speed of 240 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?  Choose one:
A) 677 km/hr	B) 720 km/hr	C) 790 km/hr	D) 800 km/hr	E) 820 km/hr

Solution: Distance = (240 x 5) = 1200 km.   Speed = Distance/Time   Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]   Required speed = 1200 x 3 km/hr = 720 km/hr.   720 km/hr
Answer: B
A soccer team played 280 games and won 65 percent of them. How many games did it win? Choose one.
A) 182 B) 100 C) 104 D) 150 E) 124

Solution: 65% of 280 =x   0.65*280= 
0.65*280 = 182
x   182=x   answer :182
Answer: A
In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 20 overs to reach the target of 282 runs?	Choose the correct choice from the following answers:
A) 6.25 B) 5.5 C) 7.4 D) 5 E) 12.5

Solution: 12.5xplanation:   Runs scored in the first 10 overs = 10 × 3.2 = 32   Total runs = 282   Remaining runs to be scored = 282 - 32= 
282 - 32 = 250
250   Remaining overs= 20   Run rate needed = 250/20= 
250/20 = 25/2 = around 12.5
12.5   Answer: Option 12.5
Answer: E
In a lottery, there are 9 prizes and 18 blanks. A lottery is drawn at random. What is the probability of getting a prize?
Choices.
A) 1/2  B) 1/3  C) 1/4  D) 1/5  E) 1/6

Solution: P(winning a prize) = 9 / (9+18) = 9/27 = 1/3   The answer is 1/3.
Answer: B
The difference between a positive proper fraction and its reciprocal is 9 / 20. Then the fraction is :	Choose the correct choice from the following choices:
A) 4/0
B) 4/1
C) 4/5
D) 4/2
E) 4/3

Solution: Explanation:   Let the required fraction be x. Then, (1 / x )- x = 9/20   1 - x^(2) / x = 9 / 20 => 20 - 20 * x^(2) = 9 * x.   20 * x^(2) + 9 *x - 20 = 0.   => (4 * x + 5) (5 * x - 4) = 0.   => x = 4 / 5.   Answer: 4/5) 4/5
Answer: C
Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill? Choose the correct choice from the following answers.
A) 11 1/8
B) 11 1/4
C) 11 2/4
D) 12 1/4
E) 17 1/4

Solution: 3/12 + x/15   = 1   x= 11 1/4   Answer: 11 1/4
Answer: B
A certain bag contains 100 balls â€” 10 white, 30 green, 10 yellow, 47 red, and 3 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?
Choose the correct choice from the following answers
A) 0.9 B) 0.75 C) 0.6 D) 0.8 E) 0.5

Solution: According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (10 + 30 + 10)/100 = 50/100 = 0.5.   Answer is 0.5
Answer: E
If c is 25% of a and 10% of b, what percent of a is b? Choose the correct option
A) 2.5%
B) 15%
C) 25%
D) 35%
E) 250%

Solution: c is 25% of a --> c=a/4;   c is 10% of b --> c=b/10;   Thus a/4=b/10 --> b=5/2*a=2.5a. Therefore, b is 250% of a.   Answer: 250%
Answer: E
A train running at 1/2 of its own speed reached a place in 8 hours. How much time could be saved if the train would have run at its own speed?  Choose one
A) 8hrs	B) 10hrs	C) 4 hrs	D) 15hrs	E) 6hrs

Solution: time taken if run its own speed = 1/2*8= 
1/2*8 = 4
4 hrs   Time saved= 8 - 4= 
8 - 4 = 4
4 hrs   Answer : 4 hrs
Answer: C
A car covers a distance of 813 km in 3 hours. Find its speed?	Choose the correct choice from the following answers.
A) 104	B) 288	C) 271	D) 276	E) 128

Solution: 813/3= 
813/3 = 271
271 kmph   Answer: 271
Answer: C
How many 3 letter (not necessarily distinct) words can be formed using the letters from the word TWIST ?
Choices:
A) 33  B) 54  C) 45  D) 60  E) None of the above

Solution: Two T's are used   In this case we have to select just one letter out of the remaining 33 (W, I, S) which can be arranges in 3 places.   So, the total possibilities are 3∗3=9   Total possibilities 24+9=332   So, the answer is 33.
Answer: A
In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much? Look at this series: 120, 30, 240, 25, ___, 20, 480, 15... Which number is missing? Choose the correct answer.
A) 120	B) 360	C) 340	D) 960	E) 280

Solution: B 360This is an alternating addition and subtraction series. In the first pattern, 120 is added to each number to arrive at the next. In the second, 5 is subtracted from each number to arrive at the next.
Answer: B
If x+y=250, x-y=200, for integers of x and y, y=? Choose the correct choice from the following choices:
A) 200	B) 225	C) 50	D) 115	E) 150

Solution: x+y = 250   x-y = 200   2x = 50   x = 25   y = 225   Answer is 225
Answer: B
A tank is 25m long 12m wide and 6m deep. The cost of plastering its walls and bottom at 75 paise per sq m is  Select the correct option:	A) Rs. 258	B) Rs. 358	C) Rs. 458	D) Rs. 558	E) None of these

Solution: Explanation:   Area to be plastered = [2(l + b) × h] + (l × b)   = [2(25 + 12) × 6] + (25 × 12) = 744 sq m   Cost of plastering = 744 × (75/100) = Rs.558 Answer: Rs. 558
Answer: D
A student scored an average of 80 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics? Answers
A) 86	B) 16	C) 76	D) 80	E) 26

Solution: Given M + P + C = 80 * 3= 
80 * 3 = 240
240 --- (1)   M + P= 90 * 2= 
90 * 2 = 180
180 --- (2)   P + C= 70 * 2= 
70 * 2 = 140
140 --- (3)   Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.   P= (2) + (3) - (1) = 180 + 140 - 240= 
180 + 140 - 240 = 80
80   Answer:80
Answer: D
A man can ride on cycle at 35 kmph upward road and 70 kmph downward road. He takes 6 hours to cycle uphill from lower point A to upper point B and back to A. What is the total distance traveled by him in 6 hours? He must return back to base point A in remaining time  Choices:
A) 120
B) 140
C) 160
D) 280
E) 180

Solution: Upward distance traveled per hour - 35 km,   distance traveled after 4 hours = 140 km.   He remained with 2 hours travel downward, i.e. distance traveled in remaining 2 hours downward = 140 km   so total distance traveled from A to B and Back to point A = 140 km upward + 140 km downhill = 280 km   (Answer : 280)
Answer: D
When 52416 is divided by 312, the quotient is 168. what will be the quotient when 52.416 is divided by 0.000168?	Choose the correct answer
A) 5	B) 6	C) 4	D) 3	E) 8

Solution: for the 1st no. there are 2 digits after decimal   for the 2nd no. there are 7 digits after decimal   total no. of decimals = 9   req. no. of digits=(n-1)=(9-1)= 
(9-1) = 8
8   ANSW8R :8
Answer: E
At a certain bowling alley, it costs $0.50 to rent bowling shoes for the day and $1.25 to bowl 2 games. If a person has $12.80 and must rent shoes, what is the greatest number of complete games that person can bowl in one day? Select:  A) 7  B) 8  C) 9  D) 19  E) 21

Solution: After renting bowling shoes the person is left with $12.80-$0.5=$12.30, which is enough for 12.3/1.2512.80- 0.5= 
12.80- 0.5 = 12.3
$12.30, which is enough for 12.3/1.25= 
12.3/1.25 = 9.84
9.84(2)=19.68<21. ~ 19 games   Answer: 19.
Answer: D
Ram has $100 in her piggy bank. How much will she have in her bank 25 weeks from now if she puts $1 in the bank next week, $2 two weeks from now, $3 three weeks from now, and continues to increase the amount that she puts in by $1 each week?  Choose one.
A) 400  B) 415  C) 425  D) 435  E) 445

Solution: The dollar deposits are in an A.P.   1,2,3,4...25 with common difference 1   Sum of the terms is n(n+1) / 2   i.e 25* (25+1) /2   = 25* 26/2= 
25* 26/2 = 325
325   Total deposit therefore with 425hiu-Lihas is 100 + 325= 
100 + 325 = 425
425$
Answer: C
Ada and Paul received their scores on three tests. On the first test, Ada's score was 12 points higher than Paul's score. On the second test, Ada's score was 4 points higher than Paul's score. If Paul's average (arithmetic mean) score on the three tests was 3 points higher than Ada's average score on the three tests, then Paul's score on the third test was how many points higher than Ada's score? Pick one.
A) 9	B) 14	C) 17	D) 23	E) 25

Solution: My take is Option D (23)   I followed a simple approach (explained below):   Test 1: Ada's score = Paul's score + 10   Test 2: Ada's score = Paul's score + 4   Avg. of Paul's score = 3 points higher than Avg. of Ada's score   This implies that : Sum of Paul's score [3 Tests] = 9 points higher than Sum of Ada's score [3 Tests] (9 points higher since 3 points were given in terms of average of 3 scores)   So, Paul needs to score 25 points higher than Ada in Test 3, since Paul needs to compensate for the lower score in test 1 and Test 2 ( 25= 12 + 4 + 9)   25
Answer: E
If the price of petrol increases by 20, by how much must a user cut down his consumption so that his expenditure on petrol remains constant?  Pick one:	A) 16.7%	B) 20%	C) 24.67%	D) 33.33%	E) None of these

Solution: Explanation :   let us assume before increase the petrol will be Rs. 100.   After increase it will be Rs (100+20) i.e 120.   Now, his consumption should be reduced to :-   =(120−100)/120 ∗ 100.   Hence, the consumption should be reduced to 16.7%.   16.7%nswer : 16.7%
Answer: A
The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is? Choose the correct answer
A) 12	B) 14	C) 16	D) 18	E) 20

Solution: 3:4   Total parts = 7   = 7 parts --> 28 (7 × 4 = 28)   = 1 part ---->4 (1 × 4 = 4)   = The greater of the two number is = 4   = 4 parts ----> 16 (4 × 4 = 16)   16
Answer: C
probability that guy1 will succesfully hit a shot is 2/3. probabilty of guy2 succesfully hitting a shot is 2/3. if they shoot two shots each, what is the probability that they have equal number of hits?
Select the correct option
A) 9/27  B) 10/27  C) 11/27  D) 12/27  E) 11/26

Solution: (1/3*1/3)[guy1]*(1/3*1/3)[guy2]   for 1 hit each: (4 ways)   (2/3*1/3)*(2/3*1/3), (2/3*1/3)*(1/3*2/3), (1/3*2/3)*(2/3*1/3), (1/3*2/3)*(1/3*2/3)   for 2 hits each:(1 way)   (2/3*2/3)*(2/3*2/3)   Add all these cases, you will get answer as 11/27.   ANSWER:11/27
Answer: C
It takes Tammy 15 minutes to do one oil change, and it takes Jill 10 minutes. At 2:30 pm, they both finish an oil change simultaneously. If Tammy and Jill both began doing oil changes at exactly the same time and worked without pausing, when did they both start doing oil changes?
Choose the correct choice from the following:
A) 2:00 pm
B) 2:05 pm
C) 2:10 pm
D) 2:15 pm
E) 2:20 pm

Solution: Since Tammy finishes s oil changes after s × 15 minutes and Jill finishes c oil changes after c × 10 minutes, they both finished doing an oil change at the same time when s × 15 = c × 10. Since s and c must be integers (they represent the number of oil changes finished) this question is asking you to find a common multiple of 15 and 10. The question asks for the first time they began a car simultaneously, so you must find the least common multiple and subtract. The least common multiple of 15 and 10 is 30, so in the context of the question, this would be 30 minutes. Therefore, they began changing the oil of a car at the same time at 2:30 - 30 minutes, or 2:00 p.m. The answer is (2:00 pm).
Answer: A
How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?
Choose the correct choice from the following answers: A) 360 B) 838 C) 372 D) 737 E) 273

Solution: The given digits are six.   The number of four digit numbers that can be formed using six digits is ⁶P₄ = 6 * 5 * 4 * 3= 
6 * 5 * 4 * 3 = 360
360.   360nswer:360
Answer: A
If TRAIN is coded as 12 and PANDA is coded as 18, then CURED is coded as  Choose the most appropriate option:
A) 5	B) 10	C) 13	D) 20	E) None

Solution: TR5IN= 20+18+1+9+14= 
20+18+1+9+14 = 62
62 i.e 6*2=12   P5ND5= 16+1+14+4+1= 
16+1+14+4+1 = 36
36 i.e 3*6=18   CURED= 3+21+18+5+4= 
3+21+18+5+4 = 51
51 5*1=5   5NSWER:5
Answer: A
24 people are there, they are shaking hands together, how many hand shakes possible,if they are in pair of cyclic sequence.	Pick one:
A) 19  B) 20  C) 21  D) 22  E) 24

Solution: in case of cycle no of handshakes = no of persons   hence ans = 24   ANSW24R:24
Answer: E
A, B and C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 280, how much must C pay as his share of rent?
Choose one: A) 45 B) 50 C) 55 D) 65 E) none

Solution: Sol.   A : B : C = 10 * 7 : 12 * 5 : 15 * 3 = 70 : 60 : 45 = 14 : 12 : 9.   âˆ´ Câ€™s rent = Rs. [280 * 9/35] = Rs. 72.   Answer none
Answer: E
Eight years back, a father was 52 years older than his son. At present the father is 5 times as old as the son. How old will the son be three years from now?  Choose the correct choice:
A) 10 years  B) 12 years  C) 14 years  D) 16 years  E) 18 years

Solution: Using linear equations to convert the word problem:   ** F = fathers current ageS = sons current age   #1 Eight years back, a father was 52 years older than his son: F-8 = 52 + (S - 8)   #2 At present the father is 5 times as old as the son: F = 5*S   How old will the son be three years from now?: S + 3 = ?   With two variables and two linear equations we are able to solve the problem:   (S*5) - 8 = 52 +S -8   4S=52   S = 13   S + 3 = 13+ 3= 
13+ 3 = 16
16   Answer: 16 years
Answer: D
A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?	Pick one.
A) 2 min. to empty
B) 3 min. to empty
C) 6 min. to empty
D) 7 min. to empty
E) 5 min. to empty

Solution: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.   Part to be emptied = 2/5   Part emptied by (A + B) in 1 minute = (1/6 - 1/10) = 1/15   1/15 : 2/5 :: 1 : x   x = (2/5 * 1 * 15)= 
(2/5 * 1 * 15) = 6
6 min.   So, the tank will be emptied in 6 min.   ANSWER:6 min. to empty
Answer: C
A Shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed. The ratio of the cost price and the printed price of the book is:
Choose the most appropriate option
A) 12:24
B) 29:23
C) 32:41
D) 45:56
E) 40:42

Solution: Explanation:   Printed price of the book is Rs. 100   After a discount of 10% S.P = Rs. 90   Profit earned = 12%   C.P of the book = Rs. (100/112 × 90) = Rs. 1125/14   (C.P) : (Printed price) = 1125/14 : 100 or 45 : 56   Answer: Option 45:56
Answer: D
It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:  Choices
A) 1:3	B) 2:4	C) 9:3	D) 7:8	E) 3:4

Solution: Let the speed of the train be x km/hr and that of the car be y km/hr.   Then,	120/x + 480/y= 8 1/x	+	4/y	=	1/15	....(i)   And,	200/x + 400/y = 25/3 1/x	+	2/y	=	1/24	....(ii)   Solving (i) and (ii), we get: x = 60 and y = 80.   Ratio of speeds = 60 : 80 = 3 : 4.   answer :3:4
Answer: E
A can do a piece of work in 4 days. B can do it in 6 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
Select the correct option: A) 87 days B) 12 days C) 16 days D) 19 days E) 36 days

Solution: C = 1/2 - 1/4 - 1/6 = 1/12   => 12 days   Answer:12 days
Answer: B
In 10 years, A will be twice as old as B was 10 years ago. If A is now 6 years older than B the present age of B is  Choose the most appropriate option
A) 37 B) 36 C) 39 D) 40 E) 41

Solution: let present age of A be a and 36 be b   a+10 = 2*(b-10)   => 2b-a = 30 ......(i)   a = b+6   =>2b-b-6 = 30   b=36   so the present age of b is 36 years   ANSWER:36
Answer: B